Max-plus to solve the cyclic job shop problem with time lags

Abstract

A cyclic job shop problem with minimum and maximum time lags (JSPTL) has been considered. The paper contributes to the extension of the method for job shop problem, presented in a previous work, to cyclic scheduling. A framework with predefined control flow for iterative execution of schedules dedicated to a set of machines. The proposed framework allows to set up certain operations belonging to a set of jobs into predefined set of machines. The scheduling method is based on potential inequalities and disjunctive constraints, that are formulated in the max-Plus Algebra, in terms of inequalities. The computation of the eigenvalue of the corresponding matrices provides bounds, and a feasibility test that is used in a branch and bound procedure that permits to solve the problem. Effective computations make use of the MATLAB and its Howard algorithm implementation. One can evaluate whether or not a solution exists to the problem, compute one solution, or compute the set of solutions minimizing the completion time. The method is applied to a case study from the literature, which permits to point out its advantages and drawbacks.