Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear Programming

Abstract

The scheduling of parallel machines with and without a job-splitting property, deterministic demand, and sequence-independent setup time with the goal of minimizing makespan is examined in this work. For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random (job) sections. When a job starts to be processed on a machine, an operator has to setup the machine for an hour. By creating two Mixed Integer Linear Programming models, this work proposes a mathematical programming strategy (MILP). A MILP model takes the job-splitting property into account. Another model, however, does not include the job-splitting property. This study investigates the performance of the proposed models using Gurobi solver. These programs' numerical calculations are based on actual problems in the Indonesian city of Bandung's plastics industry. On four identical parallel injection molding machines, 318 jobs must be finished in 22 periods. The real scheduling method is contrasted with these two MILP models. The maximum workload imbalance, the maximum relative percentage of imbalance, and the makespan of these three scheduling systems are used to evaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue of scheduling identical parallel machines on injection molding machines to reduce makespan, resulting in a 36% average decrease. The MILP model's job-splitting property can reduce makespan by an additional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP without job-splitting property, and actual scheduling based on the makespan minimization, workload imbalance, and relative percentage of imbalance.