Single-machine scheduling with past-sequence-dependent delivery times and learning effect

In this study we consider single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a learning effect. The objectives are to minimize the makespan, the total completion time, the total weighted completion time, the total waiting time, and the total weighted waiting time. We show that the makespan, the total completion time, and the total waiting time minimization problems can be optimally solved in polynomial time algorithms. For the total weighted completion time and the total weighted waiting time minimization problems, we prove that they remain polynomially solvable with certain conditions. Furthermore, we analyze the worst-case bounds for the total weighted completion time and the total weighted waiting time minimization problems and propose two heuristic algorithms to find near optimal solutions. Our numerical results indicate that the two heuristic algorithms are efficient and effective in obtaining near optimal solutions for both problems.