Iterated Greedy Algorithms for a Complex Parallel Machine Scheduling Problem

TL;DR

This paper introduces Iterated Greedy algorithms with local search techniques to effectively solve a complex parallel machine scheduling problem involving multiple constraints, outperforming existing methods on benchmark instances.

Contribution

The paper proposes novel Iterated Greedy algorithms with specific destroy and repair operators, achieving superior solutions and providing new upper bounds for complex scheduling instances.

Findings

Best algorithm variants outperform current literature in solution quality and computational time.

Two variants using greedy repair operators find over 70% of the best solutions.

The simple method with common operators performs best across multiple criteria.

Abstract

This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and operations grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by the combination of one setup-time and a sequence of operations from a unique family. Other aspects are also considered in the problem, such as release dates for operations and machines, operation's sizes, and machine's eligibility and capacity. We consider item availability to define the completion times of the operations within the batches, to minimize the total weighted completion time of jobs. We developed Iterated Greedy (IG) algorithms combining destroy and repair operators with a Random Variable Neighborhood Descent (RVND) local search procedure, using four neighborhood structures to solve the problem. The best algorithm variant outperforms the current literature methods for the problem, in terms of average deviation for the best solutions and computational times, in a known benchmark set of 72 instances. New upper bounds are also provided for some instances within this set. Besides, computational experiments are conducted to evaluate the proposed methods' performance in a more challenging set of instances introduced in this work. Two IG variants using a greedy repair operator showed superior performance with more than 70% of the best solutions found uniquely by these variants. Despite the simplicity, the method using the most common destruction and repair operators presented the best results in different evaluated criteria, highlighting its potential and applicability in solving a complex machine scheduling problem.