ORIGINAL_ARTICLE
Type-2 fuzzy rule-based expert system for diagnosis of spinal cord disorders
The majority of people have experienced pain in their low back or neck in their lives. In this paper a type-2 fuzzy rule based expert system is presented for diagnosing the spinal cord disorders. The interval type-2 fuzzy logic system permits us to handle the high uncertainty of diagnosing the type of disorder and its severity. The spinal cord disorders are studied in five categories using historical data and clinical symptoms of the patients. The main novelty of this paper lies in presentation of the interval type-2 fuzzy hybrid rule-based system, which is a combination of the forward and backward chaining approaches in its inference engine and avoids unnecessary medical questions. Using of parametric operations for fuzzy calculations increases the robustness of the system and the compatibility of the diagnosis with a wide range of physicians’ diagnosis. The outputs of the system are comprised of type of disorder, location and severity as well as the necessity of taking a M.R. Image. A comparison of the performance of the developed system with the expert shows an acceptable accuracy of the system in diagnosing the disorders and determining the necessity of the M.R. Image.
http://scientiairanica.sharif.edu/article_20228_1fe06ea6deeea83d795d5249f3d08063.pdf
2019-02-01
455
471
10.24200/sci.2018.20228
type-2 fuzzy expert system
forward-backward chaining
parameter optimization
spinal cord disorder
rule-based expert system
S.
Rahimi Damirchi-Darasi
1
Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
AUTHOR
M. H.
Fazel Zarandi
zarandi@aku.ac.ir
2
-. Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran. - Knowledge Intelligent System Laboratory, University of Toronto, Toronto, Canada.
LEAD_AUTHOR
I.B.
Turksen
3
- Knowledge Intelligent System Laboratory, University of Toronto, Toronto, Canada. - Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey
AUTHOR
M.
Izadi
4
Fayyazbakhsh and Erfan Hospitals, Tehran, Iran
AUTHOR
Andersson, G.B. Epidemiological features of chronic low-back pain", The Lancet, 354(9178), pp. 581-585 (1999). 2. Koh, J., Chaudhary, V., Dhillon, G. Disc herniation diagnosis in MRI using a CAD framework and a twolevel classi_er", Int J Comput Assist Radiol Surg, 7(6), pp. 861-869 (2012). 3. Patel, V.L., Shortli_e, E.H., Stefanelli, M., Szolovits, P., Berthold, M.R., Bellazzi, R., and Abu-Hanna, A. The coming of age of arti_cial intelligence in medicine", Arti_cial Intelligence in Medicine, 46(1), pp. 5-17 (2009). 4. Miller, P.L. The evaluation of arti_cial intelligence systems in medicine", Comput Methods Programs Biomed, 22(1), pp. 5-11 (1986). 5. Seising, R. From vagueness in medical thought to the foundations of fuzzy reasoning in medical diagnosis", Artif Intell Med, 38(3), pp. 237-256 (2006). 6. Bharti, P.K., Silawat, N., Singh, P.P., Singh, M.P., Shukla, M., Chand G., and Singh, N. The usefulness of a new rapid diagnostic test, the _rst response malaria combo (pLDH/HRP2) card test, for malaria diagnosis in the forested belt of central India", Malar J, 7, p.126 (2008). 7. Obot, O.U. and Uzoka, F.M. Experimental study of fuzzy-rule based management of tropical diseases: case of malaria diagnosis", Stud Health Technol Inform, 137(1), pp. 328-339 (2008). 8. Akinyokun, C.O., Obot, O.U., Uzoka, F.M., and Andy, J.J. A neuro-fuzzy decision support system for the 470 S. Rahimi Damirchi-Darasi et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 455{471 diagnosis of heart failure", Stud Health Technol Inform, 156(1), pp. 231-244 (2010). 9. Fazel Zaranid, M.H., Zolnoori, M., Moin, M., and Heidarnejad, H. Fuzzy rule-based expert system for diagnosing asthma", Scientia Iranica, 17(2), pp. 129- 142 (2010). 10. Kadhim, M.A., Alam, M.A., and Kaur, H. Design and implementation of fuzzy expert system for back pain diagnosis", Int Journal of Innovative Technology & Creative Engineering, 1(9), pp. 16-22 (2011). 11. Sari, M., Gulbandilar, E., and Cimbiz, A. Prediction of low back pain with two expert systems", J Med Sys, 36(3), pp. 1523-1527 (2012). 12. Esteban, B., Tejeda-Lorente, A., Porcel, C., Arroyo, M., and Herrera-Viedma, E. TPLUFIB-WEB: A fuzzy linguistic Web system to help in the treatment of low back pain problems", Knowledge-Based Systems, 67(1), pp. 429-438 (2014). 13. Gulbandialr, E., Sari, M., and Cimbiz, A. Prediction of low back pain using a fuzzy logic algorithm", American Journal of Biomedical Science and Engineering, 1(5), pp. 58-62 (2015). 14. Ohri, K., Singh, H., and Sharma, A. Fuzzy expert system for diagnosis of breast cancer", Wireless Communications, Signal Processing and Networking (WiSPNET), International Conference on, Chennai, India, pp. 2487-2492 (2016). 15. Gal, N., Andrei D., Stoicu-Tivadar V., Neme_s D.I., and N_nd_a_san E. Fuzzy expert system prediction of lumbar spine subchondral sclerosis and lumbar disk hernia", Soft Computing Applications, pp. 2487-2492, Springer, Cham (2016). 16. Katigari, M.R., Ayatollahi, H., Malek, M., and Haghighi, M.K. Fuzzy expert system for diagnosing diabetic neuropathy", World Journal of Diabetes, 8(2), p. 80 (2017). 17. Fazel Zarandi, M.H., Zarinbal, M., and Izadi, M. Systematic image processing for diagnosing brain tumors: A type-II fuzzy expert system approach", Applied Soft Computing, 11(1), pp. 285-294 (2011). 18. Rahimi Damirchi-Darasi, S., Fazel Zarandi, M.H., and Izadi, M. Type-2 fuzzy hybrid expert system for diagnosis of degenerative disc diseases", Modeling, Identi_cation, Simulation & Control (AIJ-MISC), 45(2), pp. 53-62 (2013). 19. Zarinbal, M., Turksen, L.B., Fazel Zarandi, M.H., and Izadi, M. Interval type-2 fuzzy image processing expert system for diagnosing brain tumors", Norbert Wiener in the 21st Century (21CW), 2014 IEEE Conference on, Boston, MA, USA, pp. 1-8 (2014). 20. Zarinbal, M., Fazel Zarandi, M.H., Turksen, L.B., and Izadi, M. A type-2 fuzzy image processing expert system for diagnosing brain tumors", Journal of Medical Systems, 39(10), p. 1 (2015). 21. Fazel Zarandi, M.H., Rahimi Damirchi-Darasi, S., Izadi, M., Turksen, I.B., and Arabzadeh Ghahazi, M. Fuzzy rule based expert system to diagnose spinal cord disorders", Norbert Wiener in the 21st Century (21CW), 2014 IEEE Conference on, Boston, MA, USA, pp. 1-5 (2014). 22. Mechanical pain de_nition", Retrieved 1/15/2016, from: http://www.spine-health.com/glossary/mechanicalpain 23. Diseases and conditions herniated disk", Retrieved 1/15/2016, from http://www.mayoclinic.org/diseasesconditions/ herniated-disk/basics/de_nition/c on-20029957 (2014). 24. Diseases and conditions spinal stenosis", Retrieved 1/15/2016, from http://www.mayoclinic.org/diseasesconditions/ spinal-stenosis/basics/de_nition/ con-20036105. 25. Revord, J.P. Typical symptoms of a herniated disc", Retrieved 1/15/2016, from http://www.spinehealth. com/conditions/herniated-disc/typicalsymptoms- a-herniated-disc. 26. Staehler, R.A. Cervical herniated disc symptoms and treatment options", Retrieved 1/15/2016, from http://www.spine-health.com/conditions/herniateddisc/ cervical-herniated-disc-symptoms-andtreatment- options 27. Marieb, E.N. and Hoehn, K., Human Anatomy & Physiology, Pearson Education (2007). 28. Yellow ags in back pain", Retrieved 1/15/2016, from: http://www.she_eldbackpain.com/professionalresources/ learning/in-detail/yellow-ags-in-back-pain. 29. Mendel, J.M. and John, R.I.B. Type-2 fuzzy sets made simple", Fuzzy Systems, IEEE Transactions on, 10(2), pp. 117-127 (2002). 30. Mendel, J.M. Advances in type-2 fuzzy sets and systems", Information Sciences, 177(1), pp. 84-110 (2007). 31. Emami, M.R., Turksen, I.B., and Goldenberg, A.A. A uni_ed parameterized formulation of reasoning in fuzzy modeling and control", Fuzzy Sets and Systems, 108(1), pp. 59-81 (1999). 32. Mendel, J., Hagras, H., Tan, W.-W., Melek, W.W., and Ying, H., Introduction to Type-2 Fuzzy Logic Control: Theory and Applications, John Wiley & Sons (2014). 33. Karnik, N.N. and Mendel, J.M. Introduction to type- 2 fuzzy logic systems", IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98CH36228), Anchorage, AK, pp. 915-920 (1998). 34. Karnik, N.N., Mendel, J.M., and Qilian, L. Type-2 fuzzy logic systems", Fuzzy Systems, IEEE Transactions on, 7(6), pp. 643-658 (1999). 35. Leekwijck, W.V. and Kerre, E.E. Defuzzi_cation: criteria and classi_cation", Fuzzy Sets and Systems, 108(2), pp. 159-78 (1999). S. Rahimi Damirchi-Darasi et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 455{471 471 36. Spinal disc problems (including red ag signs)", Retrieved 1/15/2016, from http://patient. info/doctor/ spinal-disc-problems-including-red-ag-signs. 37. Hochschuler, S.H. Back pain risk factors: What can increase the potential for back problems?" Retrieved 1/15/2016, from http://www.spine-health. com/conditions/lower-back-pain/back-pain-riskfactorswhat- can-increase-potential-back-problems 38. Liang, Q. and Mendel, J.M. Interval type-2 fuzzy logic systems: theory and design", Fuzzy Systems, IEEE Transactions on, 8(5), pp. 535-550 (2000)
1
ORIGINAL_ARTICLE
Cost function and optimal boundaries for a two-level inventory system with information sharing and two identical retailers
In this paper, we consider a two-echelon inventory system with a central warehouse and two identical retailers employing information sharing. Transportation times to each retailer and the warehouse are constant. Retailers face independent Poisson demand and apply continuous review policy, -policy. The warehouse initiates with m batches (of given size ) and places an order to an outside supplier when a retailer’s inventory position reaches , where is the inventory position considered by central warehouse and is a non-negative constant. So far, an approximate cost function as well as exact analysis of system for only one retailer has been proposed. However, the derivation of the exact value of the expected total cost of this system for more than one retailer, is still an open question. This paper attempts to meet this challenge and derive the exact cost function for two retailers. To achieve this purpose, we resort to conditional probability to split the problem into two simpler problems then we obtain the exact expected total cost of the system.
http://scientiairanica.sharif.edu/article_20144_e69f675693d8cfcb2c6e7ed85d8dd827.pdf
2019-02-01
472
485
10.24200/sci.2018.20144
Two-echelon inventory system
Supply chain management
Information sharing
Poisson demand
Continues review
A. H.
Afshar Sedigh
1
Department of Information Science, University of Otago, Dunedin 9054, P.O. Box 56, New Zealand
AUTHOR
R.
