Heuristic methods for the multi-product dynamic lot size problem

Many heuristics exist for the single-item dynamic lot-size problem, for example, the Silver-Meal, the part period balancing and a simple variant of the part period balancing. The worst case performances of these heuristics have been shown to be zero, 1/3 and 1/2 respectively. These heuristics can be generalized to the dynamic version of the joint replenishment problem, that is, the multi-product dynamic lot-size problem. Such a generalization of the Silver-Meal heuristic has been shown to perform well on a set of test problems. This paper generalizes the part period balancing heuristic, and a simple variant of it to the multi-product dynamic lot-size problem, and shows that the worst case performances of the generalized heuristics remain 1/3 and 1/2 respectively. An improved version of the generalized Silver-Meal heuristic is also given.