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Optimal ordering quantities for substitutable items under joint replenishment with cost of substitution

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  • Vinod Kumar Mishra
  • Kripa Shanker

Abstract

An inventory system of two mutually substitutable items has been studied where an item is out of stock, demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted item. The demands are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle, in order to take advantage of joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. The critical value of the substitution rate is defined to help in deciding the optimal value of decision parameters. Extensive numerical experimentation is carried out, which shows that prior knowledge of the critical value of the substitution rate helps to minimize the total inventory cost. Sensitivity analysis is carried out for the improvement in the optimal total cost with substitution as compared to the case without substitution to draw insights into the behaviour of the model.

Suggested Citation

  • Vinod Kumar Mishra & Kripa Shanker, 2017. "Optimal ordering quantities for substitutable items under joint replenishment with cost of substitution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(1), pages 77-104.
  • Handle: RePEc:wut:journl:v:1:y:2017:p:77-104:id:1219
    DOI: 10.5277/ord170105
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    References listed on IDEAS

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    1. H Gurnani & Z Drezner, 2000. "Deterministic hierarchical substitution inventory models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(1), pages 129-133, January.
    2. Ye, Taofeng, 2014. "Inventory management with simultaneously horizontal and vertical substitution," International Journal of Production Economics, Elsevier, vol. 156(C), pages 316-324.
    3. Kim, Sang-Won & Bell, Peter C., 2011. "Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution," Omega, Elsevier, vol. 39(5), pages 528-538, October.
    4. Birendra K. Mishra & Srinivasan Raghunathan, 2004. "Retailer- vs. Vendor-Managed Inventory and Brand Competition," Management Science, INFORMS, vol. 50(4), pages 445-457, April.
    5. Barry A. Pasternack & Zvi Drezner, 1991. "Optimal inventory policies for substitutable commodities with stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 221-240, April.
    6. Porras, Eric & Dekker, Rommert, 2006. "An efficient optimal solution method for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1595-1615, November.
    7. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    8. Zhao, Jing & Wei, Jie & Li, Yongjian, 2014. "Pricing decisions for substitutable products in a two-echelon supply chain with firms׳ different channel powers," International Journal of Production Economics, Elsevier, vol. 153(C), pages 243-252.
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    Cited by:

    1. Mokhtari, Hadi, 2018. "Economic order quantity for joint complementary and substitutable items," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 34-47.

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