Single machine and group scheduling with random learning rates

This study mainly considers the scheduling problems with learning effects, where the learning rate is a random variable and obeys a uniform distribution. In the first part, we introduce a single machine model with location-based learning effects. We have given the theoretical proof of the optimal solution for the five objective functions. In the second part, we study the problem with group technology. Both intra-group and inter-group have location-based learning effects, and the learning rate of intra-group jobs follows a uniform distribution. We also give the optimal ranking method and proof for the two problems proposed

Competitive Two-Agent Scheduling with Learning Effect and Release Times on a Single Machine

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