The way to gain knowledge and experience of producing a product in a firm can be seen as new solution for reducing the unit cost in scheduling problems, which is known as “learning effects.” In the scheduling of batch processing machines, it is sometimes advantageous to form a nonfull batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. However, research with learning effect and release times is relatively unexplored. Motivated by this observation, we consider a single-machine problem with learning effect and release times where the objective is to minimize the total completion times. We develop a branch-and-bound algorithm and a genetic algorithm-based heuristic for this problem. The performances of the proposed algorithms are evaluated and compared via computational experiments, which showed that our approach has superior ability in this scenario.
The learning effect has gained much attention in the scheduling research recently, where many researchers have focused their problems on only one optimization. This study further addresses the scheduling problem in which two agents compete to perform their own jobs with release times on a common single machine with learning effect. The aim is to minimize the total weighted completion time of the first agent, subject to an upper bound on the maximum lateness of the second agent. We propose a branch-and-bound approach with several useful dominance properties and an effective lower bound for searching the optimal solution and three simulated-annealing algorithms for the near-optimal solutions. The computational results show that the proposed algorithms perform effectively and efficiently.
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