Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times

[EN] A novel scheduling problem that results from the addition of resource-assignable setups is presented in this paper. We consider an unrelated parallel machine problem with machine and job sequence-dependent setup times. The new characteristic is that the amount of setup time does not only depend on the machine and job sequence but also on the amount of resources assigned, which can vary between a minimum and a maximum. The aim is to give solution to real problems arising in several industries where frequent setup operations in production lines have to be carried out. These operations are indeed setups whose length can be reduced or extended according to the amount of resources assigned to them. The objective function considered is a linear combination of total completion time and the total amount of resources assigned. We present a mixed integer program (MIP) model and some fast dispatching heuristics. We carry out careful and comprehensive statistical analyses to study what characteristics of the problem affect the MIP model performance. We also study the effectiveness of the different heuristics proposed. © 2011 Springer-Verlag London Limited.The authors are indebted to the referees and editor for a close examination of the paper, which has increased its quality and presentation. This work is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI. The authors should also thank the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198, and IMIDIC/2010/175.Ruiz García, R.; Andrés Romano, C. (2011). Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times. International Journal of Advanced Manufacturing Technology. 57(5):777-794. https://doi.org/10.1007/S00170-011-3318-2S777794575Allahverdi A, Gupta JND, Aldowaisan T (1999) A review of scheduling research involving setup considerations. OMEGA Int J Manag Sci 27(2):219–239Allahverdi A, Ng CT, Cheng TCE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187(3):985–1032Balakrishnan N, Kanet JJ, Sridharan SV (1999) Early/tardy scheduling with sequence dependent setups on uniform parallel machines. Comput Oper Res 26(2):127–141Biggs D, De Ville B, and Suen E (1991) A method of choosing multiway partitions for classification and decision trees. J Appl Stat 18(1):49–62Chen J-F (2006) Unrelated parallel machine scheduling with secondary resource constraints. Int J Adv Manuf Technol 26(3):285–292Cheng TCE, Sin CCS (1990) A state-of-the-art review of parallel machine scheduling research. Eur J Oper Res 47(3):271–292Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326Grigoriev E, Sviridenko M, Uetz M (2007) Unrelated parallel machine scheduling with resource dependent processing times. Math Program Ser A and B 110(1):209–228Guinet A (1991) Textile production systems: a succession of non-identical parallel processor shops. J Oper Res Soc 42(8):655–671Guinet A, Dussauchoy A (1993) Scheduling sequence dependent jobs on identical parallel machines to minimize completion time criteria. Int J Prod Res 31(7):1579–1594Horn WA (1973) Minimizing average flow time with parallel machines. Oper Res 21(3):846–847Kass GV (1980) An exploratory technique for investigating large quantities of categorical data. Appl Stat 29(2):119–127Kim DW, Kim KH, Jang W, Chen FF (2002) Unrelated parallel machine scheduling with setup times using simulated annealing. Robot Comput-Integr Manuf 18(3–4):223–231Lam K, Xing W (1997) New trends in parallel machine scheduling. Int J Oper Prod Manage 17(3):326–338Lee YH, Pinedo M (1997) Scheduling jobs on parallel machines with sequence dependent setup times. Eur J Oper Res 100(3):464–474Marsh JD, Montgomery DC (1973) Optimal procedures for scheduling jobs with sequence-dependent changeover times on parallel processors. AIIE Technical Papers, pp 279–286Mokotoff E (2001) Parallel machine scheduling problems: a survey. Asia-Pac J Oper Res 18(2):193–242Morgan JA, Sonquist JN (1963) Problems in the analysis of survey data and a proposal. J Am Stat Assoc 58:415–434Ng CT, Edwin Cheng TC, Janiak A, Kovalyov MY (2005) Group scheduling with controllable setup and processing times: minimizing total weighted completion time. Ann Oper Res 133:163–174Nowicki E, Zdrzalka S (1990) A survey of results for sequencing problems with controllable processing times. Discrete Appl Math 26(2–3):271–287Pinedo M (2002) Scheduling: theory, algorithms, and systems, 2nd edn. Prentice Hall, Upper SaddleRabadi G, Moraga RJ, Al-Salem A (2006) Heuristics for the unrelated parallel machine scheduling problem with setup times. J Intell Manuf 17(1):85–97Radhakrishnan S, Ventura JA (2000) Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence-dependent set-up times. Int J Prod Res 38(10):2233–2252Ruiz R, Sivrikaya Şerifoğlu F, Urlings T (2008) Modeling realistic hybrid flexible flowshop scheduling problems. Comput Oper Res 35(4):1151–1175Sivrikaya-Serifoglu F, Ulusoy G (1999) Parallel machine scheduling with earliness and tardiness penalties. Comput Oper Res 26(8):773–787Webster ST (1997) The complexity of scheduling job families about a common due date. Oper Res Lett 20(2):65–74Weng MX, Lu J, Ren H (2001) Unrelated parallel machines scheduling with setup consideration and a total weighted completion time objective. Int J Prod Econ 70(3):215–226Yang W-H, Liao C-J (1999) Survey of scheduling research involving setup times. Int J Syst Sci 30(2):143–155Zhang F, Tang GC, Chen ZL (2001) A 3/2-approximation algorithm for parallel machine scheduling with controllable processing times. Oper Res Lett 29(1):41–47Zhu Z, Heady R (2000) Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach. Comput Ind Eng 38(2):297–30

A Predictive-reactive Approach for JSP with Uncertain Processing Times

The paper is supported by the Asia-Link project funded by the European Commission (CN/ASIA-LINK/024 (109093)), the National Natural Science Foundation of China (50705076, 50705077), and the National Hi-Tech R&D Program of China (2007AA04Z187)JSP with discretely controllable processing times (JSP-DCPT) that are perturbed in a turbulent environment is formulated, based on which, a time-cost tradeoff based predictive-reactive scheduling approach is proposed for solving the problem. In the predictive scheduling process, on the basis of a proposed three-step decomposition approach for solving JSP-DCPT, a solution initialization algorithm is presented by incorporating a hybrid algorithm of tabu search and simulated annealing and a fast elitist non-dominated sorting genetic algorithm; in the reactive scheduling process, Pareto-optimal schedules are generated, among which every schedule that is not dominated by any initial schedule can be selected as the responding schedule so as to maintain optimality of the objective that is to minimize both the makespan and the cost. Experimental simulations demonstrate the effectiveness of the proposed approach

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Scheduling under Linear Constraints

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An O(nlogn) algorithm for the two-machine flow shop problem with controllable machine speeds

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