A neighborhood for complex job shop scheduling problems with regular objectives

Abstract

Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings.This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems.The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.Keywords job shop scheduling • general regular objective • sequence-dependent setup times • blocking job shop • job insertion • neighborhood • tabu search

The job shop scheduling problem with convex costs

“…See Bülbül and Kaminsky (2013) for a more in-depth discussion on the issue. Thus, our work joins a growing but still a small group of job shop scheduling studies with an emphasis on generality (Wennink, 1995;Gélinas and Soumis, 2005;Mati et al, 2011;Bülbül and Kaminsky, 2013;Grimes and Hebrard, 2015;Bürgy, 2017). Our numerical results on two different types of problems support our vision, and the extensive computational study on a just-in-time job shop scheduling problem with a non-linear objective in Section 5.3 is the first of its kind - Kaskavelis and Caramanis (1998) report results from just a few instances.…”

“…The underlying pillar of any local search is a neighborhood function N that associates a set of neighbor selections N (S) with each feasible selection S. Many well-known neighborhoods for job shop scheduling problems are based on swapping two critical consecutive operations on a machine. This concept was used, for example, by Balas (1969) in the classical job shop, by De Bontridder (2005) in the job shop total weighted tardiness problem, by Bürgy (2017) in a job shop problem with a general regular objective, and by Wennink (1995); Brandimarte and Maiocco (1999); Avci and Storer (2004) in job shop problems with non-regular objectives.…”

“…Tabu search is a prominent local search approach in combinatorial optimization (see e.g., Glover and Laguna, 1997;Glover, 1996). In particular, it has been successfully applied for solving various job shop scheduling problems, such as, for example, the classical job shop problem (Nowicki and Smutnicki, 1996;Peng et al, 2015), job shop problems with routing flexibility (Brandimarte, 1993;Kis, 2003), and more complex job shop scheduling problems (Hurink and Knust, 2005;Drótos et al, 2009;Bürgy, 2017). We present a simple tabu search for JS-CONV using the neighborhood developed in the previous section.…”

“…In the domain of regular scheduling objectives, the papers by Mati et al (2011) and Bürgy (2017) deserve special credit for attacking job shop scheduling problems with a general regular objective. In particular, Mati et al (2011) demonstrate that the most basic neighborhood of reversing a single arc on a critical path enhanced with a novel and fast move evaluation procedure gives rise to a local search method which performs on a par with custom-made algorithms for five common regular objectives.…”

“…In particular, Mati et al (2011) demonstrate that the most basic neighborhood of reversing a single arc on a critical path enhanced with a novel and fast move evaluation procedure gives rise to a local search method which performs on a par with custom-made algorithms for five common regular objectives. Bürgy (2017), on the other hand, addresses complex process attributes on top of a general regular objective. The author proposes a tabu search employing a neighborhood constructed by extracting a job and re-inserting it in a new position, which in some sense corresponds to generalizing the reversal of critical arcs to complex job shops.…”