Efficient calculation of the makespan for job-shop systems without recirculation using max-plus algebra

Abstract

In this paper, max-plus algebraic techniques are used to develop an efficient method to calculate the makespan of a perturbed job-shop manufacturing system. The methodology assumes that the perturbations in schedule are confined to a particular sub-system which is termed the variant and the rest of the system is called the invariant . The paper further develops a very efficient algorithm that calculates the makespan, for a given schedule, of a system when consists of only a single machine. Recirculation of jobs is not allowed in the system. In other words, the arrival times of the parts for are not dependent on the departure times of these parts. The complexity of the algorithm is O(N), where N is the number of jobs. It is interesting to note that the model for the sub-system contains only two vectors and a scalar regardless of its size and complexity.