Generating Experimental Data for the Generalized Assignment Problem

H. Edwin Romeijn, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The Generalized Assignment Problem (GAP) is the problem of finding the minimal cost assignment of jobs to machines such that each job is assigned to exactly one machine, subject to capacity restrictions on the machines. We propose a new stochastic model for the GAP. A tight condition on this stochastic model under which the GAP is feasible with probability one when the number of jobs goes to infinity is derived. This new stochastic model enables us to analyze the adequacy of most of the random generators given for the GAP in the literature. We demonstrate that the random generators commonly used to test solution procedures for the GAP tend to create easier problem instances when the number of machines m increases. We describe a greedy heuristic for the GAP, and use it to illustrate the results from the paper.
Original languageEnglish
JournalOperations Research
Volume49
Issue number6
Pages (from-to)866-878
ISSN0030-364X
DOIs
Publication statusPublished - 2001
Externally publishedYes

Cite this

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title = "Generating Experimental Data for the Generalized Assignment Problem",
abstract = "The Generalized Assignment Problem (GAP) is the problem of finding the minimal cost assignment of jobs to machines such that each job is assigned to exactly one machine, subject to capacity restrictions on the machines. We propose a new stochastic model for the GAP. A tight condition on this stochastic model under which the GAP is feasible with probability one when the number of jobs goes to infinity is derived. This new stochastic model enables us to analyze the adequacy of most of the random generators given for the GAP in the literature. We demonstrate that the random generators commonly used to test solution procedures for the GAP tend to create easier problem instances when the number of machines m increases. We describe a greedy heuristic for the GAP, and use it to illustrate the results from the paper.",
keywords = "Programming, Integer: Generalized assignment problem, Statistics: Generation of random data",
author = "Romeijn, {H. Edwin} and {Romero Morales}, Dolores",
year = "2001",
doi = "10.1287/opre.49.6.866.10021",
language = "English",
volume = "49",
pages = "866--878",
journal = "Operations Research",
issn = "0030-364X",
publisher = "Institute for Operations Research and the Management Sciences",
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}

Generating Experimental Data for the Generalized Assignment Problem. / Romeijn, H. Edwin; Romero Morales, Dolores .

In: Operations Research, Vol. 49, No. 6, 2001, p. 866-878.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Generating Experimental Data for the Generalized Assignment Problem

AU - Romeijn, H. Edwin

AU - Romero Morales, Dolores

PY - 2001

Y1 - 2001

N2 - The Generalized Assignment Problem (GAP) is the problem of finding the minimal cost assignment of jobs to machines such that each job is assigned to exactly one machine, subject to capacity restrictions on the machines. We propose a new stochastic model for the GAP. A tight condition on this stochastic model under which the GAP is feasible with probability one when the number of jobs goes to infinity is derived. This new stochastic model enables us to analyze the adequacy of most of the random generators given for the GAP in the literature. We demonstrate that the random generators commonly used to test solution procedures for the GAP tend to create easier problem instances when the number of machines m increases. We describe a greedy heuristic for the GAP, and use it to illustrate the results from the paper.

AB - The Generalized Assignment Problem (GAP) is the problem of finding the minimal cost assignment of jobs to machines such that each job is assigned to exactly one machine, subject to capacity restrictions on the machines. We propose a new stochastic model for the GAP. A tight condition on this stochastic model under which the GAP is feasible with probability one when the number of jobs goes to infinity is derived. This new stochastic model enables us to analyze the adequacy of most of the random generators given for the GAP in the literature. We demonstrate that the random generators commonly used to test solution procedures for the GAP tend to create easier problem instances when the number of machines m increases. We describe a greedy heuristic for the GAP, and use it to illustrate the results from the paper.

KW - Programming

KW - Integer: Generalized assignment problem

KW - Statistics: Generation of random data

U2 - 10.1287/opre.49.6.866.10021

DO - 10.1287/opre.49.6.866.10021

M3 - Journal article

VL - 49

SP - 866

EP - 878

JO - Operations Research

JF - Operations Research

SN - 0030-364X

IS - 6

ER -