Haji
haji@sharif.ir
2
Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11365, Iran
AUTHOR
S. M.
Sajadifar
sajadifar@usc.ac.ir
3
Department of Industrial Engineering, University of Science and Culture, Tehran, P.O. Box 13145/871, Iran
LEAD_AUTHOR
Forrester, J.W. Industrial dynamics: a major breakthrough for decision makers", Harvard Business Review, 36(4), pp. 37-66 (1958). 2. Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E., Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies, The McGraw-Hill/Irwin Series in Operations and Decision Sciences, McGraw- Hill, Illinois (2003). 3. Lee, H.L., So, K.C., and Tang, C.S. The value A.H. Afshar Sedigh et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 472{485 483 of information sharing in a two-level supply chain", Management Science, 46(5), pp. 626-643 (2000). 4. Raghunathan, S. and Yeh, A.B. Beyond EDI: impact of continuous replenishment program (CRP) between a manufacturer and its retailers", Information Systems Research, 12(4), pp. 406-419 (2001). 5. Yao, Y. and Dresner, M. The inventory value of information sharing, continuous replenishment, and vendor-managed inventory", Transportation Research Part E: Logistics and Transportation Review, 44(3), pp. 361-378 (2008). 6. Dong, Y., Dresner, M., and Yao, Y. Beyond information sharing: An empirical analysis of vendor-managed inventory", Production and Operations Management, 23(5), pp. 817-828 (2014). 7. Cui, R., Allon, G., Bassamboo, A., and Van Mieghem, J.A. Information sharing in supply chains: An empirical and theoretical valuation", Management Science, 61(11), pp. 2803-2824 (2015). 8. Chen, M.-C., Yang, T., and Yen, C.-T. Investigating the value of information sharing in multi-echelon supply chains", Quality & Quantity, 41(3), pp. 497-511 (2007). 9. Razmi, J., Rad, R.H., and Sangari, M.S. Developing a two-echelon mathematical model for a vendormanaged inventory (VMI) system", The International Journal of Advanced Manufacturing Technology, 48(5- 8), pp. 773-783 (2010). 10. Li, C. Controlling the bullwhip e_ect in a supply chain system with constrained information ows", Applied Mathematical Modelling, 37(4), pp. 1897-1909 (2013). 11. Cannella, S., Dominguez, R., Framinan, J.M., and Bruccoleri, M. Insights on partial information sharing in supply chain dynamics", International Conference on Industrial Engineering and Systems Management (IESM), Seville, Spain, pp. 344-350 (2015). 12. Cannella, S., Framinan, J.M., and Barbosa-P_ovoa, A. An IT-enabled supply chain model: a simulation study", International Journal of Systems Science, 45(11), pp. 2327-2341 (2014). 13. Cannella, S., and Ciancimino, E. Up-to-date supply chain management: The coordinated (S, R) orderup- to", In Advanced Manufacturing and Sustainable Logistics, Dangelmaier, W., Blecken, A., Delius, A., and S. Klopfer, Eds., pp. 175-185, Springer, Berlin, Germany (2010). 14. Cannella, S. Order-up-to policies in information exchange supply chains", Applied Mathematical Modelling, 38(23), pp. 5553-5561 (2014). 15. Prajogo, D. and Olhager, J. Supply chain integration and performance: The e_ects of long-term relationships, information technology and sharing, and logistics integration", International Journal of Production Economics, 135(1), pp. 514-522 (2012). 16. Ganesh, M., Raghunathan, S., and Rajendran, C. The value of information sharing in a multi-product, multi-level supply chain: Impact of product substitution, demand correlation, and partial information sharing", Decision Support Systems, 58, pp. 79-94 (2014). 17. Sabitha, D., Rajendran, C., Kalpakam, S., and Ziegler, H. The value of information sharing in a serial supply chain with AR (1) demand and non-zero replenishment lead times", European Journal of Operational Research, 255(3), pp. 758-777 (2016). 18. Ali, M.M., Boylan, J.E., and Syntetos, A.A. Forecast errors and inventory performance under forecast information sharing", International Journal of Forecasting, 28(4), pp. 830-841 (2012). 19. Babai, M.Z., Boylan, J.E., Syntetos, A.A., and Ali, M.M. Reduction of the value of information sharing as demand becomes strongly auto-correlated", International Journal of Production Economics, 181, pp. 130-135 (2016). 20. Trapero, J.R., Kourentzes, N., and Fildes, R. Impact of information exchange on supplier forecasting performance", Omega, 40(6), pp. 738-747 (2012). 21. Cannella, S., L_opez-Campos, M., Dominguez, R., Ashayeri, J., and Miranda, P.A. A simulation model of a coordinated decentralized supply chain", International Transactions in Operational Research, 22(4), pp. 735-756 (2015). 22. Li, X. andWang, Q. Coordination mechanisms of supply chain systems", European Journal of Operational Research, 179(1), pp. 1-16 (2007). 23. Axsater, S. Simple solution procedures for a class of two-echelon inventory problems", Operations Research, 38(1), pp. 64-69 (1990). 24. Axsater, S. Exact and approximate evaluation of batch-ordering policies for two-level inventory systems", Operations Research, 41(4), pp. 777-785 (1993). 25. Forsberg, R. Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand", European Journal of Operational Research, 81(1), pp. 143-153 (1995). 26. Forsberg, R. Exact evaluation of (R, Q)-policies for two-level inventory systems with Poisson demand", European Journal of Operational Research, 96(1), pp. 130-138 (1997). 27. Axsater, S. Exact analysis of continuous review (R,Q) policies in two-echelon inventory systems with compound Poisson demand", Operations Research, 48(5), pp. 686-696 (2000). 484 A.H. Afshar Sedigh et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 472{485 28. Simchi-Levi, D. and Zhao, Y. Three generic methods for evaluating stochastic multi-echelon inventory systems", Working Paper, Massachusetts Institute of Technology, Cambridge (2007). 29. Simchi-Levi, D. and Zhao, Y. Performance evaluation of stochastic multi-echelon inventory systems: a survey", Advances in Operations Research, 2012, Article ID: 126254, 34 pages (2012). https://doi.org/10.1155/2012/126254 30. Chen, F. and Zheng, Y.-S. Evaluating echelon stock (R, nQ) policies in serial production/inventory systems with stochastic demand", Management Science, 40(10), pp. 1262-1275 (1994). 31. Chen, F. and Zheng, Y.-S. Near-optimal echelonstock (R, nQ) policies in multistage serial systems", Operations Research, 46(4), pp. 592-602 (1998). 32. Axsater, S. and Rosling, K. Notes: Installation vs. echelon stock policies for multilevel inventory control", Management Science, 39(10), pp. 1274-1280 (1993). 33. Moinzadeh, K. A multi-echelon inventory system with information exchange", Management Science, 48(3), pp. 414-426 (2002). 34. Haji, R. and Sajadifar, S.M. Deriving the exact cost function for a two-level inventory system with information sharing", Journal of Industrial and Systems Engineering, 2(1), pp. 41-50 (2008). 35. Sajadifar, S.M. and Haji, R. Optimal solution for a two-level inventory system with information exchange leading to a more computationally e_cient search", Applied Mathematics and Computation, 189(2), pp. 1341-1349 (2007). 36. Axsater, S. and Marklund, J. Optimal position-based warehouse ordering in divergent two-echelon inventory systems", Operations Research, 56(4), pp. 976-991 (2008). 37. Svoronos, A. and Zipkin, P. Estimating the performance of multi-level inventory systems", Operations Research, 36(1), pp. 57-72 (1988). 38. Deuermeyer, B.L., and Schwarz, L.B., A Model for the Analysis of System Service Level in Warehouse- Retailer Distribution Systems: the Identical Retailer Case, Purdue University (1981). 39. Cachon, G.P. and Fisher, M. Supply chain inventory management and the value of shared information", Management Science, 46(8), pp. 1032-1048 (2000). 40. Gurbuz, M.C_ ., Moinzadeh, K., and Zhou, Y.P. Coordinated replenishment strategies in inventory/ distribution systems", Management Science, 53(2), pp. 293-307 (2007). 41. Wang, Q., Chay, Y., and Wu, Z. A simple coordination strategy for a decentralized supply chain", Working Paper, Nanyang Business School, Nanyang Technological University, Singapore (2006). 42. Klastorin, T.D., Moinzadeh, K., and Son, J. Coordinating orders in supply chains through price discounts", IIE Transactions, 34(8), pp. 679-689 (2002). 43. Haji, R. and Haji, A. One-for-one period policy and its optimal solution", Journal of Industrial and Systems Engineering, 1(2), pp. 200-217 (2007). 44. Kurt Salmon Associates, Inc., E_cient Consumer Response: Enhancing Consumer Value in the Grocery Industry, Research Department Food Marketing Institute, Washington, Dc (1993). 45. Kurt Salmon Associates, Inc., Quick Response: Meeting Customer Need, Kurt Salmon Associates, Atlanta, GA (1997). 46. Stalk, G., Evans, P., and Shulman, L.E. Competing on capabilities: The new rules of corporate strategy", Harvard Business Review, 70(2), pp. 57-69 (1991). 47. Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Prentice Hall, Englewood, Cli_s, NJ (1963).
1
ORIGINAL_ARTICLE
Master surgical scheduling problem with multiple criteria and robust estimation
In this research the master surgical scheduling (MSS) problem at the tactical level of hospital planning and scheduling is studied. Before constructing the MSS, a strategic level problem, i.e. case mix planning problem (CMPP), shall be solved to allocate the capacity of operating room (OR) to each surgical specialty. In order to make an effective coordination between CMPP and MSS, the results obtained from solving the CMPP is used as an input for the respective MSS. In the MSS, frequently performed elective surgeries are planned in a cyclic manner for a pre-defined planning period. As a part of the planning process, it is required to level downstream limited resources such as intensive care unit (ICU) and ward beds with patient flow. In this study, a mathematical model is developed to construct an MSS. The proposed model is based on a lexicographic goal programming approach which is aimed at minimizing the OR spare time while considering the results of the CMPP. In this paper, data required to solve MSS, is collected from a medium-sized Iranian hospital. Hence, a robust estimation method is applied to reduce the effect of outliers in the decision making process. The results testify the performance of the proposed method against the solution put in practice in the hospital.
http://scientiairanica.sharif.edu/article_20416_1986bc98de194e6f4178d0d78dd3dbbe.pdf
2019-02-01
486
502
10.24200/sci.2018.20416
Master Surgical Scheduling
Mathematical Programming
Goal Programming
Robust Estimation
R.
Shafaei
1
Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran 15875/4416, Iran
LEAD_AUTHOR
A.
