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Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate

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  • A. Tsoularis

Abstract

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case.

Suggested Citation

  • A. Tsoularis, 2014. "Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(1), pages 41-69.
    • Handle: RePEc:ids:ijmore:v:6:y:2014:i:1:p:41-69
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    Cited by:

    1. Ali Khaleel Dhaiban, 2022. "Two models of inventory system with stochastic demand and deteriorating items: case study of a local cheese factory," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 78-101, March.
    2. Xie, Ying & Song, Dong-Ping, 2018. "Optimal planning for container prestaging, discharging, and loading processes at seaport rail terminals with uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 119(C), pages 88-109.

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