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Optimal Parallel Inspection for Finding the First Nonconforming Unit in a Batch-An Information Theoretic Approach
Yale T. Herer and Tzvi Raz
Vol. 46, No. 6 (Jun., 2000), pp. 845-857
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2661489
Page Count: 13
You can always find the topics here!Topics: Heuristics, Fixed costs, Unit costs, Mathematical problems, Information theory, Minimization of cost, Variable costs, Dynamic programming, Total costs, Mathematical vectors
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We consider the case of a batch of discrete units produced by a process subject to failures under a known probability distribution function, and apply information theory to the problem of finding the first nonconforming unit in the batch at minimum cost. Two distinct but related aspects of this problem were treated: determining which units should be inspected, and determining how many units should be sent for inspection at the same time. The solution is based on the principles of inspecting the product units that maximize the reduction in the uncertainty regarding the location of the first nonconforming unit, and of minimizing the cost per unit of uncertainty reduced. These principles are formalized by means of a series of theorems leading to an easy-to-implement algorithm for managing parallel inspection. This approach is successfully compared with the optimal solution obtained with dynamic programming and with other heuristics.
Management Science © 2000 INFORMS