Abstract
We study the problem of inventory control, with simultaneous pricing optimization in continuous time. For the classical inventory control problem in continuous time, see [ 5 ], as a recent reference. We incorporate pricing decisions together with inventory decisions. We consider the situation without fixed cost for an infinite horizon. Without pricing, under very natural assumptions, the optimal ordering policy is given by a stock, which we review briefly. With pricing, the natural generalization is the so called Base Stock list price (BSLP) term coined by E. Porteus, see [ 36 ], and was shown in discrete time by A. Federgruen and A. Herching to be the optimal strategy, see [ 14 ]. We extend the concept to continuous time which not only complicates the dynamics of the problem, which has never been considered before.
Highlights
Since without pricing a complete theory exists in discrete as well as in continuous time, it is natural to study the extension of the continuous time theory in order to incorporate pricing
Without pricing in discrete time, under very natural assumptions, the optimal ordering policy is given by a Base stock
There is a value S,such that, if the inventory x is below S, the optimal order is S − x, and if the inventory is larger than S, the optimal order is 0
Summary
Alain Bensoussan International Center for Decision and Risk Analysis Jindal School of Management, University of Texas - Dallas∗ Sonny Skaaning International Center for Decision and Risk Analysis Jindal School of Management, University of Texas - Dallas Abstract Pricing and replenishment strategies are studied separately, in general. This is done only in discrete time.
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