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The job shop scheduling problem with convex costs

Reinhard Bürgy (reinhard.burgy***at***gerad.ca)
Kerem Bülbül (bulbul***at***sabanciuniv.edu)

Abstract: The job shop scheduling literature has been dominated by a focus on regular objective functions -- in 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.

Keywords: scheduling; job shop; non-regular objective; convex costs; tabu search

Category 1: Applications -- OR and Management Sciences

Category 2: Applications -- OR and Management Sciences (Scheduling )

Category 3: Combinatorial Optimization (Meta Heuristics )

Citation: Burgy, R. and Bulbul, K. (2018). The Job Shop Scheduling Problem with Convex Costs. European Journal of Operational Research, 268(1):82-100. http://dx.doi.org/10.1016/j.ejor.2018.01.027

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Entry Submitted: 06/27/2017
Entry Accepted: 06/28/2017
Entry Last Modified: 06/24/2018

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