Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds
Mathematical Programming: Series A and B
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
A note on adapting methods for continuous global optimization to the discrete case
Annals of Operations Research
A pegging algorithm for the nonlinear resource allocation problem
Computers and Operations Research
Algorithms for Separable Nonlinear Resource Allocation Problems
Operations Research
Dynamic Programming
Operations Research Letters
An approach to product variety management in the painted sheet metal industry
Computers and Industrial Engineering
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Integer programming problems with a concave cost function are often encountered in optimization models involving economics of scale. In this paper, we propose an efficient exact algorithm for solving concave knapsack problems. The algorithm consists of an iterative process between finding lower and upper bounds by linearly underestimating the objective function and performing domain cut and partition by exploring the special structure of the problem. The lower bound is improved iteratively via cutting and partitioning the domain. This iteration process converges to the optimality in a finite number of steps. Promising computational results are reported for large-scale concave knapsack problems with up to 1200 integer variables. Comparison results with other existing methods in the literature are also presented.