Mozdgir
a.mozdgir@gmail.com
2
Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran 15875/4416, Iran
AUTHOR
Hof, S., Fugener, A., Schoenfelder, J., and Brunner, J.O. Case mix planning in hospitals: a review and future agenda", Health Care Management Science, 20(2), pp. 207-220 (2017). 2. Hartman, M., Martin, A.B., Benson, J., and Catlin, A. National Health Expenditure Accounts Team. National health spending in 2011: overall growth remains low, but some payers and services show signs of acceleration", Health A_airs, 32(1), pp. 87-99 (2013). 3. Denton, B., Viapiano, J., and Vogl, A. Optimization of surgery sequencing and scheduling decisions under uncertainty", Health Care Management Science, 10(1), pp. 13-24 (2007). 4. Healthcare Financial Management Association Achieving operating room e_ciency through process integration", Healthcare Financial Management: Journal of the Healthcare Financial Management Association, 57(3), suppl-1 (2003). 5. Yahia, Z., Eltawil, A.B., and Harraz, N.A. The operating room case-mix problem under uncertainty and nurses capacity constraints", Health Care Management Science, pp. 1-12 (2015). 6. Patterson, P. What makes a well-oiled scheduling system", OR Manager, 12(9), pp. 19-23 (1996). 7. Dexter, F., Traub, R.D., and Macario, A. How to release allocated operating room time to increase e_- ciency: predicting which surgical service will have the most underutilized operating room time", Anesthesia & Analgesia, 96(2), pp. 507-512 (2003). 8. Vacanti, C., Segal, S., Sikka, P., and Urman, R. (Eds.), Essential Clinical Anesthesia, Cambridge University Press (2011). 9. Roth, A.V. and Van Dierdonck, R. Hospital resource planning: concepts, feasibility, and framework", Production and Operations Management, 4(1), pp. 2-29 (1995). 10. Vissers, J.M., Bertrand, J.W.M., and De Vries, G. A framework for production control in health care organizations", Production Planning & Control, 12(6), pp. 591-604 (2001). 11. Hans, E.W., Van Houdenhoven, M., and Hulshof, P.J. A framework for healthcare planning and control", In Handbook of Healthcare System Scheduling, pp. 303- 320, Springer US (2012). 500 R. Shafaei and A. Mozdgir/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 486{502 12. Belien, J., and Demeulemeester, E. Building cyclic master surgery schedules with leveled resulting bed occupancy", European Journal of Operational Research, 176(2), pp. 1185-1204 (2007). 13. Samudra, M., Van Riet, C., Demeulemeester, E., Cardoen, B., Vansteenkiste, N., and Rademakers, F.E. Scheduling operating rooms: achievements, challenges and pitfalls", Journal of Scheduling, 19(5), pp. 493-525 (2016). 14. Belien, J., Demeulemeester, E., and Cardoen, B. A decision support system for cyclic master surgery scheduling with multiple objectives", Journal of Scheduling, 12(2), pp. 147-161 (2009). 15. Van Oostrum, J.M., Van Houdenhoven, M., Hurink, J.L., Hans, E.W., Wullink, G., and Kazemier, G. A master surgical scheduling approach for cyclic scheduling in operating room departments", OR Spectrum, 30(2), pp. 355-374 (2008). 16. Vissers, J.M.H., Adan, I.J., and Bekkers, J.A. Patient mix optimization in tactical cardiothoracic surgery planning: a case study", IMA Journal of Management Mathematics, 16(3), pp. 281-304 (2005). 17. Holte, M. and Mannino, C. The implementor/ adversarial algorithm for cyclic and robust scheduling problems in health-care", Department of Computer and System Sciences Antonio Ruberti Technical Reports, 3(3), 19 pages (2011). 18. Fugener, A., Hans, E.W., Kolisch, R., Kortbeek, N., and Vanberkel, P.T. Master surgery scheduling with consideration of multiple downstream units", European Journal of Operational Research, 239(1), pp. 227-236 (2014). 19. Dexter, F., Ledolter, J., and Wachtel, R.E. Tactical decision making for selective expansion of operating room resources incorporating _nancial criteria and uncertainty in subspecialties' future workloads", Anesthesia & Analgesia, 100(5), pp. 1425-1432 (2005). 20. Kharraja, S., Albert, P., and Chaabane, S. Block scheduling: Toward a master surgical schedule", In Service Systems and Service Management, 2006 International Conference on, 1, pp. 429-435, IEEE (Oct. 2006). 21. Agnetis, A., Coppi, A., Corsini, M., Dellino, G., Meloni, C., and Pranzo, M. Long term evaluation of operating theater planning policies", Operations Research for Health Care, 1(4), pp. 95-104 (2012). 22. Cappanera, P., Visintin, F., and Banditori, C. Comparing resource balancing criteria in master surgical scheduling: A combined optimisation-simulation approach", International Journal of Production Economics, 158, pp. 179-196 (2014). 23. Banditori, C., Cappanera, P., and Visintin, F. A combined optimization-simulation approach to the master surgical scheduling problem", IMA Journal of Management Mathematics, dps033, 24(2), pp. 155-187 (2013). 24. Cappanera, P., Visintin, F., and Banditori, C. A goalprogramming approach to the master surgical scheduling problem", In Health Care Systems Engineering for Scientists and Practitioners, pp. 155-166, Springer International Publishing (2016). 25. Cappanera, P., Visintin, F., and Banditori, C. Addressing conicting stakeholders' priorities in surgical scheduling by goal programming", Flexible Services and Manufacturing Journal, 30(1-2), pp. 252-271 (2018). 26. Holte, M. and Mannino, C. The implementor/ adversary algorithm for the cyclic and robust scheduling problem in health-care", European Journal of Operational Research, 226(3), pp. 551-559 (2013). 27. Visintin, F., Cappanera, P., and Banditori, C. Evaluating the impact of exible practices on the master surgical scheduling process: an empirical analysis", Flexible Services and Manufacturing Journal, 28(1-2), pp. 182-205 (2016). 28. Rowse, E., Lewis, R., Harper, P., and Thompson, J. Set partitioning methods for scheduling: an application to operating theatres", Simp_osio Brasileiro de Pesquisa Operacional (2014). 29. Fugener, A. An integrated strategic and tactical master surgery scheduling approach with stochastic resource demand", Journal of Business Logistics, 36(4), pp. 374-387 (2015). 30. Van Oostrum, J.M., Bredenho_, E., and Hans, E.W. Suitability and managerial implications of a master surgical scheduling approach", Annals of Operations Research, 178(1), pp. 91-104 (2010). 31. Visintin, F., Cappanera, P., Banditori, C., and Danese, P. Development and implementation of an operating room scheduling tool: an action research study", Production Planning & Control, 28(9), pp. 758-775 (2017). 32. Mandic, K., Delibasic, B., Knezevic, S., and Benkovic, S. Analysis of the _nancial parameters of Serbian banks through the application of the fuzzy AHP and TOPSIS methods", Economic Modelling, 43, pp. 30-37 (2014). 33. Hwang, C.L. and Yoon, K., Multiple Attribute Decision Making: Methods and Applications, New York: Springer-Verlag (1981). 34. Grubbs, F.E. Procedures for detecting outlying observations in samples", Technometrics, 11(1), pp. 1-21 (1969). 35. Maddala, G.S. and Lahiri, K., Introduction to Econometrics, 2, New York: Macmillan (1992). 36. Huber, P.J., Robust Statistics, pp. 1248-1251, Springer, Berlin, Heidelberg (2011). 37. Freitas, A., Silva-Costa, T., Lopes, F., Garcia-Lema, I., Teixeira-Pinto, A., Brazdil, P., and Costa-Pereira, A. Factors inuencing hospital high length of stay outliers", BMC Health Services Research, 12(1), p. 1 (2012). R. Shafaei and A. Mozdgir/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 486{502 501 38. Cots, F., Elvira, D., Castells, X., and Dalmau, E. Medicare's DRG-weights in a European environment: the Spanish experience", Health Policy, 51(1), pp. 31- 47 (2000). 39. Pirson, M., Dramaix, M., Leclercq, P., and Jackson, T. Analysis of cost outliers within APR-DRGs in a Belgian general hospital: two complementary approaches", Health Policy, 76(1), pp. 13-25 (2006). 40. Das, P., and Mandal, D., Statistical Outlier Detection in Large Multivariate Datasets, pp. 1-9. acsu.bu_alo.edu 41. Zimek, A., Schubert, E., and Kriegel, H.P. A survey on unsupervised outlier detection in high-dimensional numerical data", Statistical Analysis and Data Mining, 5(5), pp. 363-387 (2012). 42. Ruckstuhl, A.F. and Welsh, A.H. Robust _tting of the binomial model", Annals of Statistics, 29(4), pp. 1117-1136 (2001).
1
ORIGINAL_ARTICLE
Optimal production and ordering strategies with defective items and allowable shortage under two-part trade credit
This study investigated a production-inventory model with defective items under a two-part trade credit where the agreement of conditionally freight concession is considered in the integration supply chain. We assume the inspection process is conducted by the retailer before selling incoming items. All the defective items are discovered, stored and then sold as a single batch to a secondary market at a decreased price. Furthermore, shortages are allowed and completely backlogged for the retailer. The purpose of this study is to determine the optimal number of shipments per production cycle for the supplier, and the optimal length of time wherein there is no inventory shortage and replenishment cycle for the retailer such that the total profit function has a maximum value. In theoretical analysis, the existence and uniqueness of the optimal solutions are shown and an algorithm is developed to find the optimal solutions. Furthermore, numerical examples are presented to demonstrate the solution procedures and a sensitivity analysis of the optimal solutions regarding all parameters are also carried out.
http://scientiairanica.sharif.edu/article_20032_96987b271752d6bb4172b0eb6e74acd6.pdf
2019-02-01
503
521
10.24200/sci.2018.20032
Inventory
Supply chain
Defective items
Backlogged
Trade credit
C.-T.
Yang
1
Department of Industrial Management, Chien Hsin University of Science and Technology, Taoyuan City, Taiwan
AUTHOR
C.-H.
Huang
091552@mail.tku.edu.tw
2
Department of Management Sciences, Tamkang University, New Taipei City, Taiwan
LEAD_AUTHOR
L.-Y.
Ouyang
3
Department of Management Sciences, Tamkang University, New Taipei City, Taiwan
AUTHOR
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Yang et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 503{521 33. Yu, H.F. and Lin, S.Y. An EOQ model for items with acceptable defective part and shortages", J. Ind. Prod. Eng., 30(7), pp. 443-451 (2013). 34. Moussawi-Haidar, L. Salameh, M., and Nasr, W. E_ect of deterioration on the instantaneous replenishment model with imperfect quality items", Appl. Math. Model., 38(24), pp. 5956-5966 (2014). 35. Salameh, M.K. and Jaber, M.Y. Economic production quantity model for items with imperfect quality", Int. J. Prod. Econ., 64(1-3), pp. 59-64 (2000). 36. Chan, W.M., Ibrahim, R.N., and Lochert, P.B. A new EPQ model: integrating lower pricing, rework and reject situations", Prod. Plan. Control., 14(7), pp. 588- 595 (2003). 37. Chiu, Y.P. Determining the optimal lot size for the _nite production model with random defective rate, the rework process, and backlogging", Eng. Optimiz., 35(4), pp. 427-437 (2003). 38. Chiu, S.W. Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging", Appl. Stoch. Model.Bus., 23(2), pp. 165-178 (2007). 39. Kulkarni, S.S. Loss-based quality costs and inventory planning: General models and insights", Eur. J. Oper. Res., 188(2), pp. 428-449 (2008). 40. Sarker, B.R., Jamal, A.M.M., and Mondal, S. Optimal batch sizing in a multi-stage production system with rework consideration", Eur. J. Oper. Res., 184(3), pp. 915-929 (2008). 41. El Saadany, A.M.A. and Jaber, M.Y. A production/ remanufacturing inventory model with price and quality dependent return rate", Comput. Ind. Eng., 58(3), pp. 352-362 (2010). 42. Sana, S.S. A production-inventory model in an imperfect production process", Eur. J. Oper. Res., 200(2), pp. 451-464 (2010). 43. Sarkar, B., Chaudhuri, K., and Sana, S.S. A stockdependent inventory model in an imperfect production process", Int. J. Proc. Manage., 3(4), pp. 361-378 (2010). 44. Sarkar, B., Sana, S.S., and Chaudhuri, K. An imperfect production process for time varying demand with ination and time value of money-an EMQ model", Expert Syst. Appl., 38(11), pp. 13543-13548 (2011). 45. Sarkar, B. An inventory model with reliability in an imperfect production process", Appl. Math. Comput., 218(9), pp. 4881-4891 (2012c). 46. Ouyang, L.Y. and Chang, C.T. Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging", Int. J. Prod. Econ., 144(2), pp. 610-617 (2013). 47. Tsao, Y.C., Chen, T.H., and Huang, S.M. A production policy considering reworking of imperfect items and trade credit", Flexible Services and Manufacturing Journal, 23(1), pp. 48-63 (2011). 48. Sarkar, B., Gupta, H., Chaudhuri, K., and Goyal, S.K. An integrated inventory model with variable lead time, defective units and delay in payments", Appl. Math. Comput., 237, pp. 650-658 (2014). 49. Sarkar, B., C_ardenas-Barr_on, L.E., Sarkar, M., and Singgih, M.L. An economic production quantity model with random defective rate, rework process and backorders for a single stage production system", J. Manufact. Syst., 33(3), pp. 423-435 (2014). 50. Sarkar, B. and Moon, I. Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process", Int. J. Product. Econ., 155, pp. 204-213 (2014). 51. Banerjee, A. A joint economic-lot-size model for purchaser and vendor", Decision. Sci., 17(3), pp. 292- 311 (1986). 52. Goyal, S.K. A joint economic-lot-size model for purchaser and vendor: a comment", Decision. Sci., 19(1), pp. 236-241 (1988). 53. Lu, L. A one-vendor multi-buyer integrated inventory model", Eur. J. Oper. Res., 81(2), pp. 312-323 (1995). 