INVENTORY CONTROL WITH FIXED COST AND PRICE OPTIMIZATION IN CONTINUOUS TIME

Alain Bensoussan; Sonny Skaaning; Janos Turi

doi:10.11948/2018.805

2018 Volume 8 Issue 3

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Alain Bensoussan, Sonny Skaaning, Janos Turi. INVENTORY CONTROL WITH FIXED COST AND PRICE OPTIMIZATION IN CONTINUOUS TIME[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 805-835. doi: 10.11948/2018.805

Citation:

Alain Bensoussan, Sonny Skaaning, Janos Turi. INVENTORY CONTROL WITH FIXED COST AND PRICE OPTIMIZATION IN CONTINUOUS TIME[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 805-835. doi: 10.11948/2018.805

INVENTORY CONTROL WITH FIXED COST AND PRICE OPTIMIZATION IN CONTINUOUS TIME

1 International Center for Decision and Risk Analysis Department, Jindal School of Management, University of Texas at Dallas, 800 W Campbell Rd., 75080 Richardson Texas, USA;
2 Comerica Bank, 1717 Main Street, 75201 Dallas Texas, USA;
3 Department of Mathematical Sciences, Natural Sciences & Mathematics, University of Texas at Dallas, 800 W Campbell Rd., 75080 Richardson Texas, USA

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Abstract

Abstract

We continue to study the problem of inventory control, with simultaneous pricing optimization in continuous time. In our previous paper[8], we considered the case without set up cost, and established the optimality of the base stock-list price (BSLP) policy. In this paper we consider the situation of fixed price. We prove that the discrete time optimal strategy (see[11]), i.e., the (s,S,p) policy can be extended to the continuous time case using the framework of quasi-variational inequalities (QVIs) involving the value function. In the process we show that an associated second order, nonlinear two-point boundary value problem for the value function has a unique solution yielding the triplet (s,S,p). For application purposes the explicit knowledge of this solution is needed to specify the optimal inventory and pricing strategy. Selecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.
- (s,S,p))policy /
- stochastic inventory control /
- quasi-variational inequalities /
- stochastic dynamic programming
MSC: 65L10;90B05;93E20

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References

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