K.G.J. Pauls-Worm

On solving a stochastic programming model for perishable inventory control

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.

On Computing Order Quantities for Perishable Inventory Control with Non-stationary Demand

The determination of order quantities in an inventory control problem of perishable products with non-stationary demand can be formulated as a Mixed Integer Nonlinear Programming problem (MINLP). One challenge is to deal with the \(\beta \)-service level constraint in terms of the loss function. This paper studies the properties of the optimal solution and derives specific algorithms to determine optimal quantities.

SDP in Inventory Control: Non-stationary Demand and Service Level Constraints

Inventory control implies dynamic decision making. Therefore, dynamic programming seems an appropriate approach to look for order policies. For finite horizon planning, the implementation of service level constraints provides a big challenge. This paper illustrates with small instances the implementation of stochastic dynamic programming (SDP) to derive order policies in a straightforward way for systems with non-stationary demand and service level constraints. The small instances allow to perform a full enumeration of possible policies and show that the SDP derived policies are not necessarily optimal.

A Sample-Based Method for Perishable Good Inventory Control with a Service Level Constraint

This paper studies the computation of so-called order-up-to levels for a stochastic programming inventory problem of a perishable product. Finding a solution is a challenge as the problem enhances a perishable product, fixed ordering cost and non-stationary stochastic demand with a service level constraint. An earlier study [7] derived order-up-to values via an MILP approximation. We consider a computational method based on the so-called Smoothed Monte Carlo method using sampled demand to optimize values. The resulting MINLP approach uses enumeration, bounding and iterative nonlinear optimization.