On Solving a Stochastic Programming Model for Perishable Inventory Control

Abstract

Abstract. This paper describes and analyses a Stochastic Programming (SP) model that is used for a specific inventory control problem for a perishable product. The decision maker is confronted with a non-stationary random demand for a fixed shelf life product and wants to make an ordering plan for a finite horizon that satisfies a service level constraint. In literature several approaches have been described to generate approximate solutions. The question dealt with here is whether exact approaches can be developed that generate solutions up to a guaranteed accuracy. Specifically, we look into the implications of a Stochastic Dynamic Programming (SDP) approach.

An MILP approximation for ordering perishable products with non-stationary demand and service level constraints

“…SDP does not and cannot take the difference on probability of occurrence of all inventory states into account. That is the reason that the SDP overachieves the service levels at higher total costs, as noticed in Hendrix et al (2012). The SDP generates a feasible, not necessarily optimal solution to the problem we defined.…”

“…First of all, we discuss the MILP production plan for the base case in detail and compare its results with a Stochastic Dynamic Programming (SDP) benchmark from Hendrix et al (2012) designed for the same SP model. The SDP policy is not a replenishment cycle policy with fixed order periods Y t but an order is placed given the state of the inventory levels of all ages.…”

Stochastic Dynamic Programming for Three-Echelon Inventory System of Limited Shelf Life Products

“…The inventory replenishment policy problem for products with limited life time has been modeled via the dynamic programming approach in the literature [12][13][14][15]. All the models targeted the minimization of costs taking into consideration purchasing, holding and disposal costs to achieve a specific service level [14,15].…”

“…All the models targeted the minimization of costs taking into consideration purchasing, holding and disposal costs to achieve a specific service level [14,15]. The developed models were multi-period models to benefit from the capability of dynamic programming in modeling multiple stages.…”

“…The developed models were multi-period models to benefit from the capability of dynamic programming in modeling multiple stages. Both deterministic and stochastic demands have been considered [14]. As to the lead time aspect, authors either assumed it fixed, positive, zero or very long.…”