Optimal integrated policies for a single-vendor single-buyer time-varying demand model

This paper presents a procedure for finding the optimal replenishment and production schedule for a single-vendor single-buyer inventory model and where the objective is to minimize the total integrated inventory costs of the vendor and the buyer over one production schedule and a finite-planning horizon. The production rate of the vendor is assumed fixed and the demand rate of the buyer is assumed to take some general form and is a function of time. It is shown that for a fixed number of replenishment schedules, nn, the optimal times of ordering are unique and can be found as a solution of some system of nonlinear equations. These in turn give the optimal order quantities of the buyer in each period. Moreover, the optimal value function is shown to be convex in nn.