The job shop scheduling problem with convex costs

Abstract

The job shop scheduling literature has been dominated by a focus on regular objective functionsin particular the makespan -in its half a century long history. The last twenty years have encountered a spike of interest in other objectives, such as the total weighted tardiness, but research on non-regular objective functions has always been isolated and scattered. Motivated by this observation, we present a tabu search heuristic for a large class of job shop scheduling problems, where the objective is non-regular in general and minimizes a sum of separable convex cost functions attached to the operation start times and the differences between the start times of arbitrary pairs of operations. This problem definition generalizes a number of problems considered earlier in the literature. A particular notion of "critical paths" derived from the so-called timing problem is at the core of the proposed neighborhood definition exploited successfully in a tabu search algorithm. The computational results attest to the promise of our work.

Application of Heuristics in Logistics and Job-Shop Scheduling

“…In a job-shop scheduling problem the target is to minimize the completion of each operation within stipulated schedule. We can classify just-in-time manufacturing into two categories, one is completion of jobs within due dates and the other one is completion of operation level (Bürgy & Bülbül, 2018) within due dates. The researchers applied tabu search heuristics to minimize cost functions for operation start time and the differences between the start times of arbitrary pairs of operations.…”

Shop scheduling in manufacturing environments: a review

“…(2018), Shoval and Efatmaneshnik (2018), Wang et al. (2018b), Bürgy and Bülbül (2018), Masmoudi et al. (2019), Gong et al.…”

“…,,Afsar et al (2016),Scaria et al (2016),Asadzadeh (2016),Akram et al (2016),Kandace and Kulak (2016),Hsu et al (2016),Teschemacher and Reinhart (2016),Benttaleb et al (2016),Palacios et al (2017),Bierwirth and Kuhpfahl (2017),Kurdi (2017),Yazdani et al (2017,Bożejko et al (2017),Huang and Yu (2017),Xiong et al (2017),Wang et al (2018c,Shoval and Efatmaneshnik (2018),Wang et al (2018b),Bürgy and Bülbül (2018),Masmoudi et al (2019),Gong et al (2019), Jamili (2019), Morikawa et al (2019), Gondran et al (2019), and Luo et al (2020a). • Flexible job shop (FJ s ): The flexible job shop is a combination of the job shop and parallel machine environments.…”

Efficient Approaches for Solving a Multiobjective Energy-aware Job Shop Scheduling Problem

“…Notice that the NPE can be increased if we are able to decrease the starting time of the first operation of a machine, while maintaining all other operations intact, and also it can be decreased by delaying the starting time of some operations. As stated in [57], research on non-regular objective functions has always been isolated and scattered, compared to regular objectives, as they are more difficult to minimize.…”