54. Pal, B., Sana, S.S., and Chaudhuri, K. Two-echelon competitive integrated supply chain model with price and credit period dependent demand", Int. J. Syst. Sci., 47(5), pp. 995-1007 (2016). 55. Goyal, S.K. On improving the single-vendor singlebuyer integrated production inventory model with a generalized policy", Eur. J. Oper. Res., 125(2), pp. 429-430 (2000). 56. Yao, M.J. and Chiou, C.C. On a replenishment coordination model in an integrated supply chain with one vendor and multiple buyers", Eur. J. Oper. Res., 159(2), pp. 406-419 (2004). 57. Chung, C.J. and Wee, H.M. Optimizing the economic lot size of a three-stage supply chain with backordering derived without derivatives", Eur. J. Oper. Res., 183(2), pp. 933-943 (2007). 58. Chang, H.C., Ho, C.H., Ouyang, L.Y., and Su, C.H. The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity", Appl. Math. Model., 33(7), pp. 2978- 2991 (2009). 59. Lin, C.C. and Lin, C.W. Defective item inventory model with remanufacturing or replenishing in an integrated supply chain", Int. J. Integr. Supply Manag., 6(3-4), pp. 254-269 (2011). 60. C_ardenas-Barr_ona, L.E., Teng, J.T., Trevi~no-Garza, G.,Wee, H.M., and Lou, K.R. An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain", Int. J. Prod. Econ., 36(2), pp. 384-388 (2012). 61. Lin, Y.J., Ouyang, L.Y., and Dang, Y.F. A joint optimal ordering and delivery policy for an integrated supplier-retailer inventory model with trade credit and defective items", Appl. Math. Comput., 218(14), pp. 7498-7514 (2012). C.-T. Yang et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 503{521 521 62. Su, C.H. Optimal replenishment policy for an integrated inventory system with defective items and allowable shortage under trade credit", Int. J. Prod. Econ., 139(1), pp. 247-256 (2012). 63. Sana, S.S. Optimal contract strategies for two stage supply chain", Econ. Model., 30, pp. 253-260 (2013). 64. Das, B.C., Das, B., and Mondal, S.K. An integrated inventory model with delay in payment for deteriorating item under Weibull distribution and advertisement cum price-dependent demand", Int. J. Oper. Res., 20(3), pp. 341-368 (2014). 65. Ouyang, L.Y., Chuang, C.J., Ho, C.H., and Wu, C.W. An integrated inventory model with quality improvement and two-part credit policy", Top, 22(3), pp. 1042-1061 (2014). 66. Giri, B.C., and S. Sharma. An integrated inventory model for a deteriorating item with allowable shortages and credit linked wholesale price", Optimization Letters, 9(6), pp. 1149-1175 (2015). 67. Ouyang, L.Y., Ho, C.H., Su. C.H., and Yang, C.T. An integrated inventory model with capacity constraint and order-size dependent trade credit", Comput. Ind. Eng., 84, pp. 133-143 (2015). 68. Sana, S.S. Optimal production lot size and reorder point of a two-stage supply chain while random demand is sensitive with sales teams' initiatives", Int. J. Syst. Sci., 47(2), pp. 450-465 (2016). 69. Sarkar, B. Supply chain coordination with variable backorder, inspections, and discount policy for _xed lifetime products", Math. Probl. Eng., 2016, pp. 1-14 (2016). 70. Mahata, P., Mahata, G.C., and De, S.K. Optimal replenishment and credit policy in supply chain inventory model under two levels of trade credit with timeand credit-sensitive demand involving default risk", J. Ind. Eng. Int., pp. 1-12 (2017). 71. Sarkar, B., Saren, S., Sinha, D., and Hur, S. E_ect of unequal lot sizes, variable setup cost, and carbon emission cost in a supply chain model", Math. Probl. Eng., 2015, pp. 1-13 (2015b). 72. Sett, B.K., Sarkar, S., Sarkar, B., and Yun, W.Y. Optimal replenishment policy with variable deterioration for _xed-lifetime products", Sci. Iran., 23(5), pp. 2318- 2329 (2016). 73. Yang, C.T., Ho, C.H., Lee, H.M., and Ouyang, L.Y. Supplier-retailer production and inventory models with defective items and inspection erroes in noncooperative and cooperative environments", RAIROOper. 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1
ORIGINAL_ARTICLE
Optimal fleet composition and mix periodic location-routing problem with time windows in an offshore oil and gas industry: A case study of National Iranian Oil Company
This paper presents a new Mixed-Integer Non-Linear Programming (MINLP) model for a Supply Vessel Planning (SVP) problem. The traditional SVP, which is a maritime transportation problem, is developed to a Maritime Fleet Sizing Mix Periodic Location-Routing Problem with Time Windows (MFSMPLRPTW) by considering suppliers, location of onshore-base(s) and some real life aspects. The objective of this model is to decide the composition of fleets, optimal voyages, schedules and also the optimal location(s) for onshore-base(s) in such a way that the total cost is minimized and the needs of operation regions are fulfilled. The MFSMPLPRTW model is solved by an exact two-phase solution approach for both small and medium cases. Also, two meta-heuristic algorithms are used to solve the large-sized instances. In order to justify and show how the model and solution can lead to significant economic improvements for real life instances, a case study by the IOOC is considered, which is the only offshore oil and gas producer in Iran that has lots of installations and operation regions in the Persian Gulf and the Sea of Oman.
http://scientiairanica.sharif.edu/article_20412_ef800c9d9c869e9c3a12c5e6c785da0b.pdf
2019-02-01
522
537
10.24200/sci.2018.20412
Maritime transportation
Supply vessel
Fleet composition
Location-routing problem
M.
Amiri
mamiri@shirazu.ac.ir
1
Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
AUTHOR
S.J.
Sadjadi
2
School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
LEAD_AUTHOR
R.
Tavakkoli-Moghaddam
3
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
AUTHOR
A.
Jabbarzadeh
4
School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
AUTHOR
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Murotsu, Y. and Taguchi, K. optimization of ship eet-size", Bulletin of University of Osaka Prefecture, Series A: Engineering and Natural Science, 23, pp. 171-192 (1975). 7. Larson, R.C. Transporting sludge to the 106-mile site: an inventory/routing model for eet sizing and logistics system design", Transportation Science, 22, pp. 186- 198 (1988). 8. Pesenti, R., Hierarchical resource planning for shipping companies", European Journal of Operational Research, 86(1), pp. 91-102 (1995). 9. Sigurd, M.M., Ulstein, N.L., Nygreen, B., and Ryan, D.M., Ship scheduling with recurring visits and visit separation requirements", In Column Generation, Springer, pp. 225-245 (2005). 10. Zeng, Q. and Yang, Z. Model integrating eet design and ship routing problems for coal shipping", Lecture Notes in Computer Science, 4489, pp. 1000-1003 (2007). 11. Gogna, A. and Tayal, A. Meta-heuristics: review and application", Journal of Experimental & Theoretical Arti_cial Intelligence, 25(4), pp. 503-526 (2013). 12. Fagerholt, K., Christiansen, M., Hvattum, L.M., Johnsen, T.A.V., and Vab, T.J. A decision support methodology for strategic planning in maritime transportation", Omega, 38(6), pp. 465-474 (2010). 13. Dantzig, G. and Ramser, J. The truck dispatching problem", Management Science, 6(1), pp. 80-91 (1959). 14. Kocu, C., Bektasu, T., Jabali, O., and Laporte, G. The eet size and mix location-routing problem with time windows: formulations and a heuristic algorithm", European Journal of Operation Research, 248 (1), pp. 33-51 (2016). 15. Fagerholt, K. and Lindstad, H. Optimal policies for maintaining a supply service in the Norwegian Sea", Omega, 28(3), pp. 269-275 (2000). 16. Aas, B., Gribkovskaia, I., Halskau, _., and Shlopak, A. Routing of supply vessels to petroleum installations", International Journal of Physical Distribution & Logistics Management, 37(2), pp. 164-179 (2007). 17. Gribkovskaia, I., Laporte, G., and Shlopak, A. A tabu search heuristic for a routing problem arising in servicing of o_shore oil and gas platforms", Journal of the Operational Research Society, 59(11), pp. 1449- 1459 (2007). 18. Iachan, R. A Brazilian experience: 40 years using operations research at Petrobras", International Transactions in Operational Research, 16(5), pp. 585- 593 (2009). 19. Aas, B., Halskau Sr, _., and Wallace, S.W. The role of supply vessels in o_shore logistics", Maritime Economics and Logistics, 11(3), pp. 302-325 (2009). 20. Shyshou, A., Gribkovskaia, I., and Barcel_o, J. A simulation study of the eet sizing problem arising in o_shore anchor handling operations", European Journal of Operational Research, 203(1), pp. 230-240 (2010). 21. Halvorsen-Weare, E.E. and Fagerholt, K. Robust supply vessel planning", Network Optimization, 6701, pp. 559- 573 (2011). 22. Shyshou, A., Gribkovskaia, I., Laporte, G., and Fagerholt, K. A large neighbourhood search heuristic for a periodic supply vessel planning problem arising in o_shore oil and gas operations", Information Systems and Operational Research, 50(4), pp. 195-204 (2012). 23. Norlund, E.K., Gribkovskaia, I., and Laporte, G. Supply vessel planning under cost, environment and robustness considerations", Omega, 57(B), pp. 271-281 (2015). 24. Christiansen, M., Fagerholt, K., Rachaniotis, N., and St_alhane, M. Operational planning of routes and schedules for a eet of fuel supply vessels", Transportation Research Part E: Logistics and Transportation Review, 105, pp. 163-175 (2017). 25. Prodhon, C. and Prins, C. A survey of recent research on location-routing problems", European Journal of Operational Research, 238(1), pp. 1-17 (2014). 26. Nagy, G. and Salhi, S. Location-routing: Issues, models and methods", European Journal of Operational Research, 177(2), pp. 649-672 (2007). 536 M. Amiri et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 522{537 27. Prins, C., Prodhon, C., andWoler-Calvo, R. Solving the capacitated location routing problem by a GRASP complemented by a learning process and a path relinking", 4OR: A Quarterly Journal of Operations Research, 4(3), pp. 221-238 (2006). 28. Derbel, H., Jarboui, B., Hana_, S., and Chabchoub, H. Genetic algorithm with iterated local search for solving a location-routing problem", Expert Systems with Applications, 39(3), pp. 2865-2871 (2012). 29. Yu, V.F., Lin, S.W., Lee, W., and Ting, C.J. A simulated annealing heuristic for the capacitated location routing problem", Computers and Industrial Engineering, 58(2), pp. 288-299 (2010). 30. Hemmelmayr, V.C., Cordeau, J.-F., and Crainic, T.G. An adaptive large neighborhood search heuristic for two-echelon vehicle routing problems arising in city logistics", Computers and Operations Research, 39(12), pp. 3215-3228 (2012). 31. Jarboui, B., Derbel, H., Hana_, S., and Mladenovic, N. Variable neighborhood search for location routing", Computers and Operations Research, 40(1), pp. 47-57 (2013). 32. Laporte, G. and Nobert, Y. An exact algorithm for minimizing routing and operating costs in depot location", European Journal of Operational Research, 6(2), pp. 224-226 (1981). 33. Albareda-Sambola, M., Diaz, J.A., and Fernandez, E. A compact model and tight bounds for a combined location-routing problem", Computers and Operations Research, 32(3), pp. 407-428 (2005). 34. Belenguer, J.M., Benavent, E., Prins, C., Prodhon, C., and Woler-Calvo, R. A branch-and-cut method for the capacitated location-routing problem", Computers and Operations Research, 38(6), pp. 931-941 (2011). 35. Kennedy, J. and Eberhart, R. Particle swarm optimization", Proceedings of the 1995 IEEE International Conference on Neural Networks, pp. 1942-1948 (1995). 36. Mirjalili, S., Lewis, A. The whale optimazation algorithm", Advances in Engineering Software, 95, pp. 51-67 (2016). 37. Marinakis, Y. and Marinaki, M. A particle swarm optimization algorithm with path relinking for the location routing problem", Journal of Mathematical Modeling and Algorithms, 7(1), pp. 59-78 (2008). 38. Belmecheri, F., Prins, C. Yalaoui, F., and Amodeo, L. A particle swarm optimization algorithm for a vehicle routing problem with heterogeneous eet, mixed backhauls, and time windows", Journal of Intelligent Manufacturing, 24(4), pp. 775-789 (2013). 39. Onwunalu, J.E. and Durlofsky, L.J. Application of a particle swarm optimization algorithm for determining optimum well location and type", Computational Geosciences, 14(1), pp. 183-198 (2010). 40. Kaveh, A. and Ghazaan, M.I Enhanced whale optimization algorithm for sizing optimization of skeletal structures", Mechanics Based Design of Structures and Machines, 45(3), pp. 345-362 (2016). 41. Mafarja, M.M. and Mirjalili, S. Hybrid whale optimization algorithm with simulated annealing for feature selection", Neurocomputing, 260, pp. 302-312 (2017). 42. Prakash, D.B. and Lakshminarayana, C. Optimal siting of capacitors in radial distribution network using whale optimization algorithm", Alexandria Engineering Journal, 56(4), pp. 499-509 (2017). 43. Reddy, P.D.P., Reddy, V.C.V., and Manohar, T.G. Whale optimization algorithm for optimal sizing of renewable resources for loss reduction in distribution systems", Renewables: Wind, Water and Solar, 4(1), 3 (2017). 44. Abd El Aziz, M., Ewees, A.A., and Ella Hassanein, A. Whale optimization algorithm and moth-ame optimization for multilevel thresholding image segmentation", Expert Systems With Applications, 83(C), pp. 242-256 (2017). 45. Fruggiero, F., Lambiase, A., Macchiaroli, R., and Miranda, S. The role of uncertainty in supply chains under dynamic modeling", International Journal of Industrial Engineering Computations, 8(1), pp. 119- 140 (2017). 46. Rincon-Garcia, N., Waterson, B.J., and Cherrett, T.J. A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows", International Journal of Industrial Engineering Computations, 8(1), pp. 141-160 (2017).
