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Optimal solutions to a stochastic knapsack problem with contagious distributional capacity

Author Affiliations

  • 1Department of Mathematics and statistics, University of Port Harcourt, Nigeria
  • 2Department of Mathematics and statistics, University of Port Harcourt, Nigeria

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (5), Pages 1-10, May,12 (2018)

Abstract

The stochastic knapsack problem has continued to generate interest in many areas especially in the area of resource allocation. Of the two forms of the stochastic knapsack problem, the static knapsack problem has been studied over the years by considering the distribution of one of the parameters of a knapsack such as weight, capacity, profit, etc. however, optimal solutions for parameters having contagious distributions have not been considered. This study therefore seeks to obtain optimal solutions to a stochastic knapsack problem following a contagion capacity of Poisson and Gamma distribution. The simplex method of Witchakul et al. (2007) was adopted in developing an algorithm as well as a Monte Carlo and Heuristics algorithms. The result shows optimal solutions were gotten for up to 75,000 variables and the Heuristics algorithm performed much better than the main algorithm and Monte Carlo algorithms respectively.

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