We study the generalized assignment problem, under a probabilistic model for its cost and requirement parameters. First we address the issue of feasibility by deriving a tight condition on the probabilistic model that ensures that the corresponding problem instances are feasible with the probability one as the number of jobs goes to infinity. Then, under an additional condition on the parameters, we show that the optimal value, normalized by dividing by the number of jobs, converges almost surely to a constant, again as the number of jobs goes to infinity. Finally, we discuss various examples.
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Paper provided by Erasmus University of Rotterdam - Econometric Institute in its series Papers with number
9661/a.
Find related papers by JEL classification: C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
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Romeijn, H.E. & Romero Morales, D., 2000.
"A Greedy Heuristic for a Three-Level Multi-Period Single-Sourcing Problem,"
Research Paper
ERS-2000-04-LIS Revision_, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
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