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Volume 8, Number 3, 2018, Pages 805-835                                                                DOI:10.11948/2018.805
Inventory control with fixed cost and price optimization in continuous time
Alain Bensoussan,Sonny Skaaning and Janos Turi
Keywords:$(s,S,p)$ policy, stochastic inventory control, quasi-variational inequalities, stochastic dynamic programming.
      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. Se- lecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.
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