A Class of Greedy Algorithms for the Generalized Assignment Problem

H. Edwin Romeijn, Dolores Romero Morales

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Abstrakt

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 class of greedy algorithms for the GAP. A family of weight functions is defined to measure a pseudo-cost of assigning a job to a machine. This weight function in turn is used to measure the desirability of assigning each job to each of the machines. The greedy algorithm then schedules jobs according to a decreasing order of desirability. A relationship with the partial solution given by the LP-relaxation of the GAP is found, and we derive conditions under which the algorithm is asymptotically optimal in a probabilistic sense.
OriginalsprogEngelsk
TidsskriftDiscrete Applied Mathematics
Vol/bind103
Udgave nummer1-3
Sider (fra-til)209–235
ISSN0166-218X
DOI
StatusUdgivet - 2000
Udgivet eksterntJa

Emneord

  • Generalized Assignment Problem
  • Greedy heuristic
  • Asymptotic feasibility
  • Asymptotic optimality

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