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An adaptive stochastic knapsack problem
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DOI：10.1016/j.ejor.2014.06.027.png)
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Abstract
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We consider a stochastic knapsack problem in which the event of overflow results in the problem ending with zero return. We assume that there are n types of items available where each type has infinite supply. An item has an exponentially distributed random weight with a known mean depending on its type and the item's value is proportional to its weight with a given factor depending on the item's type. We have to make a decision on each stage whether to stop, or continue to put an item of a selected type in the knapsack. An item's weight is learned when placed to the knapsack. The objective of this problem is to find a policy that maximizes the expected total values. Using the framework of dynamic programming, the optimal policy is found when n = 2 and a heuristic policy is suggested for n > 2. (C) 2014 Elsevier B.V. All rights reserved.
Keywords:
Decision process
Dynamic programming
Stochastic knapsack
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