Title: Max-plus-based mathematical formulation for cyclic permutation flow-shops

Authors: A.N. Nambiar, R.P. Judd

Addresses: Department of Industrial Technology, California State University, Fresno, CA 93740, USA. ' Department of Industrial and Systems Engineering, Ohio University, Athens, OH 45701, USA

Abstract: Scheduling is a decision-making process that concerns the allocation of limited resources to a set of tasks with the view of optimising one or more objectives. In this work, we are concerned with the cyclic permutation flow-shop problem where a set of parts is repeatedly produced (cyclic) and the sequence of parts on all the machines remains the same (permutation). We develop a mathematical formulation for the above problem using max-plus algebra. We show that this formulation makes it easier to compute the period of a cyclic system and can be used to evaluate solutions in a cyclic flow-shop scheduling problem.

Keywords: flow shop scheduling; max-plus algebra; mathematical modelling; cyclic permutation flow shops.

DOI: 10.1504/IJMMNO.2011.037201

International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.1, pp.85 - 97

Published online: 30 Nov 2010 *

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