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

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.