Inventory control for a non-stationary demand perishable product: comparing policies and solution methods

This paper summarizes our findings with respect to order policies for an inventory control problem for a perishable product with a maximum fixed shelf life in a periodic review system, where chance constraints play a role. A Stochastic Programming (SP) problem is presented which models a practical production planning problem over a finite horizon. Perishability, non-stationary demand, fixed ordering cost and a service level (chance) constraint make this problem complex. Inventory control handles this type of models with so-called order policies. We compare three different policies: a) production timing is fixed in advance combined with an order up-to level, b) production timing is fixed in advance and the production quantity takes the age distribution into account and c) the decision of the order quantity depends on the age-distribution of the items in stock. Several theoretical properties for the optimal solutions of the policies are presented. In this paper, four different solution approaches from earlier studies are used to derive parameter values for the order policies. For policy a), we use MILP approximations and alternatively the so-called Smoothed Monte Carlo method with sampled demand to optimize values. For policy b), we outline a sample based approach to determine the order quantities. The flexible policy c) is derived by SDP. All policies are compared on feasibility regarding the α-service level, computation time and ease of implementation to support management in the choice for an order policy.National project TIN2015-66680-C2-2-R, in part financed by the European Regional Development Fund (ERDF)

On order policies with pre-specified order schedules for a perishable product in retail.

This paper studies a retail inventory system for a perishable product, based on a practical setting in Dutch retail. The product has a fixed shelf life of three days upon delivery at the store and product demand has a weekly pattern, which is stationary over the weeks, but varies over the days of the week. Items of varying age occur in stock. However, in retail practice, the age-distribution is often unknown, which complicates order decisions. Depending on the type of product or the size of the supermarket, replenishment cycle lengths may vary. We study a situation where a store is replenished either three or four times a week on pre-specified days. The research aim is to find practical and efficient order policies that can deal with the lack of information about the age distribution of items in stock, considering mixed LIFO and FIFO withdrawal. Reducing potential waste goes along with cost minimization, while the retailer aims at meeting a cycle service level requirement. We present four new heuristics that do not require knowledge of the inventory age-distribution. A heuristic, based on a constant order quantity for each order moment, often generates least waste and lowest costs. However, this requires a few minutes of computation time. A new base stock policy appears second best

Generating order policies by SDP: 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.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A sample-based method for perishable good inventory control with a service level constraint

This paper studies the computation of so-called order-upto 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.</p