A TOPSIS-Based Improved Weighting Approach With Evolutionary Computation

Subject Areas : Transactions on Fuzzy Sets and Systems

Mithat Zeydan ¹ , Murat Güngör ² , Burak Urazel ³

1 - Department of Industrial Engineering, Istanbul Medeniyet University, Istanbul, Turkey.
2 - Department of Industrial Engineering, Istanbul Medeniyet University, Istanbul, Turkey.
3 - Department of Electrical and Electronics Engineering, Eskisehir Osmangazi University, Eskisehir, Turkey.

Received: 2024-03-08 Accepted : 2024-05-07 Published : 2024-05-07

Keywords: Covariance matrix adaptation evolutionary strategy, Technique for order of preference by similarity to ideal solution, Weighted single machine scheduling, Mixed-integer linear programming.,

Abstract :

Although optimization of weighted objectives is ubiquitous in production scheduling, the literature concerning the determination of weights used in these objectives is scarce. Authors usually suppose that weights are given in advance, and focus on the solution methods for the specific problem at hand. However, weights directly settle the class of optimal solutions, and are of utmost importance in any practical scheduling problem. In this study, we propose a new weighting approach for single machine scheduling problems. First, factor weights to be used in customer evaluation are found by solving a nonlinear optimization problem using the covariance matrix adaptation evolutionary strategy (CMAES) under fuzzy environment that takes a pairwise comparison matrix as input. Next, customers are sorted using the technique for order of preference by similarity to ideal solution (TOPSIS) by means of which job weights are obtained. Finally, taking these weights as an input, a total weighted tardiness minimization problem is solved by using mixed-integer linear programming to find the best job sequence. This combined methodology may help companies make robust schedules not based purely on subjective judgment, find the best compromise between customer satisfaction and business needs, and thereby ensure profitability in the long run.

References:

[1] Lin D, Lee CKM, Wu Z. Integrating analytical hierarchy process to genetic algorithm for reentrant flow shop scheduling problem. International Journal of Production Research. 2012; 50(7): 1813-1824. DOI: http://doi.org/10.1080/00207543.2011.561884
[2] Deliktas D, Torkul O, Ustun O, Kiris S. An integrated approach for single machine scheduling with sequence-dependent setup times. International Journal of the Analytic Hierarchy Process. 2015; 7(1): 50-67. DOI: http://doi.org/10.13033/ijahp.v7i1.291
[3] Onemli BC. ¨ Customer Order Scheduling Problem for the Box Packaging Industry: An Application. Master’s thesis; 2019.
[4] Ortiz-Barrios M, Petrillo A, De Felice F, Jaramillo-Rueda N, Jimenez-Delgado G, Borrero-Lopez L. A dispatching-fuzzy AHP-TOPSIS model for scheduling flexible job-shop systems in industry 4.0 context. Applied Sciences. 2021; 11(11): 5107. DOI: http://doi.org/10.3390/app11115107
[5] Utku, DH, Ozyi˘git K, Farizo˘glu EY. A mixed-integer programming model for the job ¨ scheduling problem in a production company. Verimlilik Dergisi . 2022; (1): 110-119. DOI: http://doi.org/10.51551/verimlilik.819041
[6] Stoop PPM, Wiers VCS. The complexity of scheduling in practice. International Journal of Operations & Production Management. 1996; 16(10): 37-53. DOI: http://doi.org/10.1108/01443579610130682
[7] Wiers VCS. A review of the applicability of OR and AI scheduling techniques in practice. Omega. 1997; 25(2): 145-153. DOI: http://doi.org/10.1016/S0305-0483(96)00050-3
[8] McKay KN, Wiers VCS. Unifying the theory and practice of production scheduling. Journal of Manufacturing Systems. 1999; 18(4): 241-255. DOI: http://doi.org/10.1016/S0278-6125(00)86628-5
[9] Dudek RA, Panwalkar SS, Smith ML. The lessons of flowshop scheduling research. Operations Research. 1992; 40(1): 7-13. DOI: http://doi.org/10.1287/opre.40.1.7
[10] Gupta JND, Stafford Jr EF. Flowshop scheduling research after five decades. European Journal of Operational Research. 2006; 169(3): 699-711. DOI: http://doi.org/10.1016/j.ejor.2005.02.001
[11] Choo EU, Wedley WC. A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research. 2004; 31(6): 893908. DOI: http://doi.org/10.1016/S0305- 0548(03)00042-X
[12] Blanquero R, Carrizosa E, Conde E, Messine F. On weights estimation in multiple criteria decision analysis. In: International Workshop on Global Optimization. 2005. p.53-56.
[13] Zeydan M, Bostanc B, Oralhan B. A new hybrid decision making approach for housing suitability mapping of an urban area. Mathematical Problems in Engineering. 2018; 2018. DOI: http://doi.org/10.1155/2018/7038643
[14] Rios LM, Sahinidis NV. Derivative-free optimization: A review of algorithms and comparison of software implementations. Journal of Global Optimization. 2013; 56(3): 1247-1293. DOI: http://doi.org/10.1007/s10898-012-9951-y
[15] Hansen N. The CMA Evolution Strategy: A Tutorial. HAL open science [Preprint] 2005. HAL Id: hal01297037 [Accessed: May 3rd, 2024].
[16] Hwang CL, Yoon K. Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag; 1981.
[17] Graham RL, Lawler EL, Kenstra JK, Rinnooy Kan AHG. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics. 1979; 5: 287-326. DOI:
http://doi.org/10.1016/S0167-5060(08)70356-X
[18] Pinedo ML. Scheduling: Theory, Algorithms, and Systems. Springer; 2012.
[19] Lenstra JK, Rinnooy Kan AHG, Bruker P. Complexity of machine scheduling problems. Annals of Discrete Mathematics. 1977; 1: 343-362. DOI: http://doi.org/10.1016/S0167-5060(08)70743-X
[20] Abdul-Razaq TS, Potts CN, Van Wassenhove LN. A survey of algorithms for the single machine total weighted tardiness scheduling problem. Discrete Applied Mathematics. 1990; 26(2-3): 235-253. DOI:
http://doi.org/10.1016/0166-218X(90)90103-J
[21] Sen T, Sulek JM, Dileepan P. Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey. International Journal of Production Economics. 2003; 83(1): 1-12. DOI:
http://doi.org/10.1016/S0925-5273(02)00265-7
[22] Cheng TCE, Ng CT, Yuan JJ, Liu ZH. Single machine scheduling to minimize total weighted tardiness. European Journal of Operational Research. 2005; 165(2): 423-443. DOI: http://doi.org/10.1016/j.ejor.2004.04.013
[23] Baker KR, Trietsch D. Principles of Sequencing and Scheduling. Wiley; 2009.
[24] Kaminsky P, Hochbaum D. Due date quotation models and algorithms. In: Leung JYT. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis. Chapman & Hall/CRC; 2004. DOI: http://doi.org/10.1201/9780203489802