The Combination of Discrete-Event Simulation and Genetic Algorithm for Solving the Stochastic Multi-Product Inventory Optimization Problem

Ilya Jackson 1 , Jurijs Tolujevs 1  and Tobias Reggelin 2
  • 1 Transport and Telecommunication Institute (TTI), , Riga, Latvia
  • 2 Otto-von-Guericke University, Institute of Logistics and Material Handling Systems, Magdeburg, Germany

Abstract

The paper describes an eventual combination of discrete-event simulation and genetic algorithm to define the optimal inventory policy in stochastic multi-product inventory systems. The discrete-event model under consideration corresponds to the just-in-time inventory control system with a flexible reorder point. The system operates under stochastic demand and replenishment lead time. The utilized genetic algorithm is distinguished for a non-binary chromosome encoding, uniform crossover and two mutation operators. The paper contains a detailed description of the optimization technique and the numerical example of six- product inventory model. The proposed approach contributes to the field of industrial engineering by providing a simple, but still efficient way to compute nearly-optimal inventory parameters with regard to risk and reliability policy. Besides, the method may be applied in automated ordering systems.

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  • 1. Alizadeh, M., Eskandari, H., Sajadifar, S. and Geiger, C. (2011) Analysing a stochastic inventory system for deteriorating items with stochastic lead time using simulation modelling. In: Proceedings of the 2011 winter simulation conference. Winter Simulation Conference, pp. 1650-1662.

  • 2. Altiparmak, F., Gen, M., Lin, L. and Paksoy, T. (2006) A genetic algorithm approach for multi- objective optimization of supply chain networks. Computers & industrial engineering, 51(1), 196–215. DOI:10.1016/j.cie.2006.07.011

  • 3. Bijvank, M. and Vis, I.F.A. (2011) Lost-sales inventory theory: A review. European Journal of Operational Research, 215(1), 1 – 13. DOI:10.1016/j.ejor.2011.02.004

  • 4. Bookbinder, J.H. and Cakanyildirim, M. (1999) Random lead times and expedited orders in (Q, r) inventory systems. European Journal of Operational Research, 115(2), 300–313.

  • 5. Brandel, W. (2009) Free Up Cash!; Inventory optimization save working capital in tough times. Computerworld. [online] www.computerworld.com. Available at: https://www.computerworld.com/article/2549533/it-industry/free-up-cash [Accessed 9 Mar. 2018]

  • 6. Fortin, F.A., Rainville, F.M.D., Gardner, M.A., Parizeau, M. and Gagné, C. (2012) DEAP: Evolutionary algorithms made easy. Journal of Machine Learning Research, 13(Jul), 2171–2175.

  • 7. Holland, J.H. (1975) Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press.

  • 8. Hopp, W.H. and Spearman M.L. (2008) Factory Physics. Waveland Press.

  • 9. Juan, A.A., Faulin, J., Grasman, S.E., Rabe, M. and Figueria, G. (2015) A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems. Operations Research Perspective, 2, 62–72. DOI:10.1016/j.orp.2015.03.001

  • 10. Juan, A.A., Grasman, S.E., Caceres-Cruz, J. and Bektaş, T. (2014) A simheuristic algorithm for the single-period stochastic inventory-routing problem with stock-outs. Simulation Modelling Practice and Theory, 46, 40–52. DOI:10.1016/j.simpat.2013.11.008

  • 11. Kotz, S. and Van Dorp, R.J. (2004) Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications. World Scientific.

  • 12. Kouki, C., Jemai, K. and Minner, S. (2015) A Lost Sales (r,Q) Inventory Control Model for Perishables with Fixed Lifetime and Lead Time. Int. J. Production Economics, 168, 143–157.

  • 13. Luke, S. (2015) Essentials of Metaheuristics. A Set of Undergraduate Lecture Notes. Second Edition, 2.2, pp. 31-55.

  • 14. Man, K.F., Tang, K.S. and Kwong, S. (1996) Genetic algorithms: concepts and applications [in engineering design]. IEEE transactions on Industrial Electronics, 43(5), 519–534. DOI:10.1109/41.538609

  • 15. Michalewicz, Z. (1996) Evolution strategies and other methods. In: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin, Heidelberg, pp. 159-177.

  • 16. Miller, B.L. and Goldberg, D.E. (1995) Genetic algorithms, tournament selection, and the effects of noise. Complex systems, 9(3), pp. 193–212. DOI:10.1162/evco.1996.4.2.113

  • 17. Min, Z. and Lindu, Z. (2016) Arena Simulation of Multi-Level Medicine Inventory Control in Hospital Pharmacy. International Journal of Hybrid Information Technology, 9(6), pp.283-294.

  • 18. Pasandideh, S.H.R. and Niaki, S.T.A. (2008) A genetic algorithm approach to optimize a multi- products EPQ model with discrete delivery orders and constrained space. Applied Mathematics and Computation, 195(2), 506–514. DOI:10.1016/j.amc.2007.05.007

  • 19. Pidd, M. (1998) Computer simulation in management science. ISBN:0471979317.

  • 20. Scherfke, S. (2014) Discrete-event simulation with SimPy. OFFIS – Institute for Information Technologie, USA.

  • 21. Stack Exchange (2017) Why do we use binary encoding when it seems so inefficient? [online] softwareengineering.stackexchange.com. Available at: https://softwareengineering.stackexchange.com/questions/339705/why-do-we-use-binary-encoding-when-it-seems-so-inefficient/339709 [Accessed 8 Mar. 2018].

  • 22. Subramanian, D., Pekny, J.F. and Gintaras, V.R. (2000) A simulation—optimization framework for addressing combinatorial and stochastic aspects of an R&D pipeline management problem. Computers & Chemical Engineering, 24(2-7), 1005–1011.

  • 23. Sinaga, S., Pertiwi, L.S. and Ardian, T. (2016) Inventory Simulation Optimization under Non Stationary Demand. International Journal of Applied Engineering Research, 11(1), pp. 524-529.

  • 24. Williams, E.A. and Crossley, W.A. (1998) Empirically-derived population size and mutation rate guidelines for a genetic algorithm with uniform crossover. In: soft computing in engineering design and manufacturing. Springer, London, pp. 163-172.

  • 25. Yeh, W.C. and Chuang, M.C. (2011) Using multi-objective genetic algorithm for partner selection in green supply chain problems. Expert Systems with applications, 38(4), 4244–4253. DOI:10.1016/j.eswa.2010.09.091

  • 26. Zipkin, P.H. (2000) Foundations of inventory management. McGrawHill. ISBN-13:978-0256113792. Zvirgzdiņa, B. and Tolujew, J. (2016) Experience in Optimization of Discrete Rate Models Using ExtendSim Optimizer. In: 9th International Doctoral Students Workshop on Logistics, June, 2016. Magdeburg, Otto von Guericke University, pp. 95-100.

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