Multi-product Inventory Model Research Articles

On optimal strategies in inventory systems with Wiener demand process

In this note continuous review multiproduct inventory models are considered. Conditions ensuring the optimality of simple policies which are closely related to Johnson's (σ, S) policies in the periodic review case are given.

Optimal policies in multiproduct inventory models

We consider a period review, dynamic multiproduct inventory model with stochastic demand, in which the cost of ordering consists of linear portions for each product as well as a nonlinear term. This nonlinear term depends for example, on the products we order. We prove the existence of an optimal policy and characterize such a policy. We show that an optimal policy reduces to the well-known (σ, S)-policy, if we spezialise the nonlinear ordering cost in a proper way. Finite horizon results are given.

On the Optimality of (σ, S) Policies

A standard periodic review, stochastic, dynamic multiproduct inventory model is considered in which the ordering cost consists of linear portions for each product and a setup cost. This setup cost is incurred if an order is placed for any number of products. There is no separate setup cost incurred for each product ordered. This basic problem has been studied by Johnson (Johnson, E. L. 1967. Optimality and computation of (σ, S) policies in the multi item-infinite horizon inventory problem. Management Sci. 13 475–491.) and Wheeler (Wheeler, A. 1968. Multiproduct inventory models with set-up. Technical report, Stanford University, Stanford.) among others. We extend their results by providing general conditions for the existence of an optimal policy and by further characterizing the optimal policy. In particular, we show that there exists an optimal (σ, S) policy. Such a policy does not order when the initial stock level is in σ and orders up to the vector level S otherwise (provided that such an order is feasible). Furthermore, the set σ is an upper layer (equivalently, an increasing set) with respect to a certain partial ordering. Such a policy reduces to an (s, S) policy in the single product case, in which case our conditions are very similar to those of Veinott (Veinott, A. F., Jr. 1966. On the optimality of (s, S) inventory policies. New conditions and a new proof. SIAM J. Appl. Math. 14 1067–1083.) and amount to a special case of the model of Schäl (Schäl, M. 1976. On the optimality of (s, S) policies in dynamic inventory models with finite horizon. SIAM J. Appl. Math. 30 518–537.). Our analysis is based in part on a generalization of quasi-convex functions (in the terminology of Porteus [Porteus, E. L. 1971. On the optimality of generalized (s, S) policies. Management Sci. 17 411–426.]). Finite and infinite horizon results are given.

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.