1
ORIGINAL_ARTICLE
A novel robust possibilistic cellular manufacturing model considering worker skill and product quality
Design of an appropriate cellular manufacturing system (CMS) leads to system flexibility and production efficiency by using the similarities in the manufacturing process of products. One of the main issues in these systems is to consider product quality level and worker’s skill level in the production process. This study proposes a comprehensive bi-objective possibilistic nonlinear mixed-integer programming model under uncertain environment to design a suitable CMS with aims of minimizing the total costs and total inaction of workers and machines, simultaneously. In this respect, the demand of each product with a specific quality level and linguistic parameters such as product quality level, worker’s skill level and job hardness level on machines are considered under fuzzy environment. To this end, the robust possibilistic programming approach is tailored to cope with fuzzy impute parameters. Finally, a real case study is provided to show the efficiency and applicability of the proposed model. In this respect, the proposed approach could be improved the total costs by 23.6% and the total inaction of workers and machines by 11.7% regarding the real practice. In addition, the performance of the presented model is demonstrated by comparing between the results obtained from the proposed model and actual practice.
http://scientiairanica.sharif.edu/article_20424_7b5f104e3f87f1eb936ef707c7086e6d.pdf
2019-02-01
538
556
10.24200/sci.2018.4948.1002
Quality management
Cellular manufacturing problem
Worker flexibility
Route flexibility
Worker skills
Robust possibilistic programming
A.
Hashemoghli
arash_hashemoghli@yahoo.com
1
Department of Industrial and Systems Engineering, Mazandaran University of Science and Technology, Babol, Iran
AUTHOR
I.
Mahdavi
irajarash@rediffmail.com
2
Department of Industrial and Systems Engineering, Mazandaran University of Science and Technology, Babol, Iran
LEAD_AUTHOR
A.
Tajdin
ali_tajdin@yahoo.com
3
Department of Industrial and Systems Engineering, Mazandaran University of Science and Technology, Babol, Iran
AUTHOR
Wemmerlov, U. and Hyer, N.L. Procedures for the part family/machine group identi_cation problem in cellular manufacturing", Journal of Operations Management, 6(2), pp. 125-147 (1986). 2. Aalaei, A. and Davoudpour, H. A robust optimization model for cellular manufacturing system into supply chain management", International Journal of Production Economics, 183, pp. 667-679 (2017). 3. Ra_ei, H. and Ghodsi, R. A bi-objective mathematical model toward dynamic cell formation considering labor utilization", Applied Mathematical Modelling, 37(4), pp. 2308-2316 (2013). 4. Rheault, M., Drolet, J.R., and Abdulnour, G. Physically recon_gurable virtual cells: a dynamic model for a highly dynamic environment", Computers & Industrial Engineering, 29(1), pp. 221-225 (1995). 5. Rosenblatt, M.J. The dynamics of plant layout", Management Science, 32(1), pp. 76-86 (1986). 6. Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M. Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment", Computers & 554 A. Hashemoghli et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 538{556 Mathematics with Applications, 60(4), pp. 1014-1025 (2010). 7. Saxena, L.K. and Jain, P.K. Dynamic cellular manufacturing systems design-a comprehensive model", The International Journal of Advanced Manufacturing Technology, 53(1-4), pp. 11-34 (2011). 8. Paydar, M.M., Saidi-Mehrabad, M., and Kia, R. Designing a new integrated model for dynamic cellular manufacturing systems with production planning and intra-cell layout", International Journal of Applied Decision Sciences, 6(2), pp. 117-143 (2013). 9. Kia, R., Javadian, N., and Tavakkoli-Moghaddam, R. A simulated annealing algorithm to determine a group layout and production plan in a dynamic cellular manufacturing system", Journal of Optimization in Industrial Engineering, 7(14), pp. 37-52 (2014). 10. Norman, B.A., Tharmmaphornphilas, W., Needy, K.L., Bidanda, B., and Warner, R.C. Worker assignment in cellular manufacturing considering technical and human skills", International Journal of Production Research, 40(6), pp. 1479-1492 (2002). 11. Suksawat, B., Hiraoka, H., and Ihara, T. A new approach manufacturing cell scheduling based on skill-based manufacturing integrated to genetic algorithm", In Towards Synthesis of Micro-/Nano- Systems, Springer, pp. 325-326 (2007). 12. Duan, F., Tan, J.T.C., Tong, J.G., Kato, R., and Arai, T. Application of the assembly skill transfer system in an actual cellular manufacturing system", Automation Science and Engineering, IEEE Transactions on, 9(1), pp. 31-41 (2012). 13. Egilmez, G., Erenay, B., and Suer, G.A. Stochastic skill-based manpower allocation in a cellular manufacturing system", Journal of Manufacturing Systems, 33(4), pp. 578-588 (2014). 14. Lim, Z.Y., Ponnambalam, S., and Izui, K. Multiobjective hybrid algorithms for layout optimization in multi-robot cellular manufacturing systems", Knowledge-Based Systems, 120, pp. 87-98 (2017). 15. Rezazadeh, H. and Khiali-Miab, A. A two-layer genetic algorithm for the design of reliable cellular manufacturing systems", International Journal of Industrial Engineering Computations, 8(3), pp. 315-332 (2017). 16. Aalaei, A. and Davoudpour, H. Revised multi-choice goal programming for incorporated dynamic virtual cellular manufacturing into supply chain management: a case study", Engineering Applications of Arti_cial Intelligence, 47, pp. 3-15 (2016). 17. Forghani, K. and Mohammadi, M. A genetic algorithm for solving integrated cell formation and layout problem considering alternative routings and machine capacities", Scientia Iranica. Transaction E, Industrial Engineering, 21(6), pp. 2326-2346 (2014). 18. Sahinidis, N.V. Optimization under uncertainty: state-of-the-art and opportunities", Computers & Chemical Engineering, 28(6), pp. 971-983 (2004). 19. Mirzapour Al-E-Hashem, S., Malekly, H., and Aryanezhad, M. A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty", International Journal of Production Economics, 134(1), pp. 28-42 (2011). 20. Safaei, N. and Tavakkoli-Moghaddam, R. An extended fuzzy parametric programming-based approach for designing cellular manufacturing systems under uncertainty and dynamic conditions", International Journal of Computer Integrated Manufacturing, 22(6), pp. 538-548 (2009). 21. Kia, R., Paydar, M.M., Jondabeh, M.A., Javadian, N., and Nejatbakhsh, Y. A fuzzy linear programming approach to layout design of dynamic cellular manufacturing systems with route selection and cell recon _guration", International Journal of Management Science and Engineering Management, 6(3), pp. 219- 230 (2011). 22. Behret, H. and Satoglu, S.I. Fuzzy logic applications in cellular manufacturing system design", In Computational Intelligence Systems in Industrial Engineering, Springer, pp. 505-533 (2012). 23. Paydar, M.M. and Saidi-Mehrabad, M. Revised multi-choice goal programming for integrated supply chain design and dynamic virtual cell formation with fuzzy parameters", International Journal of Computer Integrated Manufacturing, 28(3), pp. 251-265 (2014). 24. Tavakkoli-Moghaddam, R., Javadian, N., Javadi, B., and Safaei, N. Design of a facility layout problem in cellular manufacturing systems with stochastic demands", Applied Mathematics and Computation, 184(2), pp. 721-728 (2007). 25. Ghezavati, V. and Saidi-Mehrabad, M. Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time", The International Journal of Advanced Manufacturing Technology, 48(5-8), pp. 701-717 (2010). 26. Ghezavati, V. and Saidi-Mehrabad, M. An e_cient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis", Expert Systems with Applications, 38(3), pp. 1326- 1335 (2011). 27. Egilmez, G., Suer, G.A., and Huang, J. Stochastic cellular manufacturing system design subject to maximum acceptable risk level", Computers & Industrial Engineering, 63(4), pp. 842-854 (2012). 28. Salarian, R., Fazlollahtabar, H., and Mahdavi, I. Inter-cell movement minimisation in a cellular manufacturing system having stochastic parameters", International Journal of Services and Operations Management, 17(1), pp. 67-87 (2014). A. Hashemoghli et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 538{556 555 29. Bagheri, M., Sadeghi, S., and Saidi-Mehrabad, M. A benders decomposition approach for dynamic cellular manufacturing system in the presence of unreliable machines", Journal of Optimization in Industrial Engineering, 8(17), pp. 37-49 (2015). 30. Rabbani, M., Akbari, E., and Dolatkhah, M. Manpower allocation in a cellular manufacturing system considering the impact of learning, training and combination of learning and training in operator skills", Management Science Letters, 7(1), pp. 9-22 (2017). 31. Ghezavati, V., Sadjadi, S., and Dehghan Nayeri, M. Integrating strategic and tactical decisions to robust designing of cellular manufacturing under uncertainty: Fixed suppliers in supply chain", International Journal of Computational Intelligence Systems, 4(5), pp. 837- 854 (2011). 32. Forghani, K., Mohammadi, M., and Ghezavati, V. Designing robust layout in cellular manufacturing systems with uncertain demands", International Journal of Industrial Engineering Computations, 4(2), pp. 215- 226 (2013). 33. Tavakkoli-Moghaddam, R., Sakhaii, M., and Vatani, B. A robust model for a dynamic cellular manufacturing system with production planning", International Journal of Engineering-Transactions A: Basics, 27(4), pp. 587-598 (2013). 34. Sakhaii, M., Tavakkoli-Moghaddam, R., Bagheri, M., and Vatani, B. A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines", Applied Mathematical Modelling, 40(1), pp. 169-191 (2016). 35. Paydar, M.M. and Saidi-Mehrabad, M. Revised multi-choice goal programming for integrated supply chain design and dynamic virtual cell formation with fuzzy parameters", International Journal of Computer Integrated Manufacturing, 28(3), pp. 251-265 (2015). 36. Pishvaee, M., Razmi, J., and Torabi, S. Robust possibilistic programming for socially responsible supply chain network design: A new approach", Fuzzy Sets and Systems, 206, pp. 1-20 (2012). 37. Zhang, W. and Reimann, M. A simple augmented _-constraint method for multi-objective mathematical integer programming problems", European Journal of Operational Research, 234(1), pp. 15-24 (2014). 38. Defersha, F.M. and Chen, M. A comprehensive mathematical model for the design of cellular manufacturing systems", International Journal of Production Economics, 103(2), pp. 767-783 (2006). 39. Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M. Production planning and cell formation in dynamic virtual cellular manufacturing systems with worker exibility", In Computers & Industrial Engineering, 2009. CIE 2009, International Conference on. 2009: IEEE (2009). 40. Solimanpur, M., Saeedi, S., and Mahdavi, I. Solving cell formation problem in cellular manufacturing using ant-colony-based optimization", The International Journal of Advanced Manufacturing Technology, 50(9- 12), pp. 1135-1144 (2010). 41. Mahdavi, I., Aalaei, A., Paydar, M.M., and Solimanpur, M. Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems", International Journal of Production Research, 49(21), pp. 6517-6537 (2011). 42. Kia, R., Baboli, A., Javadian, N., Tavakkoli- Moghaddam, R., Kazemi, M., and Khorrami, J. Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and exible recon_guration by simulated annealing", Computers & Operations Research, 39(11), pp. 2642-2658 (2012). 43. Torabi, S. and Amiri, A.S. A possibilistic approach for designing hybrid cellular manufacturing systems", International Journal of Production Research, 50(15), pp. 4090-4104 (2012). 44. Chang, C.-C., Wu, T.-H., and Wu, C.-W. An e_cient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing systems", Computers & Industrial Engineering, 66(2), pp. 438-450 (2013). 45. Kia, R., Shirazi, H., Javadian, N., and Tavakkoli- Moghaddam, R. A multi-objective model for designing a group layout of a dynamic cellular manufacturing system", Journal of Industrial Engineering International, 9(1), pp. 1-14 (2013). 46. Shirazi, H., Kia, R., Javadian, N., and Tavakkoli- Moghaddam, R. An archived multi-objective simulated annealing for a dynamic cellular manufacturing system", Journal of Industrial Engineering International, 10(2), pp. 1-17 (2014). 47. Deep, K. and Singh, P.K. Design of robust cellular manufacturing system for dynamic part population considering multiple processing routes using genetic algorithm", Journal of Manufacturing Systems, 35, pp. 155-163 (2015).
