M.J.G. van Eijs

A Note on the Joint Replenishment Problem under Constant Demand

This note considers the joint replenishment inventory problem for N items under constant demand. The frequently-used cyclic strategy (T; k1, …, kN) is investigated: a family replenishment is made every T time units and item i is included in each ki th replenishment. Goyal proposed a solution to find the global optimum within the class of cyclic strategies. However, we will show that the algorithm of Goyal does not always lead to the optimal cyclic strategy. A simple correction is suggested.

Multi-item inventory systems with joint ordering and transportation decisions

Abstract In many practical situations joint determination of ordering and transportation decisions for a family of items may lead to a considerable cost saving. In this paper we consider a multi-item inventory system with a freight rate schedule that is a function of the volume shipped and the capacity of a standard container. Orders for the family of items are all triggered by a coordinated periodic ( R, S ) policy. Economies of scale exist because of the reduced freight rates when ordering a full-container load instead of a less-than-container load. A full-container load can be achieved by enlarging the initial order quantities. A heuristic is proposed to decide whether an initial order should be enlarged or not. The heuristic is based on a comparison of the expected saved shipping cost, the expected saved ordering cost and the expected extra holding cost, caused by an enlargement. Some numerical examples show that the heuristic works quite satisfactorily.

On the determination of the control parameters of the optimal can-order policy

This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.

Coordinated replenishment systems with discount opportunities

Abstract In many practical situations, coordination of replenishment orders for a family of items can lead to considerable cost savings. A well-known class of strategies for the case where cost savings are due to reduced joint ordering costs is the class of can-order strategies. However, these strategies, which are simple to implement in practice, do not take discount possibilities into account. We propose a method to incorporate discounts in the framework of can-order strategies. A continuous review multi-item inventory system is considered with independent compound Poisson demand processes for each of the individual items. Discounts are offered by the supplier as a percentage of the total dollar value whenever this value exceeds a given threshold. Starting from the can-order strategy as a basic decision rule, we develop a simple heuristic to evaluate these discount opportunities. The performance of the can-order strategy with discount evaluation is compared with that of another class of discount evaluat...