Synchronising Lot Sizing and Job Scheduling
Pages 647 - 654
Abstract
We deal here with the production by a subcontractor of resources that a final job scheduler will use to achieve a sequence of jobs. Both are provided with limited storage capacities and must synchronise respective production and consumption processes. The resulting scheduling problem appears, from the point of view of the resource producer, as a multi-stage Lot Sizing problem, where every stage has to be delimited by transfers, which become the core of the decision. Such a problem may typically arise in contexts when the resource is some renewable energy (hydrogen, photo-voltaic,...) required by the jobs and stored inside tanks or batteries. We first set the SLSS: Synchronised Lot Sizing/Scheduling problem in the MILP format and handle it through branch and cut. Next, we get rid of the non {0, 1} decision variables by applying Benders’ cut generation. Finally, we reformulate the SLSS problem as a path search problem set in a specific Transfer space and handle it through an adaptation of the A* algorithm.
References
[1]
Yossiri Adulyasak, Jean François Cordeau, and Raf Jans. 2015. The production routing problem: A review of formulations and solution algorithms. Computers and Operations Research 55 (2015), 141–152. https://doi.org/10.1016/j.cor.2014.01.011
[2]
Konstantin Biel and Christoph H. Glock. 2016. Systematic literature review of decision support models for energy-efficient production planning. Computers and Industrial Engineering 101 (nov 2016), 243–259. https://doi.org/10.1016/j.cie.2016.08.021
[3]
Alistair Clark, Bernardo Almada-Lobo, and Christian Almeder. 2011. Lot sizing and scheduling: Industrial extensions and research opportunities. International Journal of Production Research 49, 9 (may 2011), 2457–2461. https://doi.org/10.1080/00207543.2010.532908
[4]
Benoît Colson, Patrice Marcotte, and Gilles Savard. 2005. Bilevel programming: A survey. 4or 3, 2 (2005), 87–107. https://doi.org/10.1007/s10288-005-0071-0
[5]
A. Drexl and A. Kimms. 1997. Lot sizing and scheduling - Survey and extensions. European Journal of Operational Research 99, 2 (1997), 221–235. https://doi.org/10.1016/S0377-2217(97)00030-1
[6]
Tomislav Erdelic, Tonči Carić, and Eduardo Lalla-Ruiz. 2019. A Survey on the Electric Vehicle Routing Problem: Variants and Solution Approaches. Journal of Advanced Transportation 2019 (2019). https://doi.org/10.1155/2019/5075671
[7]
András Frank. 1980. On chain and antichain families of a partially ordered set. Journal of Combinatorial Theory. Series B 29, 2 (oct 1980), 176–184. https://doi.org/10.1016/0095-8956(80)90079-9
[8]
Guillaume Goisque and Christophe Rapine. 2017. An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels. European Journal of Operational Research 261, 3 (2017), 918–928. https://doi.org/10.1016/j.ejor.2017.02.024
[9]
Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. 1968. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics 4, 2 (1968), 100–107. https://doi.org/10.1109/TSSC.1968.300136
[10]
Y. F. Hung and K. L. Chien. 2000. A multi-class multi-level capacitated lot sizing model. Journal of the Operational Research Society 51, 11 (2000), 1309–1318. https://doi.org/10.1057/palgrave.jors.2601026
[11]
Sandy Irani and Kirk R. Pruhs. 2005. Algorithmic problems in power management. ACM SIGACT News 36, 2 (jun 2005), 63–76. https://doi.org/10.1145/1067309.1067324
[12]
Philip Kaminsky and David Simchi-Levi. 2003. Production and distribution lot sizing in a two stage supply Chain. IIE Transactions (Institute of Industrial Engineers) 35, 11 (2003), 1065–1075. https://doi.org/10.1080/07408170304401
[13]
Hans Kellerer, Ulrich Pferschy, and David Pisinger. 2004. Multidimensional Knapsack Problems. Knapsack Problems (2004), 235–283. https://doi.org/10.1007/978-3-540-24777-7_9
[14]
Thomas Kleinert, Martine Labbé, Ivana Ljubić, and Martin Schmidt. 2021. A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization. EURO Journal on Computational Optimization 9 (2021). https://doi.org/10.1016/j.ejco.2021.100007
[15]
Martine Labbé, Fränk Plein, and Martin Schmidt. 2020. Bookings in the European gas market: characterisation of feasibility and computational complexity results. Optimization and Engineering 21, 1 (mar 2020), 305–334. https://doi.org/10.1007/s11081-019-09447-0
[16]
Giusy Macrina, Luigi Di Puglia Pugliese, and Francesca Guerriero. 2020. The Green-Vehicle Routing Problem: A Survey. Modeling and Optimization in Green Logistics (2020), 1–26. https://doi.org/10.1007/978-3-030-45308-4_1
[17]
Joon Yung Moon and Jinwoo Park. 2014. Smart production scheduling with time-dependent and machine-dependent electricity cost by considering distributed energy resources and energy storage. International Journal of Production Research 52, 13 (2014), 3922–3939. https://doi.org/10.1080/00207543.2013.860251
[18]
Agnes Pechmann and Ilka Schöler. 2011. Optimizing energy costs by intelligent production scheduling. Glocalized Solutions for Sustainability in Manufacturing - Proceedings of the 18th CIRP International Conference on Life Cycle Engineering (2011), 293–298. https://doi.org/10.1007/978-3-642-19692-8_51
[19]
F. Zeynep Sargut and H. Edwin Romeijn. 2007. Capacitated production and subcontracting in a serial supply chain. IIE Transactions (Institute of Industrial Engineers) 39, 11 (nov 2007), 1031–1043. https://doi.org/10.1080/07408170601091899
[20]
Yang Song, Chi Zhang, and Yuguang Fang. 2008. Multiple multidimensional knapsack problem and its applications in cognitive radio networks. Proceedings - IEEE Military Communications Conference MILCOM (2008). https://doi.org/10.1109/MILCOM.2008.4753629
[21]
Franck Taillandier, Christophe Fernandez, and Amadou Ndiaye. 2017. Real Estate Property Maintenance Optimization Based on Multiobjective Multidimensional Knapsack Problem. Computer-Aided Civil and Infrastructure Engineering 32, 3 (mar 2017), 227–251. https://doi.org/10.1111/mice.12246
Index Terms
- Synchronising Lot Sizing and Job Scheduling
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December 2023
1058 pages
ISBN:9798400708916
DOI:10.1145/3628797
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Association for Computing Machinery
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Published: 07 December 2023
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SOICT 2023
SOICT 2023: The 12th International Symposium on Information and Communication Technology
December 7 - 8, 2023
Ho Chi Minh, Vietnam
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Overall Acceptance Rate 147 of 318 submissions, 46%
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