Single Machine Scheduling with Nonlinear Processing Times and Learning Effect*

The problem of scheduling n jobs on a single machine is investigated, where the concept of deteriorating and the learning effect are considered simultaneously. In this model, the optimal schedule of the problem may be different from that of the classical version of the problem. We prove some properties of the problems for the following optimization criteria: makespan and total completion time. Based on these properties, we introduce polynomial solutions for some special problems