A Hybrid Large Neighborhood Search Method for Minimizing Makespan on Unrelated Parallel Batch Processing Machines with Incompatible Job Families

Abstract

This paper studies a scheduling problem with non-identical job sizes, arbitrary job ready times, and incompatible family constraints for unrelated parallel batch processing machines, where the batches are limited to the jobs from the same family. The scheduling objective is to minimize the maximum completion time (makespan). The problem is important and has wide applications in the semiconductor manufacturing industries. This study proposes a mixed integer programming (MIP) model, which can be efficiently and optimally solved by commercial solvers for small-scale instances. Since the problem is known to be NP-hard, a hybrid large neighborhood search (HLNS) combined with tabu strategy and local search is proposed to solve large-scale problems, and a lower bound is proposed to evaluate the effectiveness of the proposed algorithm. The proposed algorithm is evaluated on numerous compatible benchmark instances and newly generated incompatible instances. The results of computational experiments indicate that the HLNS outperforms the commercial solver and the lower bound for incompatible problems, while for compatible problems, the HLNS outperforms the existing algorithm. Meanwhile, the comparison results indicate the effectiveness of the tabu and local search strategies.

A Cooperated Imperialist Competitive Algorithm for Unrelated Parallel Batch Machine Scheduling Problem

“…2 that CICA with following combination N = 60, α = 5, Q = 6, R = 0.5, I = 6 can be obtain better results than CICA with other combinations, so above combination is adopted. [24][25][26]. The experimental results show that those setting of each comparative algorithm are still effective and comparative algorithms with those setting can produce better results than MEASL, IG and HLNS with other settings.…”

“…Jiang et al [25] presented IG algorithm for parallel BPM scheduling problem with release time, job sizes, incompatible job families. Ji et al [26] provided HLNS to solve parallel BPM scheduling problem with release time, job sizes, incompatible job families and makespan minimization.…”

“…Jiang et al [25] applied an iterated greedy (IG) algorithm for the problem of release times, job sizes, and incompatible job families. Ji et al [26] developed a hybrid large neighborhood search (HLNS) with a tabu strategy and local search to solve the problem with job sizes, ready times, and incompatible family. Ou et al [27] presented an efficient polynomial time approximation scheme with near-linear-time complexity to solve the problem with dynamic arrivals job and rejection.…”

Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

“…2 s m and s 1 represent the speed of the fastest and slowest machine, respectively, and m represents the number of machines. 3 ub represents the parametric upper bound for performance guarantee.…”

“…Therefore, the development and analysis of approximate solution methods become imperative. In recent studies, scheduling problems in parallel machine environments have been investigated across various industries, including semiconductor manufacturing [2,3], metalworking [4], textile manufacturing [5], automotive manufacturing [6,7], chemical processes [8], offshore oil and gas extraction [9], as well as manufacturing scheduling for contingent new requirements [10][11][12][13][14][15]. Additionally, scheduling challenges within service-related sectors have been studied, encompassing healthcare [7,16,17], audit [18], transport and cross-docking [19,20], hospital waste collection [21], emergency response for forest fire extinguishing [22], and drone scheduling problems [23], among others.…”