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A stochastic periodic review inventory model with back-order discounts and ordering cost dependent on lead time for the mixtures of distributions

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  • Hsien-Jen Lin

Abstract

A mixture inventory system analyzed in this paper explores the problem that the lead time and ordering cost reductions are inter-dependent in a periodic review inventory model with back-order price discounts for protection interval demand with the mixture of normal distributions. The objectives of this paper are twofold. First, we want to correct and improve the recently studied model by optimizing the review period, back-order price discount, target level and lead time simultaneously to achieve significant savings in the total related cost and higher service level. Second, we consider that the demands of the different customers are not identical in the protection interval to accommodate more practical features of the real inventory systems. For the proposed model, a computational algorithm with the help of the software Mathematica 7 is furnished to derive the optimal solution. Finally, we provide numerical examples to illustrate the results. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Hsien-Jen Lin, 2015. "A stochastic periodic review inventory model with back-order discounts and ordering cost dependent on lead time for the mixtures of distributions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 386-400, July.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:2:p:386-400
    DOI: 10.1007/s11750-014-0345-9
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    References listed on IDEAS

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    1. Lin, Yu-Jen, 2008. "Minimax distribution free procedure with backorder price discount," International Journal of Production Economics, Elsevier, vol. 111(1), pages 118-128, January.
    2. Hayya, Jack C. & Harrison, Terry P. & He, X. James, 2011. "The impact of stochastic lead time reduction on inventory cost under order crossover," European Journal of Operational Research, Elsevier, vol. 211(2), pages 274-281, June.
    3. M A Hoque & S K Goyal, 2004. "Some comments on ‘Inventory models with fixed and variable lead time crash costs consideration’," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 674-676, June.
    4. Hariga, Moncer & Ben-Daya, Mohamed, 1999. "Some stochastic inventory models with deterministic variable lead time," European Journal of Operational Research, Elsevier, vol. 113(1), pages 42-51, February.
    5. Lee, Wen-Chuan & Wu, Jong-Wuu & Hou, Wen-Bin, 2004. "A note on inventory model involving variable lead time with defective units for mixtures of distribution," International Journal of Production Economics, Elsevier, vol. 89(1), pages 31-44, May.
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