Inventory Control with Fixed Cost and Price Optimization in Continuous Time



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Wilmington Scientific Publisher


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.


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Stochastic programming, Inventory control--Stochastic, Variational inequalities (Mathematics), Pricing

National Science Foundation (1303775 and 1612880), the Research Grants Council of the Hong Kong Special Administrative Region (City U 500113 and 11303316) and Disruption Management of High Speed Rail and Metro Systems Project Number: T32-101/15R.


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