Scheduling with job-dependent past-sequence-dependent setup times and job-dependent position-based learning effects on a single processor

Scheduling with setup time and learning is of importance in today's manufacturing and service organisations where reliable and low cost products/services should be delivered on time. This paper addresses the problem of scheduling jobs on a single processor (or machine) where the setup times are job-dependent and past-sequence-dependent (psd), and the learning effects are job-dependent and position-based. The goal is to minimise each of the objective functions: the sum of the rho(th) (rho >= 0) powers of completion times, the maximum lateness, the maximum tardiness, the total tardiness, the total weighted completion time when the weights are non-linear functions of job positions, and the total absolute differences in waiting times. Special cases of the resulting problems are solvable polynomially. For the general cases, we introduce heuristic approaches to approximate the solutions with respect to the first four objectives, and extend the branch-and-bound (B&B) methods of Soroush (2012) to derive the optimal sequences with respect to the last two objectives. Computational results show that the proposed heuristics perform well and the solution times of B&Bs are reasonable.