A Job-Shop Scheduling Problem with Bidirectional Circular Precedence Constraints

This paper introduces a job-shop scheduling problem (JSP) with bidirectional circular precedence constraints, called BCJSP. In the problem, each job can be started from any operation and continued by its remaining operations in a circular precedence-relation chain via either a clockwise or counterclockwise direction. To solve BCJSP, this paper proposes a multilevel metaheuristic consisting of top-, middle-, and bottom-level algorithms. The top- and middle-level algorithms are population-based metaheuristics, while the bottom-level algorithm is a local search algorithm. The top-level algorithm basically controls a start operation and an operation-precedence-relation direction of each job, so that BCJSP becomes a JSP instance that is a subproblem of BCJSP. Moreover, the top-level algorithm can also be used to control input parameters of the middle-level algorithm, as an optional extra function. The middle-level algorithm controls input parameters of the bottom-level algorithm, and the bottom-level algorithm then solves the BCJSP's subproblem. The middle-level algorithm evolves the bottom-level algorithm's parameter values by using feedback from the bottom-level algorithm. Likewise, the top-level algorithm evolves the start operations, the operation-precedence-relation directions, and the middle-level algorithm's parameter values by using feedback from the middle-level algorithm. Performance of two variants of the multilevel metaheuristic (i.e., with and without the mentioned extra function) was evaluated on BCJSP instances modified from well-known JSP instances. The variant with the extra function performs significantly better in number than the other. The existing JSP-solving algorithms can also solve BCJSP; however, their results on BCJSP are clearly worse than those of the two variants of the multilevel metaheuristic.

Automated summary

This paper introduces a job-shop scheduling problem called BCJSP and proposes a multi-level metaheuristic approach to solve it. The top-, middle-, and bottom-level algorithms are utilized, with the top algorithm controlling start operations and operation-precedence-relation directions, the middle algorithm controlling input parameters, and the bottom algorithm solving the subproblem of BCJSP. Performance evaluation shows that including an extra function in the multilevel metaheuristic significantly improves results.