Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

Abstract

This paper1 considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, 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. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all.

Constraint programming for stochastic inventory systems under shortage cost

“…Such a technique has been already employed under a service level constraint (Tarim et al 2009b). It should be noted that due to the non-linearity of the cost function induced by the shortage cost scheme, the version of the problem we consider is significantly more complicated than the one under a service level constraint.…”

“…It should be noted that due to the non-linearity of the cost function induced by the shortage cost scheme, the version of the problem we consider is significantly more complicated than the one under a service level constraint. Nevertheless, despite the non-linearity of the cost function, we will see that the convexity of the cost function can be exploited to define a relaxation similar to the one employed in Tarim et al (2009b).…”

“…In Tarim et al (2009b), the authors adopt a relaxation proposed by Tarim (1996) for the CP model that computes (R n ,S n ) policy parameters under service level constraints. When the relaxed model is solved it provides good bounds for the original problem.…”

“…Tarim and Kingsman assume a fixed procurement cost each time a replenishment order is placed, whatever the size of the order, and a linear holding cost on any unit carried over in inventory from one period to the next. Instead of including a service level constraint-the probability that at the end of every time period the net inventory is not negative set at least to a certain value (see Bookbinder and Tan 1988;Tarim and Kingsman 2004;Tarim and Smith 2008;Tarim et al 2009b;Rossi et al 2008;Tempelmeier 2007;Pujawan and Silver 2008; for (R n ,S n ) under a service level constraint)-their model employs a shortage cost scheme. So far no exact approach exists for computing (R n ,S n ) policy parameters under a shortage cost scheme.…”

“…In their work it was shown that not only CP is able to provide a more compact formulation than the MIP one, but that it is also able to perform faster and to take advantage of dedicated pre-processing techniques that reduce the size of decision variable domains. Moreover dedicated cost-based filtering techniques were proposed in Tarim et al (2009b) for the same model, these techniques are able to improve the performance of several orders of magnitude.…”