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The generalized assignment problem with fixed processing times and uniform processing costs to minimize total cost

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  • Li, Weidong
  • Ou, Jinwen

Abstract

The generalized assignment problem (GAP) is a foundational problem in operations research, but its progress is quite limited. In this paper we study an important special case of the GAP with fixed processing times and uniform processing costs, where the upper bound of the makespan is given, and the objective to minimize the total processing cost. We prove a critical technical lemma, which enables us to develop an approximation algorithm with an improved performance ratio of 1+(γ−1)ϵ, where ϵ∈(0,13] can be any small constant and γ is the maximum to the minimum processing cost per unit time on a machine, improving on the existing performance ratio of 2+γ3 in the literature. For the general problem when γ is arbitrarily, we show that it is NP-hard to approximate within a constant performance ratio. For the special case when γ is a constant, we present an efficient PTAS (polynomial time approximation scheme) by applying the technical lemma. Our techniques and results bring new insights into the GAP research.

Suggested Citation

  • Li, Weidong & Ou, Jinwen, 2025. "The generalized assignment problem with fixed processing times and uniform processing costs to minimize total cost," European Journal of Operational Research, Elsevier, vol. 327(2), pages 420-431.
    • Handle: RePEc:eee:ejores:v:327:y:2025:i:2:p:420-431
    DOI: 10.1016/j.ejor.2025.05.031
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