A Global Constraint for Computing Exact Buffer Stock Levels in Stochastic Inventory Control

Inventory theory provides methods for managing and controlling inventories under different constraints and environments. We consider a class of production/inventory control problems that has a single product and a single stocking location, when a stochastic demand with a known non-stationary probability distribution is given. A control policy for this type of inventory system is the one where the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. Two different models have been presented so far to solve this problem to optimality: a MIP model and an efficient CP model. In both these models negative orders are not allowed, so that if the actual stock exceeds the order-up-to-level for that review, this excess stock is carried forward and not returned to the supply source. Since this event is assumed to be rare, in both the models its effect is ignored. We present a global constraint that lets us to compute exact buffer stock levels for the CP model by considering the effect that carrying excess stock has on the service level in each period of our planning horizon. An extended version of this paper hasn’t been submitted to the technical programme.