A multi-item, single level, joint replenishment inventory problem is considered. It consists in scheduling n items over a finite horizon of T periods. Demands are given and should be satisfied without backlogging. The objective is to minimize the sum of production and inventory holding costs over the horizon. In each period, the total production and inventory holding costs are represented by nonlinear and linear functions, respectively. An auxiliary allocation problem is studied. Some relationship to the inventory problem is given and necessary conditions for optimal schedule of n items are discussed. A Wagner–Whitin-type condition for nonlinear joint replenishment cost is formulated. An application to the dynamic lot-sizing problem is presented.
