Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search

Abstract

We introduce a simple technique for disjunctive machine scheduling problems and show that this method can match or even outperform state of the art algorithms on a number of problem types. Our approach combines a number of generic search techniques such as restarts, adaptive heuristics and solution guided branching on a simple model based on a decomposition of disjunctive constraints and on the reification of these disjuncts. This paper describes the method and its application to variants of the job shop scheduling problem (JSP ).We show that our method can easily be adapted to handle additional side constraints and different objective functions, often outperforming the state of the art and closing a number of open problems.* Moreover, we perform in-depth analysis of the various factors that makes this approach efficient. We show that, while most of the factors give moderate benefits, the variable and value ordering components are key.

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 next three studies require a special emphasis because together with this paper they constitute the body of literature on generic job shop scheduling problem definitions, allowing for both non-regular and non-linear objectives and various processing features. In particular, Grimes and Hebrard (2015) recently considered a generic disjunctive machine scheduling problem within a constraint programming framework compatible with both regular and non-regular scheduling objectives, and problem characteristics such as maximal time lags between successive operations of the same job and sequence-dependent setup times. In Gélinas and Soumis (2005), each operation completion time is associated with a piecewise linear -and not necessarily monotone -cost function, and the overall objective is flexible enough to combine these functions in a min-max or min-sum form.…”

“…This objective function is very similar to that we address because we ask for integer start times, and our convex objective function can therefore be replaced by a convex piecewise-linear objective with integer breakpoints -see Section 3 for more details. The punch line of this discussion is that JS-CONV subsumes all job shop scheduling problem definitions pointed out up to this point -with the exception of Grimes and Hebrard (2015) and Gélinas and Soumis (2005) because these studies do not require the convexity of the objective, and Wennink (1995) who incorporates additional processing characteristics.…”

“…We are only aware of three exact methods in this domain. The recent work of Grimes and Hebrard (2015) is a pure constraint programming algorithm, which combines a number of generic search techniques. While the basic approach is generic, some problem-specific knowledge is incorporated to enhance the computational effectiveness for certain problem types.…”

“…The advantage this method enjoys is that it attains optimal solutions for instances with up to 10 machines and 500 operations of a just-in-time scheduling problem similar to that studied in Baptiste et al (2008) in one hour of computation time as long as the number of operations per job is kept small. It is also worth underlining that both Grimes and Hebrard (2015) and Gélinas and Soumis (2005) apply their solution techniques to linear problems only despite their more general modeling frameworks -see earlier in this section.…”