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