Heuristical Solution for Scheduling Single Stage Parallel Machines Production of Calcium Silicate Masonry Units with Sequence-Dependent Changeover Times to Improve Energy Efficiency


Article Preview

Determination of optimal production schedules is a complex combinatorial task and may be dependent on various objectives. Hence, many mathematical problem formulations and solving strategies have already been proposed each considering individually constrained applications in order to minimize non-value-adding times or other cost driving factors. Nevertheless, obtaining optimal solutions is still related to extensive computational resources and time efforts.As a result, heuristical approaches or combinations of heuristics and exact algorithms are of major importance when it comes to automatically creating optimal production schedules. Considering the manufacturing of calcium silicate masonry units (CS), this paper describes an advancement for the General Lot-Sizing Problem (GLSP) in order to allow sequence-dependent changeovers as well as multiple different machines and backlogging (GLSPPLB). For solving the GLSPPLB, a heuristical algorithm consisting of neighborhood search and threshold accepting techniques was implemented. To validate the results of the heuristic and compare required computational resources to accurate mathematical solvers, a test set of a realistic scenario has been used.The developed heuristic is able to create nearly optimal production schedules and thereby minimizing the trade off between energy demand regarding idle times of production machinery and stocks. It is transferable to every discrete single stage production with similar constraints and can be used as an input for further simulations to improve energy consumption.



Edited by:

Jörg Franke, Sven Kreitlein, Gunther Reinhart, Christian Gebbe, Rolf Steinhilper and Johannes Böhner




L. Baier et al., "Heuristical Solution for Scheduling Single Stage Parallel Machines Production of Calcium Silicate Masonry Units with Sequence-Dependent Changeover Times to Improve Energy Efficiency", Applied Mechanics and Materials, Vol. 871, pp. 208-219, 2017

Online since:

October 2017




* - Corresponding Author

[1] T. Donhauser et al., Simulation-Based Optimization of the Energy Consumption in the Hardening Process for Calcium Silicate Masonry Units, in: Applied Mechanics and Materials, volume 805, (2015), pp.249-256.

DOI: https://doi.org/10.4028/www.scientific.net/amm.805.249

[2] T. Donhauser et al., Valid Methodology for Using Discrete Event Simulation to Improve the Resource Consumption for the Manufacturing of Masonry Units, in: Procedia CIRP, Research and Innovation in Manufacturing: Key Enabling Technologies for the Factories of the Future - Proceedings of the 48th CIRP Conference on Manufacturing Systems, volume 41, (2016).

DOI: https://doi.org/10.1016/j.procir.2015.12.016

[3] F. W. Harris, How Many Parts to Make at Once, in: Factory - The Magazine of Management, volume 10, no. 2, (1913), pp.135-136.

[4] K. Andler, Rationalisierung der Fabrikation und optimale Losgröße, München: Oldenbourg, (1929).

[5] M. E. Salveson, On a Quantitative Method in Production Planning and Scheduling, in: Econometrica, volume 20, no. 4, (1952), pp.554-590.

[6] C. C. Holt, F. Modigliani, H.A. Simon, A Linear Decision Rule for Production and Employment Scheduling, in: Management Science, volume 2, no. 1, (1955), pp.1-30.

DOI: https://doi.org/10.21236/ad0089515

[7] R. G. Brown, Decision Rules for Inventory Management., New York: Holt, Rinehart and Winston, (1967).

[8] H. M. Wagner, T. M. Whitin, Dynamic Version of the Economic Lot Size Model, in: Management Science, volume 5, no. 1, (1958), pp.89-96.

[9] E. A. Silver, H. C. Meal, A Heuristic for Selecting Lot Size Quantities for the Case of a Deterministic Time-Varying Demand Rate and Discrete Opportunities for Replenishment, in: Production and Inventory Management Journal, volume 14, no. 2, (1973).

[10] J. J. DeMatteis, An Economic Lot-Sizing Technique, I: The Part-Period Algorithm, in: IBM Systems Journal, volume 7, no. 1, (1968), pp.30-38.

DOI: https://doi.org/10.1147/sj.71.0030

[11] A. S. Manne, Programming of Economic Lot Sizes, in: Management Science, volume 4, no. 2, (1958), pp.115-135.

[12] P. S. Dixon, E. A. Silver, A Heuristic Solution Procedure for the Multi-Item, Single-Level, Limited Capacity, Lot-Sizing Problem, in: Journal of Operations Management, volume 2, no. 1, (1981), pp.23-39.

DOI: https://doi.org/10.1016/0272-6963(81)90033-4

[13] C. Dillenberger et al., On Solving a Large-Scale Resource Allocation Problem in Production Planning, in: Operations Research in Production Planning and Control (1993), pp.105-119.

DOI: https://doi.org/10.1007/978-3-642-78063-9_7

[14] A. R. Clark, S. J. Clark, Rolling-Horizon Lot-Sizing When Set-up Times Are SequenceDependent, in: International Journal of Production Research, volume 38, no. 10, (2000), pp.2287-2307.

DOI: https://doi.org/10.1080/00207540050028106

[15] B. Almada-lobo et al., Single Machine Multi-Product Capacitated Lot Sizing with SequenceDependent Setups, in: International Journal of Production Research, volume 45, no. 20, (2007), pp.4873-4894.

DOI: https://doi.org/10.1080/00207540601094465

[16] C. R. Glassey, Minimum Change-Over Scheduling of Several Products on One Machine, in: Operations Research, volume 16, no. 2, (1968), pp.342-352.

DOI: https://doi.org/10.1287/opre.16.2.342

[17] B. Fleischmann, The Discrete Lot-Sizing and Scheduling Problem, in: European Journal of Operational Research, volume 44, no. 3, (1990), pp.337-348.

DOI: https://doi.org/10.1016/0377-2217(90)90245-7

[18] U. S. Karmarkar, L. Schrage, The Deterministic Dynamic Product Cycling Problem, in: Operations Research, volume 33, no. 2, (1985), pp.326-345.

DOI: https://doi.org/10.1287/opre.33.2.326

[19] A. Drexl, K. Haase, Proportional Lotsizing and Scheduling, in: International Journal of Production Economics, volume 40, no. 1, (1995), pp.73-87.

DOI: https://doi.org/10.1016/0925-5273(95)00040-u

[20] B. Fleischmann, H. Meyr, The General Lotsizing and Scheduling Problem, in: OperationsResearch-Spektrum, volume 19, no. 1, (1997), pp.11-21.

DOI: https://doi.org/10.1007/bf01539800

[21] H. Meyr, B. Fleischmann, Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produktionslinien: Modelle und Methoden im Rahmen des Supply Chain Management, GablerEdition Wissenschaft Produktion und Logistik, Wiesbaden: Deutscher Universitäts-Verlag, (1999).

DOI: https://doi.org/10.1007/978-3-322-89140-2_3

[22] H. Meyr, Simultaneous Lotsizing and Scheduling on Parallel Machines, in: European Journal of Operational Research, EURO XVI: O.R. for Innovation and Quality of Life, volume 139, no. 2, (2002), pp.277-292.

DOI: https://doi.org/10.1016/s0377-2217(01)00373-3

[23] D. Quadt, H. Kuhn, Capacitated Lot-Sizing and Scheduling with Parallel Machines, BackOrders, and Setup Carry-Over, in: Naval Research Logistics, volume 56, no. 4, (2009), pp.366-384.

DOI: https://doi.org/10.1002/nav.20345