Max-plus-based mathematical formulation for cyclic permutation flow-shops
by A.N. Nambiar, R.P. Judd
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 2, No. 1, 2011

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.

Online publication date: Thu, 26-Mar-2015

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