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A Stackelberg equilibrium for a missile procurement problem

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  • Hohzaki, Ryusuke
  • Nagashima, Shinichi

Abstract

This paper deals with a procurement problem of missiles involving the efficient assignment of the missiles to some targets. Within a fixed amount of budget, a leader purchases several types of missiles, by which he aims to damage as much value as possible a follower hides into some facilities later. The effectiveness of the missile depends on the type of missile and facility. A payoff of the game is the expected amount of destroyed value. The problem is generalized as a two-person zero-sum game of distributing discrete resources with a leader and a follower. Our problem is to derive a Stackelberg equilibrium for the game. This type of game has an abundance of applications. The problem is first formulated into an integer programming problem with a non-separable objective function of variables and it is further equivalently transformed into a maximin integer knapsack problem. We propose three exacts methods and an approximation method for an optimal solution.

Suggested Citation

  • Hohzaki, Ryusuke & Nagashima, Shinichi, 2009. "A Stackelberg equilibrium for a missile procurement problem," European Journal of Operational Research, Elsevier, vol. 193(1), pages 238-249, February.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:238-249
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    References listed on IDEAS

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    1. F. Lemus & K. H. David, 1963. "An Optimum Allocation of Different Weapons to a Target Complex," Operations Research, INFORMS, vol. 11(5), pages 787-794, October.
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