Exact and metaheuristic approaches for unrelated parallel machine scheduling

Abstract

In this paper, we study an important real-life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence-dependent setup times, due dates, and machine eligibility constraints. The objective is to minimise total tardiness and makespan. We adapt and extend a mathematical model to find optimal solutions for small instances. Additionally, we propose several variants of simulated annealing to solve very large-scale instances as they appear in practice. We utilise several different search neighbourhoods and additionally investigate the use of innovative heuristic move selection strategies. Further, we provide a set of real-life problem instances as well as a random instance generator that we use to generate a large number of test instances. We perform a thorough evaluation of the proposed techniques and analyse their performance. We also apply our metaheuristics to approach a similar problem from the literature. Experimental results show that our methods are able to improve the results produced with state-of-the-art approaches for a large number of instances.

Problems and Solution Methods of Machine Scheduling in Semiconductor Manufacturing Operations: A Survey

“…A two-phase MILP model and a hybrid TS algorithm were applied, in which experiments showed the latter performs better on solution quality and computational time. Moser et al studied R m s lk , M j Lex ∑ T j , C max [87]. They modelled the problem as a MILP and proposed several variants of SA with different neighbourhood search procedures.…”

Scheduling a Real-World Photolithography Area With Constraint Programming

“…Changing a reticle or pod increases the setup time. (3) There is interest to optimize both the throughput and the due date satisfaction, which are two conflicting objectives.…”

“…Thus, we set the scope of our work to only solving the first sub-decision by ensuring that a suitable reticle and pod are available for each job. The resulting problem is an unrelated parallel machine scheduling problem (see [3]) with sequence-and machine-dependent setup times, machine eligibility constraints, auxiliary resources and transfer times for auxiliary resources. Setup times occur between subsequent jobs on the same machine, and transfer times occur when an auxiliary resource has to be transferred from one machine to another.…”