1
ORIGINAL_ARTICLE
An imperfect multi-item single-machine production system with shortage, rework, and scrap considering inspection, dissimilar deficiency levels, and non-zero setup times
In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified by 100% inspection during production, then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where machines require some preparations before starting a new production cycle. Thus, we introduce an economic production quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes inventory system costs including setup costs in reworks, holding costs, production costs, inspection costs, disposal costs, and shortage. Finally, a numerical example is proposed to assess efficiency and validation of the proposed algorithm.
http://scientiairanica.sharif.edu/article_20038_1bedf4e0f6d6d4321cfdee8a642a6f8b.pdf
2019-02-01
557
570
10.24200/sci.2018.4984.1031
Lot sizing
imperfect manufacturing
multiple rework
single machine
exact algorithm
A. H.
Nobil
amirhossein.nobil@yahoo.com
1
Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
AUTHOR
A. H.
Afshar Sedigh
amir.afshar@postgrad.otago.ac.nz
2
Information Science, University of Otago, Dunedin, New Zealand
AUTHOR
S.
Tiwari
sunil.tiwari047@gmail.com
3
The Logistics Institute-Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace, #04-01, Singapore 119613
AUTHOR
H. M.
Wee
weehm@cycu.edu.tw
4
Department of Industrial and Systems Engineering, Chung Yuan Christian University, No. 200, Chung Pei Road, Chung Li District, Taoyuan City, 32023, Taiwan
LEAD_AUTHOR
Harris, F.W. How many parts to make at once", Factory, The Magazine of Management, 10(2), pp. 135-136, 152 (1913). 2. C_ardenas-Barr_on, L.E., Chung, K.J., and Trevi~no- Garza, G. Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris", International Journal of Production Economics, 155, pp. 1-7 (2014). 3. Taft, E.W. The most economical production lot", Iron Age, 101(18), pp. 1410-1412 (1918). 4. Hadley, G. and Whitin, T.M., Analysis of Inventory Systems, Prentice-Hall, Englewood Cli_s, NJ (1963). 5. Parker, L.L. Economical reorder quantities and reorder points with uncertain demand", Naval Research Logistics Quarterly, 11(3-4), pp. 351-358 (1964). 6. Yao, J.S. and Lee, H.M. Fuzzy inventory with backorder for fuzzy order quantity", Information Sciences, 93(3), pp. 283-319 (1996). 7. Lee, H.M. and Yao, J.S. Economic order quantity in fuzzy sense for inventory without backorder model", Fuzzy Sets and Systems, 105(1), pp. 13-31 (1999). 8. Bjork, K.M. An analytical solution to a fuzzy economic order quantity problem", International Journal of Approximate Reasoning, 50(3), pp. 485-493 (2009). 9. Silver, E. Establishing the order quantity when the amount received is uncertain", INFOR: Information Systems and Operational Research, 14(1), pp. 32-39 (1976). 10. Maddah, B., and Jaber, M.Y. Economic order quantity for items with imperfect quality: revisited", International Journal of Production Economics, 112(2), pp. 808-815 (2008). 11. Khan, M., Jaber, M.Y., and Bonney, M. An economic order quantity (EOQ) for items with imperfect quality and inspection errors", International Journal of Production Economics, 133(1), pp. 113-118 (2011). 12. Whitin, T.M., Theory of Inventory Management, Princeton University Press, Princeton, NJ, USA (1957). 13. Aggarwal, S.P. and Jaggi, C.K. Ordering policies of deteriorating items under permissible delay in payments", Journal of the Operational Research Society, 46(5), pp. 658-662 (1995). 14. Wu, K.S., Ouyang, L.Y., and Yang, C.T. An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging", International Journal of Production Economics, 101(2), pp. 369-384 (2006). 15. Chang, C.T., Teng, J.T., and Goyal, S.K. Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand", International Journal of Production Economics, 123(1), pp. 62-68 (2010). 16. Wu, J., Ouyang, L.Y., C_ardenas-Barr_on, L.E., and Goyal, S.K. Optimal credit period and slot size for deteriorating items with expiration dates under twolevel trade credit _nancing", European Journal of Operational Research, 237(3), pp. 898-908 (2014). 17. Sett, B.K., Sarkar, S., Sarkar, B., and Yun, W.Y. Optimal replenishment policy with variable deterioration for _xed-lifetime products", Scientia Iranica, Transactions E, Industrial Engineering, 23(5), pp. 2318-2329 (2016). 18. Wu, C.F. and Zhao, Q.H. An inventory model for deteriorating items with inventory-dependent and linear trend demand under trade credit", Scientia Iranica, Transactions E, Industrial Engineering, 22(6), pp. 2558 -2570 (2015). 19. Mokhtari, H., Naimi-Sadigh, A., and Salmasnia, A. A computational approach to economic production quantity model for perishable products with backordering shortage and stock-dependent demand", Scientia Iranica, Transactions E, Industrial Engineering, 24(4), pp. 2138-2151 (2017). 20. Wu, J., Al-Khateeb, F.B., Teng, J.T., and C_ardenas- Barr_on, L.E. Inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit-risk customers by discounted cash-ow analysis", International Journal of Production Economics, 171, pp. 105-115 (2016). 21. Shah N.H. and C_ardenas-Barr_on, L.E. Retailer's decision for ordering and credit policies for deteriorating items when a supplier o_ers order-linked credit period or cash discount", Applied Mathematics and Computation, 259, pp. 569-578 (2015). 22. Teng, J.T., C_ardenas-Barr_on, L.E., Chang, H.J., Wu, J., and Hu, Y. Inventory lot-size policies for deteriorating items with expiration dates and advance payments", Applied Mathematical Modelling, 40(19), pp. 8605-8616 (2016). 23. Dobson, G., Pinker, E.J., and Yildiz, O. An EOQ model for perishable goods with age-dependent demand rate", European Journal of Operational Research, 257(1), pp. 84-88 (2017). 24. Salameh, M.K. and Jaber, M.Y. Economic production quantity model for items with imperfect quality", A.H. Nobil et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 557{570 567 International Journal of Production Economics, 64(1), pp. 59-64 (2000). 25. Goyal, S.K. and C_ardenas-Barr_on, L.E. Note on: economic production quantity model for items with imperfect quality-a practical approach", International Journal of Production Economics, 77(1), pp. 85-87 (2002). 26. Wee, H.M., Yu, J., and Chen, M.C. Optimal inventory model for items with imperfect quality and shortage backordering", Omega, 35(1), pp. 7-11 (2007). 27. Haji, R., Haji, A., Sajadifar, M., and Zolfaghari, S. Lot sizing with non-zero setup times for rework", Journal of Systems Science and Systems Engineering, 17(2), pp. 230-240 (2008). 28. Nobil, A.H., Nobil, E., and C_ardenas-Barr_on, L.E. Some observations to: lot sizing with non-zero setup times for rework", International Journal of Applied and Computational Mathematics, 3(1), pp. 1511-1517 (2017). 29. C_ardenas-Barr_on, L.E. Economic production quantity with rework process at a single-stage manufacturing system with planned backorders", Computers & Industrial Engineering, 57(3), pp. 1105-1113 (2009). 30. Hsu, J.T. and Hsu, L.F. Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns", Computers & Industrial Engineering, 64(1), pp. 389-402 (2013). 31. Farhangi, M., Niaki, S.T.A., and Vishkaei, B.M. Closed-form equations for optimal lot sizing in deterministic EOQ models with exchangeable imperfect quality items", Scientia Iranica, Transactions E, Industrial Engineering, 22(6), pp. 2621-2633 (2015). 32. C_ardenas-Barr_on, L.E., Sarkar, B., and Trevi~no-Garza, G. Easy and improved algorithms to joint determination of the replenishment lot size and number of shipments for an EPQ model with rework", Mathematical and Computational Applications, 18(2), pp. 132-138 (2013). 33. Shah, N.H., Patel, D.G., and Shah, D.B. EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stockdependent demand", Operational Research, pp. 1-17 (2016). 34. Jaggi, C.K., Tiwari, S., and Sha_, A. E_ect of deterioration on two-warehouse inventory model with imperfect quality", Computers & Industrial Engineering, 88, pp. 378-385 (2015). 35. Jaggi, C.K., C_ardenas-Barr_on, L.E., Tiwari, S., and Sha_, A.A. Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments", Scientia Iranica, Transactions E, Industrial Engineering, 24(1), pp. 390-412 (2017). 36. Rogers, J. A computational approach to the economic lot-scheduling problem", Management Science, 4(3), pp. 264-291 (1958). 37. Taleizadeh, A.A., C_ardenas-Barr_on, L.E., and Mohammadi, B. A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process", International Journal of Production Economics, 150, pp. 9-27 (2014). 38. Pasandideh, S.H.R., Niaki, S.T.A., Nobil, A.H., and C_ardenas-Barr_on, L.E. A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost", International Journal of Production Economics, 169, pp. 203-214 (2015). 39. Nobil, A.H., Sedigh, A.H.A., and C_ardenas-Barr_on, L.E. A multi-machine multi-product EMQ problem for an imperfect manufacturing system considering utilization and allocation decisions", Expert Systems with Applications, 56, pp. 310-319 (2016). 40. Nobil, A.H. and Taleizadeh, A.A. A single machine EPQ inventory model for a multi-product imperfect production system with rework process and auction", International Journal of Advanced Logistics, 5(3-4), pp. 141-152 (2016). 41. Nobil, A.H., Sedigh, A.H.A., and C_ardenas-Barr_on, L.E. A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints", Annals of Operations Research, pp. 1-37 (2017). doi: 10.1007/s10479-017-2650-9 42. Nobil, A.H., Sedigh, A.H.A., and C_ardenas-Barr_on, L.E. Multi-machine economic production quantity for items with scrapped and rework with shortages and allocation decisions", Scientia Iranica, Transactions E, Industrial Engineering, 25(4), pp. 2331-2346 (2018). doi:10.24200/sci.2017.4453
1
ORIGINAL_ARTICLE
Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm
Discrete phase-type (DPH) distributions have one property that is not shared by continuous phase-type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems such as stochastic scheduling where service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB) and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB applicable to represent data on certain types of service time. Therefore, we adapt an expectation-maximization (EM) algorithm to estimate the parameters of MSNB distributions that accurately fit trace data. To present the applicability of the proposed algorithm, we use it to fit real operating room times as well as a set of benchmark traces generated from continuous distributions as case studies. Finally, we illustrate the efficiency of the proposed algorithm by comparing its results to that of two existing algorithms in the literature. We conclude that our proposed algorithm outperforms other DPH algorithms in fitting trace data and distributions.
http://scientiairanica.sharif.edu/article_20040_b78670ba46acb4ec04adb7b34b4802f3.pdf
2019-02-01
571
588
10.24200/sci.2018.5130.1117
parameter estimation
discrete phase-type (DPH) distributions
expectation-maximization (EM) algorithm
mixed shifted negative binomial distributions
M.
Varmazyar
mohsen.varmazyar@gmail.com
1
Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-8639, Iran
LEAD_AUTHOR
R.
Akhavan-Tabatabaei
akhavan@sabanciuniv.edu
2
School of Management, Sabanci University, Istanbul, Turkey
AUTHOR
N.
Salmasi
nasser.salmasi@gmail.com
3
Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-8639, Iran
AUTHOR
M.
