The coupled task scheduling problem aims to schedule a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. We study the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NPhard. We obtain competitive lower bounds for the problem through different procedures, including solving 0-1 knapsack problems. We obtain an upper bound by applying a heuristic algorithm. We then propose a binary search heuristic algorithm for the coupled task scheduling problem. We perform extensive computational experiments and show that the proposed method is able to obtain quality solutions. The results also indicate that the proposed solution method outperforms the standard exact solver Gurobi.

The coupled task scheduling problem concerns scheduling a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. While research on the problem dates back to the 1980s, interests in the computational complexity of variants of the problem and solution methodologies have been evolving in the past few years. This motivates us to present an up-to-date and comprehensive literature review on the topic. Aiming to provide a complete road map for future research on the coupled task scheduling problem, we discuss all the relevant studies and potential research opportunities. In addition, we propose several sets of benchmark instances for the problem in various settings and provide a detailed evaluation of all the available models with a view to facilitating future research on the solution methods.

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This study investigates the simultaneous scheduling of production and planning of maintenance activities in the flow shop scheduling environment. The problem is considered in a bi-objective form, minimizing the makespan as the production scheduling criterion and minimizing the system unavailability as the maintenance planning criterion. We propose the coordinative production and maintenance scheduling model in which the time interval between consecutive maintenance activities as well as the number of maintenance activities on each machine are assumed to be non-fixed. The coordinative model aims to find the best permutation of jobs as the production problem and to assign the maintenance activities into the schedule as the maintenance problem, simultaneously. Moreover, a special setting called single server maintenance is introduced and discussed. A biobjective ant colony system algorithm is presented to solve the problem in focus, introducing some novel ideas. CDS and NEH heuristics are applied to define the heuristic information part of the proposed algorithm. Some experiments are carried out to select the appropriate heuristic method between CDS and NEH. Moreover, some experiments are performed using the well-known Taillard benchmark, comparing the performance of the proposed algorithm with another ant colony optimization algorithm. Computational experiments indicate the effectiveness of the proposed algorithm.