Stochastic binary problems with simple penalties for capacity constraints violations

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the proble...

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Vydáno v:Mathematical programming Ročník 138; číslo 1-2; s. 199 - 221
Hlavní autoři: Fortz, B., Labbé, M., Louveaux, F., Poss, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.04.2013
Springer Nature B.V
Springer Verlag
Témata:
Algorithms
Approximation
Assignment problem
Branch-and-cut algorithm
Business & economic sciences
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computation
Computer Science
Fines & penalties
Full Length Paper
Gaussian
Knapsack problem
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mixed-integer non-linear programming
Méthodes quantitatives en économie & gestion
Numerical Analysis
Operations Research
Optimization
Pseudo-polynomial algorithm
Quantitative methods in economics & management
Random variables
Sciences économiques & de gestion
Stochastic programming
Stochasticity
Theoretical
Travel
Traveling salesman problem
Violations
Pseudo-polynomial algorithm
Mixed-integer non-linear programming
90C11
90C15
Branch-and-cut algorithm
Stochastic programming
Knapsack problem
90C09
ISSN:0025-5610, 1436-4646, 1436-4646
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Shrnutí:This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly -hard in general. We provide pseudo-polynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and strictly positively distributed random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branch-and-cut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem.
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scopus-id:2-s2.0-84875435973
ISSN:0025-5610
1436-4646
1436-4646
DOI:10.1007/s10107-012-0520-4