Optimization of Deterministic, Multiproduct Inventory Model with Joint Replenishment

A deterministic, continuous time, nonstationary, multiproduct inventory model is formulated to find the number of joint replenishments, the order quantities, and the times at which orders should be placed which minimize the total cost over a finite time horizon. Both backlogging and no backlogging are considered. Conditions are given for the determination of the optimal policy, and their necessity and sufficiency are discussed. The case in which the costs are quadratic is dealt in detail and numerical examples are given.