Greedy approaches for a class of nonlinear Generalized Assignment Problems

Authors:
Thomas C. Sharkey;H. Edwin Romeijn
Affiliations:
Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY 12180, United States;Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48109-2117, United States
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 7
Cited 0

Probabilistic analysis of the generalised assignment problem

Mathematical Programming: Series A and B
A class of greedy algorithms for the generalized assignment problem

Discrete Applied Mathematics
A Joint Location-Inventory Model

Transportation Science
A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem

Operations Research
Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case

Journal of Heuristics
A Heuristic Approach to the Multi-Period Single-Sourcing Problem with Production and Inventory Capacities and Perishability Constraints

INFORMS Journal on Computing
The generalized assignment problem with flexible jobs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

The traditional Generalized Assignment Problem (GAP) seeks an assignment of customers to facilities that minimizes the sum of the assignment costs while respecting the capacity of each facility. We consider a nonlinear GAP where, in addition to the assignment costs, there is a nonlinear cost function associated with each facility whose argument is a linear function of the customers assigned to the facility. We propose a class of greedy algorithms for this problem that extends a family of greedy algorithms for the GAP. The effectiveness of these algorithms is based on our analysis of the continuous relaxation of our problem. We show that there exists an optimal solution to the continuous relaxation with a small number of fractional variables and provide a set of dual multipliers associated with this solution. This set of dual multipliers is then used in the greedy algorithm. We provide conditions under which our greedy algorithm is asymptotically optimal and feasible under a stochastic model of the parameters.