Computationally Simple and Unified Approach to Finite- and Infinite-Horizon Clark-Scarf Inventory Model



IIE Transactions, vol. 43, pp. 207-219, January (1st Quarter/Winter) 2011


We show that an easily computed and simply structured policy for making work-order decisions is optimal in a make-to-stock multistage serial manufacturing process with the following features. Raw materials or purchased piece parts move through successive stages of manufacturing and eventually become end-items in a finished goods inventory which experiences successive demands that are independent and identically distributed random variables. The model includes convex costs of finished goods inventory, a set-up cost for purchasing, linear costs of work-in-process inventories, and backlogging of excess demand. The criteria include the expected present value of costs (in finite and infinite horizons) and long-run average cost per period. The same policy structure is optimal for both criteria. Moreover, the policy that is optimal for the finite horizon model is also optimal for the infinite horizon model.

Matthew Sobel

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Weatherhead School of Management
Case Western Reserve University

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