The Item Dependent StockingCost Constraint

Abstract

We recently introduced a global StockingCost constraint to compute the total number of time-slots between the production times and the due dates in discrete lot-sizing problems. This total number of days can be converted into a stocking-cost by multiplying it by a unique per-time slot stocking cost fixed parameter. Unfortunately this constraint does not allow to accurately compute the stocking cost when the per-time slot stocking cost is item dependent. This work general- izes the StockingCost constraint allowing a per-time slot stocking cost that is potentially different for each item to produce and the capacity of production potentially different for each slot. We propose an efficient filtering algorithm in O(n log(n)) where n is the number of productions, and show its efficiency experimentally on a variant of Discrete Lot Sizing Problem.