Comparison of just-in-time and time window delivery policies for a single-item capacitated lot sizing problem

In this article, a comparative discussion between just-in-time (JIT) and time window (TW) policies is performed for a special case of the single-item capacitated lot sizing problem (CLSP), in which two storage levels are available, including plant and customer levels. In the JIT policy, the customer demand has to be satisfied on the due date of the demand, however, in the TW policy, the shipment can be made a few days before the due date. The influence of the two policies on the total cost is studied for a structure of a single capacitated plant which replenishes a customer, both having storage spaces. Both planning problems are shown to be NP-hard using the well-known CLSP which constitutes their subpart. A mixed integer linear program and a pseudo-polynomial dynamic program are proposed for each policy. The objective of this article is first to solve the TW problem to the optimality and, second to show the gain obtained by TW policy in terms of cost reduction. For the benchmark, we used a large data set to see the influence of different parameters on the total cost.