Abstract
In this article, we study a single-machine scheduling problem with simple linear deteriorating jobs, the processing times of which are an increasing function of their starting times. The objective is to minimize the total completion time. The addressed problem is first formulated as a mixed integer programming model and solved optimally by LINGO v11.0. Next, we present some important lemmas for the basis of solving the problem. Finally, an algorithm using these lemmas is developed. Thirty replications are tested for the problem. They reveal that the proposed algorithm solves the problem efficiently and effectively in obtaining the optimal solution.
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