Cost-Based Filtering for Stochastic Inventory Control

Abstract

Abstract. An interesting class of production/inventory control problems considers a single product and a single stocking location, given a stochastic demand with a known non-stationary probability distribution. 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 a cost-based filtering method. Our algorithm can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all.

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

“…We retain their model and we augment such a model with three cost-based filtering methods to enhance domain pruning. One of these techniques, based on a relaxation proposed by Tarim [18] and solved by means of dynamic programming, has been already presented in [19]. In this work we provide two additional cost-based filtering techniques and we extend the discussion on Tarim's relaxation and on the implementation of the respective cost-based filtering method.…”

Replenishment Planning for Stochastic Inventory Systems with Shortage Cost

“…Furthermore it is possible to incorporate in our CP model dedicated cost-based filtering methods [15] based on a dynamic programming relaxation [5] that is able to generate good bounds during the search. Such a technique has been already employed under a service level constraint [1] and preliminary results in this direction under a penalty cost suggest that our exact CP model, when enhanced with these dedicated filtering techniques, is able to produce an optimal solution for instances up to 50 periods and more in a few seconds.…”

“…In this paper 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 [1] for the same model, these techniques are able to improve performances of several orders of magnitude.…”

A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints

“…Tarim and Smith [30] introduced a more compact and efficient CP formulation for the same model. Dedicated cost-based filtering techniques for such a CP model were presented in [31] and [32]. This latter enhanced model proved to be able to solve real world problem instances considering up to a 50 periods planning horizon in a few seconds.…”

“…For a detailed discussion on this CP model see [31]. Each decision variableĨ t represents the expected inventory level at the end of period t. It should be noted that the expected inventory level at the beginning of such a period is simplyĨ t +d t and if a replenishment is scheduled in t this latter value denotes the order-up-to-level (S n ) in period t. Eachd t represents the expected demand in a given period t according to its probability mass function g t (d t ).…”