Title: The linear multiple choice knapsack problem with equity constraints

Authors: George Kozanidis, Emanuel Melachrinoudis, Marius M. Solomon

Addresses: Production Management Laboratory, Department of Mechanical & Industrial Engineering, School of Engineering, University of Thessaly, Pedion Areos, GR 38334 Volos, Greece. ' Department of Mechanical and Industrial Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA. ' Department of Management Sciences, College of Business Administration, Northeastern University, 314 Hayden Hall, 360 Huntington Avenue, Boston, MA 02115, USA

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.

Keywords: balanced resource allocation; linear multiple choice knapsack; equity constraints; greedy algorithm; highway improvements; funds allocation; road improvements; budget allocation.

DOI: 10.1504/IJOR.2005.007433

International Journal of Operational Research, 2005 Vol.1 No.1/2, pp.52 - 73

Published online: 20 Jul 2005 *

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