Developing a new approximation algorithm with a tight worst-case for a single machine scheduling problem with tool change and special jobs

Scheduling problems with tool changes considerations have been investigated extensively in the last two decades. Tool change activities applied in flexible maintenance activities where the tools may be changed at any time of their lifespan. Also, to determining the quality of the final product, considering the quality of the tools as a production condition items is inevitable. In this paper, the classical single machine scheduling problem with tool change is examined. In this problem, two sets of jobs, namely special jobs and normal jobs are considered. Special jobs must be processed during a certain time after the tool change. This problem has been studied in the literature. Mathematical programming models used to solve scheduling problems with small size and medium size. For scheduling problems with large size, six algorithms based on Bin Packing problem presented and focused on their performance. In this paper, we present a new algorithm for solving large size scheduling problems. The computational results show that the proposed algorithm performance at the half of instance problems is better than four algorithms of literature. In addition, in the other instance it is better than all developed literature algorithms.