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Hoogeveen, J.A. and van de Velde, S.L. (1995) Minimizing Total Completion Time and Maximum Cost Simultaneously Is Solvable in Polynomial Time. Operations Research Letters, 17, 205-208.
https://doi.org/10.1016/0167-6377(95)00023-D

has been cited by the following article:

• TITLE: Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

  AUTHORS: Karrar Alshaikhli, Aws Alshaikhli

  KEYWORDS: Scheduling, Single Machine, Hierarchical, Simultaneous Minimization, Algorithms, Branch and Bound, Local Search Heuristic Methods

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.2, February 29, 2024

  ABSTRACT: This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (Vmax), maximum tardy job, denoted by (Tmax), and maximum earliness (Emax). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (Vmax, Tmax, Emax) and 1//(Vmax + Tmax + Emax). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.