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A Model for Optimum Scheduling Of Non-Resumable Jobs on Parallel Production Machines with Multiple Availability Constraints

In this study, parallel machines makespan minimization problem, where the jobs are non-resumable and the machines are subject to unavailability periods of known starting times and durations, was considered. The problem was formulated as an Integer Linear Programming mathematical model. An efficient solution procedure was proposed for the problem through two algorithms. The first algorithm utilizes the Longest Processing Time dispatching rule which generates an initial solution (makespan) used to obtain an upper bound which is used to backtrack through the second algorithm. The second algorithm adopted the greedy algorithm approach to iteratively achieve an optimal solution for the scheduling problem. The developed algorithms were implemented in software using Visual Basic programming language to facilitate the solution procedure. The developed software was validated using a typical numerical example while the model was validated using two industrial problems as case studies. The makespans obtained for the first and second case studies using the developed model are respectively about 49% and 40% lower than the makespan when the jobs were carried out in the industry. This showed that, in the long run, the model would efficiently serve machine shops in machinesjobs scheduling problem.