ANALYSIS OF MIXED INTEGER PROGRAMMING FORMULATIONS FOR SINGLE MACHINE SCHEDULING PROBLEMS WITH SEQUENCE DEPENDENT SETUP TIMES AND RELEASE DATES

Thiago Henrique Nogueira Carlos Roberto Venâncio de Carvalho Martín Gómez Ravetti Maurício Cardoso de Souza About the authors

ABSTRACT

The scheduling of jobs over a single machine with sequence dependent setups is a classical problem setting that appears in many practical applications in production planning and logistics. In this work, we analyze six mixed-integer formulation paradigms for this classical context considering release dates and two objective functions: the total weighted completion time and the total weighted tardiness. For each paradigm, we present and discuss a MIP formulation, introducing in some cases new constraints to improve performance. A dominance hierarchy in terms of strength of their linear relaxations bounds is developed. We report extensive computational experiments on a variety of instances to capture several aspects of practical situations, allowing a comparison regarding size, linear relaxation and overall performance. Based on the results, discussions and recommendations are made for the considered problems.

Keywords:
Single machine scheduling; Sequence-dependent setup; Release dates

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