Stock Rationing in a Make-to-Stock Production System with Two Demand Classes and Service Level Constraint

Topics: Inventory, Optimization, Inventory control problem Pages: 11 (3759 words) Published: June 24, 2013
Stock Rationing in a Make-to-Stock Production System with Two Demand Classes and Service Level Constraint

This paper studies the stock rationing problem of a single-item make-to-stock production system with two demand classes and lost sale. There are service level requirements for both demand classes. Demands follow Poisson distributions, and production time is exponentially distributed. We derive the condition of the existence of a feasible rationing policy of the problem first. Then the optimality of rationing policy is shown. Numerical studies are used to compare rationing policy and FCFS policy, and also show how the service level constraint affects the efficiency of the rationing policy. [pic]

1. Introduction
The practice of stock rationing means that some time low priority demands are denied and inventory is held in anticipation of future high priority demand. This policy is widely applied in today’s business world. One example is the inventory control problem of common component in assemble-to-order system. Different end-products that share the same component may contribute different profit margins. The problem seeks the optimal ordering and allocation policies for the common component. Another example is the common scenario where several customers have demands of the same product. The demands from different customers may have different prices, or different service requirements over this product. In the paper, we study the stock rationing problem of a single-item make-to-stock production system with two demand classes. Demand not satisfied immediately from inventory is lost. There are service level requirements for both demand classes. Topkis (1968) is one of the first that study the stock allocation problem. He formulates an uncapacitated, discrete time, single-item inventory system with multiple demand classes to a dynamic inventory model. Topkis shows that a base stock policy is optimal for ordering. By splitting the review period into finite subintervals, he proves that the optimal allocation policy has rationing levels for each demand class. Ha (1997a) studies the rationing policy of a single-item, make-to-stock production system with several demand classes and lost sales. The system is modeled as an M/M/1 queue. Ha characterizes the optimal policy to a sequence of monotone stock rationing levels. In a later paper, Ha (1997b) considers the same rationing problem with two demand classes and a backorder setting. He shows that a base-stock type production policy is optimal, and the optimal allocation policy has a single monotone switching curve structure. Vericourt et al. (2002) completely generalize the characteristics of the two demand classes problem of Ha (1997b), and extend it to multiple-demand classes. They solve the stock allocation problem through dynamic programming, and characterize the optimal policy as a multiple threshold policy. Deshpande et al. (2003) study a periodical review inventory system with two demand classes. They focus on the (Q, r, K) policy, and show an efficient algorithm for computing stock control and rationing parameters. However, none of these studies consider the service level requirement of the demand. Nahmias and Demmy (1981) study the fill rates with and without rationing of a two-class uncapacitated inventory system under continuous review and periodic review policies. However, they focus on comparing the fill rate with given reordering point and rationing or not rather than optimizing the cost under the service level constraint. Cohen et al. (1988) consider a two-class demand multi-echelon inventory system with fill-rate constraint. They employ a (s, S) ordering policy and derive a simple priority allocation mechanism. The fill-rate constraint considered in their paper is the aggregate fill-rate instead of individual fill-rate. Bertsimas and Paschalidis (2001) consider a multi-class make-to-stock manufacturing system where each product class has a...

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