Exact and heuristic procedures for single machine scheduling with quadratic earliness and tardiness penalties

Authors:
Mariona Vilí;Jordi Pereira
Affiliations:
Escola Universitíria d'Enginyeria Tècnica Industrial de Barcelona (EUETIB), Universitat Politècnica de Catalunya, C. Comte Urgell, 187 1st. Floor, 08036 Barcelona, Spain;Escola Universitíria d'Enginyeria Tècnica Industrial de Barcelona (EUETIB), Universitat Politècnica de Catalunya, C. Comte Urgell, 187 1st. Floor, 08036 Barcelona, Spain
Venue:
Computers and Operations Research
Year:
2013

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Assignment Problems

Assignment Problems
Time-Indexed Formulations and the Total Weighted Tardiness Problem

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Abstract

The present paper studies the single machine, no-idle-time scheduling problem with a weighted quadratic earliness and tardiness objective. We investigate the relationship between this problem and the assignment problem, and we derive two lower bounds and several heuristic procedures based on this relationship. Furthermore, the applicability of the time-indexed integer programming formulation is investigated. The results of a computational experiment on a set of randomly generated instances show (1) the high-quality results of the proposed heuristics, (2) the low optimality gap of one of the proposed lower bounds and (3) the applicability of the integer programming formulation to small and medium size cases of the problem.