Modarres
modarres@sharif.edu
4
Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-8639, Iran
AUTHOR
Neuts, M.F. Computational uses of the method of phases in the theory of queues", Computers & Mathematics with Applications, 1(2), pp. 151-166 (1975). 2. Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Johns Hopkins University, Baltimore (1981). 3. Fackrell, M. Modelling healthcare systems with phase-type distributions", Health Care Management Science, 12, pp. 11-26 (2009). 4. Thummler, A., Buchholz, P., and Telek, M. A novel approach for phase-type _tting with the EM algorithm", IEEE Transactions on Dependable and Secure Computing, 3(3), pp. 245-258 (2006). 5. Hu, L., Jiang, Y., Zhu, J., and Chen, Y. Hybrid of the scatter search, improved adaptive genetic, and expectation maximization algorithms for phase-type distribution _tting", Applied Mathematics and Computation, 219(10), pp. 5495-5515 (2013). 6. Anbazhagan, N., Stochastic Processes and Models in Operations Research, Hershey, Pennsylvania 701 E. Chocolate Avenue, Hershey, PA 17033, USA: IGI Global (2016). 7. Horv_ath, A. and Telek, M. Ph_t: A general phasetype _tting tool", Computer Performance Evaluation: Modelling Techniques and Tools, pp. 82-91 (2002). 8. Bobbio, A., Horv_ath, A., Scarpa, M., and Telek, M. Acyclic discrete phase type distributions: properties and a parameter estimation algorithm", Performance Evaluation, 54(1), pp. 1-32 (2003). 9. Callut, J. and Dupont, P. Sequence discrimination using phase-type distributions", Machine Learning: ECML 2006, pp. 78-89 (2006). 10. Asmussen, S., Nerman, O., and Olsson, M. Fitting phase-type distributions via the EM algorithm", Scandinavian Journal of Statistics, 23(4), pp. 419-441 (1996). 11. Bladt, M., Esparza, L.J.R., Nielsen, B.F., et al. Fisher information and statistical inference for phase-type distributions", Journal of Applied Probability, 48, pp. 277-293 (2011). 12. Mesz_aros, A., Papp, J., and Telek, M. Fitting tra_c traces with discrete canonical phase type distributions and Markov arrival processes", International Journal of Applied Mathematics and Computer Science, 24(3), pp. 453-470 (2014). 13. Horv_ath, I., Papp, J., and Telek, M. On the canonical representation of order 3 discrete phase type distributions", Electronic Notes in Theoretical Computer Science, 318, pp. 143-158 (2015). 14. Springer, T. and Urban, K. Comparison of the EM algorithm and alternatives", Numerical Algorithms, 67(2), pp. 335-364 (2014). 15. Verbelen, R., Phase-Type Distributions & Mixtures of Erlangs, University of Leuven (2013). 16. O'Hagan, A., Murphy, T.B., and Gormley, I.C. Computational aspects of _tting mixture models via the expectation-maximization algorithm", Computational Statistics & Data Analysis, 56(12), pp. 3843-3864 (2012). 17. Xu, J. and Ma, J. Fitting _nite mixture models using iterative Monte Carlo classi_cation", Communications in Statistics-Theory and Methods, 46(13), pp. 6684- 6693 (2017). 18. Bilmes, J.A. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models", International Computer Science Institute, 4(510), p. 126 (1998). 19. McLachlan, G. and Krishnan, T., The EM Algorithm and Extensions, 382, John Wiley & Sons (2007). 20. Dougherty, J., Kohavi, R., and Sahami, M. Supervised and unsupervised discretization of continuous feature", In Proceedings of 12th International Conference of Machine Learning, pp. 194-202 (1995). 21. MATLAB Release 2014a, MathWorks, Inc. (2015). 22. Bowers, J. and Mould, G. Managing uncertainty in orthopaedic trauma theatres", European Journal of Operational Research, 154(3), pp. 599-608 (2004). 23. Perez, J. and Riano, G. Benchmarking of _tting algorithms for continuous phase-type distributions", Working Paper, COPA Universidad de los Andes, pp. 1-20 (2007). 24. Chiarandini, M., Basso, D., and Stutzle, T. Statistical methods for the comparison of stochastic optimizers", In MIC2005: The Sixth Metaheuristics International Conference, pp. 189-196 (2005). 25. SAS Release, 9.1, SAS Institute Inc. (2003). 26. Bobbio, A. and Telek, M. A benchmark for PH estimation algorithms: results for Acyclic-PH", Stochastic Models, 10(3), pp. 661-677 (1994). 586 M. Varmazyar et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 571{588 27. Latouche, G. and Ramaswami, V., Introduction to Matrix Analytic Methods in Stochastic Modeling, 5, Siam (1999). 28. Alfa, A., Applied Discrete-time Queues, Springer- Verlag New York (2016). 29. Varmazyar, M., Akhavan-Tabatabaei, R., Salmasi, N., and Modarres, M. Classi_cation and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions", Journal of Industrial Engineering International (Nov 2018).
1
ORIGINAL_ARTICLE
Measuring the satisfaction and loyalty of Chinese smartphone users: A simple symbol-based decision-making method
User satisfaction and loyalty are very important in the mobile communications market because mobile is frequently updated. It is very necessary work that builds up a scientific assessment method to assist product in understanding and knowing well the trend of customers. This paper is intend to build up a scientific assessment method for measuring user satisfaction and loyalty. First, combining the group decision making and TOPSIS (technique for order preference by similarity to ideal solution) technique, a theoretical framework of evaluation method is established. Second, the respondents are allowed to express their opinions by using some simple symbols or by leaving the lack of answers to some measurement questions, even whole questionnaire. Then the symbol information along with the nonresponses in questionnaires are fused into an intuitionistic fuzzy information. Third, the levels of user satisfaction are ranked based on TOPSIS technique and projection measure in an intuitionistic fuzzy environment. Finally, the theoretical and practical implications of current model are discussed, the important limitations are recognized and future research directions are suggested.
http://scientiairanica.sharif.edu/article_20737_60a0bd3b96a026efc64eed1980d2459f.pdf
2019-02-01
589
604
10.24200/sci.2018.3841.0
User satisfaction and loyalty
Smartphone
group decision making
interval-valued intuitionistic fuzzy information
symbol information
C.
Yue
yuechuan-1988@163.com
1
College of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China
AUTHOR
Z.
Yue
zhongliangyue@gmail.com
2
College of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China
LEAD_AUTHOR
CNNIC Statistical report on internet development in China (July 2017)", Available at: http://www1.cnnic.cn/IDR/ReportDownloads/, Accessed 30 December (2017). 2. Rahul, T. and Majhi, R. An adaptive nonlinear approach for estimation of consumer satisfaction and loyalty in mobile phone sector of India", Journal of Retailing and Consumer Services, 21(4), pp. 570-580 (2014). 3. Cronin Jr, J.J., Brady, M.K., and Hult, G.T.M. Assessing the e_ects of quality, value, and customer satisfaction on consumer behavioral intentions in service 602 C. Yue and Z. Yue/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 589{604 environments", Journal of Retailing, 76(2), pp. 193- 218 (2000). 4. Seiders, K., Voss, G.B., Grewal, D., and Godfrey, A.L. Do satis_ed customers buy more? Examining moderating inuences in a retailing context", Journal of Marketing, 69(4), pp. 26-43 (2005). 5. Li, G., Bie, Z., Xie, H., and Lin, Y. Customer satisfaction based reliability evaluation of active distribution networks", Applied Energy, 162, pp. 1571-1578 (2016). 6. Leong, L.-Y., Hew, T.-S., Lee, V.-H., and Ooi, K.-B. An SEM-arti_cial-neural-network analysis of the relationships between SERVPERF, customer satisfaction and loyalty among low-cost and full-service airline", Expert Systems with Applications, 42(19), pp. 6620- 6634 (2015). 7. Aktepe, A., Ersoz, S., and Toklu, B. Customer satisfaction and loyalty analysis with classi_cation algorithms and structural equation modeling", Computers & Industrial Engineering, 86, pp. 95-105 (2015). 8. Li, L., Liu, F., and Li, C. Customer satisfaction evaluation method for customized product development using entropy weight and analytic hierarchy process", Computers & Industrial Engineering, 77, pp. 80-87 (2014). 9. Hwang, C. and Yoon, K., Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Berlin (1981). 10. Yue, Z. An intuitionistic fuzzy projection-based approach for partner selection", Applied Mathematical Modelling, 37(23), pp. 9538-9551 (2013). 11. Yue, Z. and Jia, Y. A group decision making model with hybrid intuitionistic fuzzy information", Computers & Industrial Engineering, 87, pp. 202-212 (2015). 12. Zhao, L., Lu, Y., Zhang, L., and Chau, P.Y. Assessing the e_ects of service quality and justice on customer satisfaction and the continuance intention of mobile value-added services: An empirical test of a multidimensional model", Decision Support Systems, 52(3), pp. 645-656 (2012). 13. Bayraktar, E., Tatoglu, E., Turkyilmaz, A., Delen, D., and Zaim, S. Measuring the e_ciency of customer satisfaction and loyalty for mobile phone brands with DEA", Expert Systems with Applications, 39(1), pp. 99-106 (2012). 14. Kim, Y.H., Kim, D.J., and Wachter, K. A study of mobile user engagement (MoEN): Engagement motivations, perceived value, satisfaction, and continued engagement intention", Decision Support Systems, 56, pp. 361-370 (2013). 15. Haverila, M. Mobile phone feature preferences, customer satisfaction and repurchase intent among male users", Australasian Marketing Journal, 19(4), pp. 238-246 (2011). 16. Qi, J.-Y., Zhou, Y.-P., Chen, W.-J., and Qu, Q.- X. Are customer satisfaction and customer loyalty drivers of customer lifetime value in mobile data services: A comparative cross-country study", Information Technology and Management, 13(4), pp. 281- 296 (2012). 17. Bandarua, S., Gaura, A., Deba, K., Khareb, V., and Chougulec, R. Development, analysis and applications of a quantitative methodology for assessing customer satisfaction using evolutionary optimization", Applied Soft Computing, 30, pp. 265-278 (2015). 18. Kang D. and Park, Y. Review-based measurement of customer satisfaction in mobile service: Sentiment analysis and VIKOR approach", Expert Systems with Applications, 41(4), pp. 1041-1050 (2014). 19. Yue, Z. and Jia, Y. A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making", Applied Soft Computing, 13(5), pp. 2304-2317 (2013). 20. Yue, Z. and Jia, Y. An application of soft computing technique in group decision making under intervalvalued intuitionistic fuzzy environment", Applied Soft Computing, 13(5), pp. 2490-2503 (2013). 21. Yue, Z. Group decision making with multi-attribute interval data," Information Fusion, 14(4), pp. 551-561 (2013). 22. Yue, Z. An avoiding information loss approach to group decision making", Applied Mathematical Modelling, 37(1-2), pp. 112-126 (2013). 23. Yue, Z. A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information", Applied Mathematical Modelling, 38(2), pp. 683-698 (2014). 24. P_erez, I.J., Cabrerizo, F.J., Alonso, S., and Herrera- Viedma, E. A new consensus model for group decision making problems with non-homogeneous experts", IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(4), pp. 494-498 (2014). 25. Hashemi, H., Bazargan, J., and Mousavi, S.M. A compromise ratio method with an application to water resources management: An intuitionistic fuzzy set", Water Resources Management, 27(7), pp. 2029-2051 (2013). 26. Liu, P. Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making", IEEE Transactions on Fuzzy Systems, 22(1), pp. 83-97 (2014). 27. Vahdani, B., Mousavi, S.M., and Tavakkoli- Moghaddam, R. Group decision making based on novel fuzzy modi_ed TOPSIS method", Applied Mathematical Modelling, 35(9), pp. 4257-4269 (2011). 28. Morente-Molinera, J.A., P_erez, I.J., Ure~na, M.R., and Herrera-Viedma, E. On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends", Knowledge- Based Systems, 74, pp. 49-60 (2015). 29. Mousavi, S.M., Jolai, F., and Tavakkoli-Moghaddam, R. A fuzzy stochastic multi-attribute group decisionmaking approach for selection problems", Group Decision and Negotiation, 22(2), pp. 207-233 (2013). C. Yue and Z. Yue/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 589{604 603 30. Ebrahimnejad, S., Mousavi, S., Tavakkoli- Moghaddam, R., Hashemi, H., and Vahdani, B. A novel two-phase group decision making approach for construction project selection in a fuzzy environment", Applied Mathematical Modelling, 36(9), pp. 4197-4217 (2012). 