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

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.