Minimising the total completion time in a single machine scheduling problem under bimodal flexible periodic availability constraints

In many scheduling problems, machines can face availability constraints and as a result, they may stop for a while. In this paper, a novel definition for single machine scheduling problem with flexible periodic availability constraints has been provided. According to this definition, in each period, the duration of unavailability corresponding to the continuous working time of the machine changes in a discrete manner and it can adopt two different values. Therefore, such availability constraints are called bimodal availability constraints. The objective has been to minimise the total completion time. By considering the complexity issues through a mathematical model, a heuristic algorithm with the time complexity of and a branch-and-bound algorithm accompanied with several lemmas and efficient dominance rules are proposed in order to solve the problems optimally. Computational results for 1680 sample problems are employed to demonstrate that the branch-and-bound algorithm is able to solve problems up to 22 jobs and the mean average error for the heuristic algorithm is 1.05%.

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