An agent-based stochastic ruler approach for a stochastic knapsack problem with sequential competition

Authors:
Matthew R. Gibson;Jeffrey W. Ohlmann;Michael J. Fry
Affiliations:
Department of Computer Science, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA;Department of Management Sciences, University of Iowa, 108 John Pappajohn Business Building, Iowa City, IA 52242-1994, USA;Department of Quantitative Analysis and Operations Management, University of Cincinnati, 532 Carl H. Lindner Hall, Cincinnati, OH 45221-0130, USA
Venue:
Computers and Operations Research
Year:
2010

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Abstract

We examine a situation in which a decision-maker executes a sequence of resource allocation decisions over time, but the availability of the indivisible resources at future epochs is uncertain due to actions of competitors. We cast this problem as a specialized type of stochastic knapsack problem in which the uncertainty of item (resource) availability is induced by competitors concurrently filling their own respective knapsacks. Utilizing a multi-period bounded multiple-choice knapsack framework, we introduce a general discrete stochastic optimization model that allows a nonlinear objective function, cardinality constraints, and a knapsack capacity constraint. Utilizing a set of greedy selection rules and agent-based modeling to simulate the competitors' actions, we solve the problem with a stochastic ruler approach that incorporates beam search to determine item selection of the types specified by the solution representation. We illustrate the computational effectiveness of our approach on instances motivated by a sports league draft as well as generic problem instances based on the knapsack literature.