Integer and combinatorial optimization
Integer and combinatorial optimization
Solving multi-item capacitated lot-sizing problems using variable redefinition
Operations Research
Capacitated lot sizing with setup times
Management Science
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Polyhedra for lot-sizing with Wagner-Whitin costs
Mathematical Programming: Series A and B
A cutting plane approach to capacitated lot-sizing with start-up costs
Mathematical Programming: Series A and B
IBM Journal of Research and Development
Valid inequalities and separation for capacitated economic lot sizing
Operations Research Letters
Computers and Operations Research
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
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In this article we propose a new metaheuristic-based algorithm for the Integer Knapsack Problem with Setups. This problem is a generalization of the standard Integer Knapsack Problem, complicated by the presence of setup costs in the objective function as well as in the constraints. We propose a cross entropy based algorithm, where the metaheuristic scheme allows to relax the original problem to a series of well chosen standard Knapsack problems, solved through a dynamic programming algorithm. To increase the computational effectiveness of the proposed algorithm, we use a turnpike theorem, which sensibly reduces the number of iterations of the dynamic algorithm. Finally, to testify the robustness of the proposed scheme, we present extensive computational results. First, we illustrate the step-by-step behavior of the algorithm on a smaller, yet difficult, problem. Subsequently, to test the solution quality of the algorithm, we compare the results obtained on very large scale instances with the output of a branch and bound scheme. We conclude that the proposed algorithm is effective in terms of solution quality as well as computational time.