The linear multiple choice knapsack problem with equity constraints

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.