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The linear multiple choice knapsack problem with equity constraints

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  • George Kozanidis
  • Emanuel Melachrinoudis
  • Marius M. Solomon

Abstract

In this paper, we introduce an important variation of a well known problem, the linear multiple choice knapsack problem with equity constraints, which finds application in the allocation of funds to highway improvements. The multiple choice constraints are used to model the interactions that arise among different improvements. The equity constraints are introduced to ensure a balance on the budget amounts allocated to different sets of improvements. We present the mathematical formulation and show that this problem structure has several fundamental properties. These are used to develop an optimal two phase greedy algorithm for its solution. We report computational results which indicate that the algorithm is more efficient than a commercial linear programming package and the outperformance increases with problem size.

Suggested Citation

  • George Kozanidis & Emanuel Melachrinoudis & Marius M. Solomon, 2005. "The linear multiple choice knapsack problem with equity constraints," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 52-73.
    • Handle: RePEc:ids:ijores:v:1:y:2005:i:1/2:p:52-73
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    Citations

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    Cited by:

    1. George Kozanidis, 2009. "Solving the linear multiple choice knapsack problem with two objectives: profit and equity," Computational Optimization and Applications, Springer, vol. 43(2), pages 261-294, June.
    2. Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2017. "Price of Fairness for allocating a bounded resource," European Journal of Operational Research, Elsevier, vol. 257(3), pages 933-943.
    3. Naldi, Maurizio & Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2019. "Profit-fairness trade-off in project selection," Socio-Economic Planning Sciences, Elsevier, vol. 67(C), pages 133-146.

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