31. Liao, H., Xu, Z., and Xia, M. Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making", International Journal of Information Technology & Decision Making, 13(1), pp. 47-76 (2014). 32. Mousavi, S.M., Torabi, S.A., and Tavakkoli- Moghaddam, R. A hierarchical group decisionmaking approach for new product selection in a fuzzy environment", Arabian Journal for Science and Engineering, 38(11), pp. 3233-3248 (2013). 33. Mousavi, S.M., Jolai, F., Tavakkoli-Moghaddam, R., and Vahdani, B. A fuzzy grey model based on the compromise ranking for multi-criteria group decision making problems in manufacturing systems", Journal of Intelligent & Fuzzy Systems, 24(4), pp. 819-827 (2013). 34. Wan, S.-P. and Li, D.-F. Atanassov's intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov's intuitionistic fuzzy truth degrees", IEEE Transactions on Fuzzy Systems, 22(2), pp. 300-312 (2014). 35. Mousavi, S.M., Vahdani, B., Tavakkoli-Moghaddam, R., and Tajik, N. Soft computing based on a fuzzy grey group compromise solution approach with an application to the selection problem of material handling equipment", International Journal of Computer Integrated Manufacturing, 27(6), pp. 547-569 (2014). 36. Mousavi, S.M., Mirdamadi, S., Siadat, A., Dantan, J., and Tavakkoli-Moghaddam, R. An intuitionistic fuzzy grey model for selection problems with an application to the inspection planning in manufacturing _rms", Engineering Applications of Arti_cial Intelligence, 39, pp. 157-167 (2015). 37. Meng, F. and Chen, X. A new method for group decision making with incomplete fuzzy preference relations", Knowledge-Based Systems, 73, pp. 111-123 (2015). 38. Gitinavard, H., Mousavi, S.M., and Vahdani, B. A new multi-criteria weighting and ranking model for group decision-making analysis based on intervalvalued hesitant fuzzy sets to selection problems", Neural Computing and Applications, 27, pp. 1593-1605 (2016). 39. Gitinavard, H., Mousavi, S., Vahdani, B., and Siadat, A. A distance-based decision model in interval-valued hesitant fuzzy setting for industrial selection problems", Scientia Iranica, 23(4), pp. 1928-1940 (2016). 40. Zhang, F., Ignatius, J., Lim, C.P., and Zhao, Y. A new method for ranking fuzzy numbers and its application to group decision making", Applied Mathematical Modelling, 38(4), pp. 1563-1582 (2014). 41. Xu, J. and Shen, F. A new outranking choice method for group decision making under Atanassov's intervalvalued intuitionistic fuzzy environment", Knowledge- Based Systems, 70, pp. 177-188 (2014). 42. Yue, C. A geometric approach for ranking intervalvalued intuitionistic fuzzy numbers with an application to group decision-making", Computers & Industrial Engineering, 102, pp. 233-245 (2016). 43. Kucukvar, M., Gumus, S., Egilmez, G., and Tatari, O. Ranking the sustainability performance of pavements: An intuitionistic fuzzy decision making method", Automation in Construction, 40, pp. 33-43 (2014). 44. Chen, T.-Y. An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis", Applied Soft Computing, 42, pp. 390- 409 (2016). 45. Vahdani, B., Mousavi, S.M., Tavakkoli-Moghaddam, R., and Hashemi, H. A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment", Applied Mathematical Modelling, 37(4), pp. 1781-1799 (2013). 46. Hashemi, H., Bazargan, J., Mousavi, S.M., and Vahdani, B. An extended compromise ratio model with an application to reservoir ood control operation under an interval-valued intuitionistic fuzzy environment", Applied Mathematical Modelling, 38(14), pp. 3495- 3511 (2014). 47. Dymova, L. and Sevastjanov, P. The operations on interval-valued intuitionistic fuzzy values in the framework of Dempster-Shafer theory", Information Sciences, 360, pp. 256-272 (2016). 48. Verma, H., Agrawal, R.K., and Sharan, A. An improved intuitionistic fuzzy c-means clustering algorithm incorporating local information for brain image segmentation", Applied Soft Computing, 46, pp. 543- 557 (2016). 49. Nguyen, H. A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making", Expert Systems with Applications, 56, pp. 143-155 (2016). 50. Ouyang, Y. and Pedrycz, W. A new model for intuitionistic fuzzy multi-attributes decision making", European Journal of Operational Research, 249(2), pp. 677-682 (2016). 51. Mousavi, S.M., Vahdani, B., and Behzadi, S.S. Designing a model of intuitionistic fuzzy VIKOR in multiattribute group decision-making problems," Iranian Journal of Fuzzy Systems, 13(1), pp. 45-65 (2016). 52. Yue, C. A model for evaluating software quality based on symbol information", Journal of Guangdong Ocean University, 36(1), pp. 85-92 (2016). 53. Yue, Z. An extended TOPSIS for determining weights of decision makers with interval numbers," Knowledge- Based Systems, 24(1), pp. 146{153 (2011). 604 C. Yue and Z. Yue/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 589{604 54. Mokhtarian, M., Sadi-nezhad, S., and Makui, A. A new exible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process", Applied Soft Computing, 23, pp. 509-520 (2014). 55. Beikkhakhian, Y., Javanmardi, M., Karbasian, M., and Khayambashi, B. The application of ISM model in evaluating agile suppliers selection criteria and ranking suppliers using fuzzy TOPSIS-AHP methods", Expert Systems with Applications, 42(15), pp. 6224- 6236 (2015). 56. Roszkowska, E. and Wachowicz, T. Application of fuzzy TOPSIS to scoring the negotiation o_ers in illstructured negotiation problems", European Journal of Operational Research, 242(3), pp. 920-932 (2015). 57. Chai, J., Liu, J.N., and Ngai, E.W. Application of decision-making techniques in supplier selection: A systematic review of literature", Expert Systems with Applications, 40(10), pp. 3872-3885 (2013). 58. Yue, Z. and Jia, Y. A projection-based approach to intuitionistic fuzzy group decision making", Scientia Iranica, 24(3), pp. 1505-1518 (2017). 59. Zadeh, L. Fuzzy sets", Information and Control, 8(3), pp. 338-353 (1965). 60. Atanassov, K. Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp. 87-96 (1986). 61. Xu, Z. and Cai, X. Recent advances in intuitionistic fuzzy information aggregation", Fuzzy Optimization and Decision Making, 9(4), pp. 359-381 (2010). 62. Atanassov, G. and Gargov, G. Interval valued intuitionistic fuzzy sets", Fuzzy Sets and Systems, 31(3), pp. 343-349 (1989). 63. Xu, Z. and Chen, J. An approach to group decision making based on interval-valued intuitionistic judgment matrices", Systems Engineering: Theory and Practice, 27(4), pp. 126-132 (2007). 64. Xu, Z. and Hu, H. Projection models for intuitionistic fuzzy multiple attribute decision making", International Journal of Information Technology & Decision Making, 9(2), pp. 267-280 (2010). 65. Yue, Z. TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting", Information Sciences, 277, pp. 141-153 (2014). 66. Hu, S.-K., Lu, M.-T., and Tzeng, G.-H. Exploring smart phone improvements based on a hybrid MCDM model", Expert Systems with Applications, 41(9), pp. 4401-4413 (2014). 67. Yue, Z. A method for group decision-making based on determining weights of decision makers using TOPSIS", Applied Mathematical Modelling, 35(4), pp. 1926-1936 (2011). 68. Yue, Z. and Jia, Y. A direct projection-based group decision-making methodology with crisp values and interval data", Soft Computing, 21(9), pp. 2395{2405 (2017).
1
ORIGINAL_ARTICLE
Efficient estimation of Pareto model using modified maximum likelihood estimators
In this article, we have proposed some modifications in the maximum likelihood estimation for estimating the parameters of the Pareto distribution and evaluated performance of these modified estimators in comparison to the existing maximum likelihood estimators. Total Relative Deviation (TRD) and Mean Square Error (MSE) have been used as performance indicators for goodness of fit analysis. The modified and traditional estimators have been compared for different sample sizes and different parameter combinations using a Monto Carlo simulation in R-language. We have concluded that the modified maximum likelihood estimator based on expectation of empirical Cumulative Distribution Function (CDF) of first-order statistic performs much better than the traditional ML estimator and other modified estimators based on median and coefficient of variation. The superiority of the said estimator is independent of sample size and choice of true parameter values. The simulation results were further corroborated by employing the proposed estimation strategies on two real-life data sets.
http://scientiairanica.sharif.edu/article_20107_df9fb51e485d6be612bbd468c0cf4c03.pdf
2019-02-01
605
614
10.24200/sci.2018.20107
Maximum Likelihood Estimation
Mean square error
Modified estimators
Pareto distribution
Total relative deviation
S.
Haider Bhatti
sajjad.haider@gcuf.edu.pk
1
Department of Statistics, Government College University, Faisalabad, Pakistan
LEAD_AUTHOR
S.
Hussain
2
Department of Statistics, Government College University, Faisalabad, Pakistan
AUTHOR
T.
Ahmad
3
Department of Statistics, Government College University, Faisalabad, Pakistan
AUTHOR
M.
Aftab
4
Department of Statistics, Government College University, Faisalabad, Pakistan
AUTHOR
M. A.
Raza
5
Department of Statistics, Government College University, Faisalabad, Pakistan
AUTHOR
M.
Tahir
tahirqaustat@yahoo.com
6
Department of Statistics, Government College University, Faisalabad, Pakistan
AUTHOR
Pareto, V. The new theories of economics", J. Polit. Econ., 5(4), pp. 485-502 (1897). 2. Munir, R., Saleem, M., Aslam, M., and Ali, S. Comparison of di_erent methods of parameters estimation for Pareto model", Casp. J. Appl. Sci. Res., 2(1), pp. 45-56 (2013). 3. Arnold, B.C. Encyclopaedia of Statistical Sciences, John Wiley (2008). 4. Abdel-All, N.H., Mahmoud, M.A.W., and Abd-Ellah, H.N. Geometrical properties of Pareto distribution", Appl. Math. Comput., 145(2), pp. 321-339 (2003). 5. Sankaran, P.G. and Nair, M.T. On _nite mixture of Pareto distributions", Calcutta Stat. Assoc. Bull., 57(1-2), pp. 225-226 (2005). 6. Burroughs, S.M. and Tebbens, S.F. Upper-truncated power law distributions", Fractals, 9(1), pp. 209-222 (2001). 7. Castillo, E. and Hadi, A.S. Fitting the generalized Pareto distribution to data", J. Am. Stat. Assoc., 92(440), pp. 1609-1620 (1997). 8. Bourguignon, M., Ghosh, I., and Cordeiro, G.M. General results for the transmuted family of distributions and new models", J. Probab. Stat., 2016, pp. 1-12 (2016). 9. Quandt, R.E. Old and new methods of estimation and the Pareto distribution", Metrika, 10(1), pp. 55- 82 (1966). 10. A_fy, E.E. Order statistics from Pareto distribution", J. Appl. Sci., 6(10), pp. 2151-2157 (2006). 11. Lu, H.-L. and Tao, S.H. The estimation of Pareto distribution by a weighted least square method", Qual. Quant., 41(6), pp. 913-926 (2007). 12. Pobo_c__kov_a, I. and Sedlia_ckov_a, Z. Comparison of four methods for estimating the Weibull distribution parameters", Appl. Math. Sci., 8(83), pp. 4137-4149 (2014). 13. Shawky, A.I. and Abu-Zinadah, H.H. Exponentiated Pareto distribution: di_erent method of estimations", Int. J. Contemp. Mathematical Sci., 4(14), pp. 677-693 (2009). 14. Grimshaw, S.D. Computing maximum likelihood estimates for the generalized Pareto distribution", Technometrics, 35(2), pp. 185-191 (1993). 15. Cohen, A.C. and Whitten, B. Modi_ed maximum likelihood and modi_ed moment estimators for the three-parameterWeibull distribution", Commun. Stat. Methods, 11(23), pp. 2631-2656 (1982). S. Haider Bhatti et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 605{614 613 16. Iwase, K. and Kanefuji, K. Estimation for 3- parameter lognormal distribution with unknown shifted origin", Stat. Pap., 35(1), pp. 81-90 (1994). 17. Lalitha, S. and Mishra, A. Modi_ed maximum likelihood estimation for Rayleigh distribution", Commun. Stat. - Theory Methods, 25(2), pp. 389-401 (1996). 18. Rashid, M.Z. and Akhter, A.S. Estimation accuracy of exponential distribution parameters", Pakistan J. Stat. Oper. Res., 7(2), pp. 217-232 (2011). 19. Zaka, A. and Akhter, A.S. Modi_ed moment, maximum likelihood and percentile estimators for the parameters of the power function distribution", Pakistan J. Stat. Oper. Res., 10(4), pp. 361-368 (2014). 20. Fisher, R.A. 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