The Generalized Multiple-Choice Multi-Divisional Linear Programming Knapsack Problem

The Multiple-choice Knapsack Problem

This paper treats the multiple-choice (continuous) knapsack problem P: n mi n mi maximize L .L cijxijsubjectto(l) I I aij x ij";b,(2)0,,;xij";1,i=I,2, i=l J=l i=l J=1 ... , n, j = 1,2, .... mi and (3) at most one of x il, x i2' ... , x im. is positive for i = 1,2, ., ., n, , where n, mi are positive integers and aij' Cij' bare nonnegative real numbers. Two approximate algorithms and an exact br...

Solving multi objective linear Bilevel multi follower programming problem

APPROXIMATE ALGORITHM FOR THE MULTI-DIMENSIONAL KNAPSACK PROBLEM BY USING MULTIPLE CRITERIA DECISION MAKING

In this paper, an interesting and easy method to solve the multi-dimensional  knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA).  Finally, ite...

A Dynamic Programming Approach to the Multiple-Choice Multi-Period Knapsack Problem and the Recursive APL2 Code

The multiple-choice multi-period knapsack problem sits in the interface of multiple choice programming and knapsack problems. Previous studies of this problem had attempted to find its optimal solution through the branch-and-bound procedure using special-ordered-sets. In this paper, we propose another solution approach based on the dynamic programming to locate its optimal solution through the ...

Heuristic algorithms for the multiple-choice multidimensional knapsack problem