We consider a budgeting problem where a speciied number of projects from some disjoint classes has to be selected such that the overall gain is largest possible, and such that the costs of the chosen projects do not exceed a xed upper limit. The problem has several application in government budgeting, planning, and as relaxation from other combinatorial problems. It is demonstrated that the pro...

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 ...

We consider the minimization version of the multi-dimensional knapsack problem with bounded integer variables. We propose a greedy approximation algorithm that runs in O(mn) time and has a guarantee of m + 1, where n is the number of items and m is the number of knapsack constraints. The guarantee of the algorithm can be improved in case of easy coefficients in the constraints associated with s...

This paper considers knapsack problem with fuzzy weights, says fuzzy knapsack problem (FKP). Here we introduce possibility index which gives the possibility of choosing the items with fuzzy weights for knapsack with crisp capacity. In this paper a dynamic programming technique has been introduced to optimize the utility value of objective function. An algorithm has been proposed which gives the...

We examine a situation in which a decision-maker executes a sequence of resource allocation decisions over time, but the availability of the indivisible resources at future epochs is uncertain due to actions of competitors. We cast this problem as a specialized type of stochastic knapsack problem in which the uncertainty of item (resource) availability is induced by competitors concurrently fil...