Single-machine Scheduling with an Actual Time-dependent Learning Consideration

This paper deals with single-machine scheduling problems with an actual time-dependent learning consideration. First, we provide a mathematical description of learning effects in scheduling environment. Then we introduce an actual time-dependent learning model, in which the learning effect is defined a function of the ratio of sum of actual processing times of the jobs previously scheduled to total normal processing time of all jobs. We incorporate it into single-machine scheduling problems and show by examples that the optimal schedule for the classical version of the problem is not optimal in the presence of this new actual time-dependent learning effect for the following objective functions: the makespan, the sum of kth power of the completion times, the total weighted completion times, the maximum lateness and the number of tardy jobs. But for some special cases, we show that the shortest processing time first (SPT) rule, the weighted shortest processing time first (WSPT) rule, the earliest due date (EDD) rule and Moore’s Algorithm can also construct an optimal schedule for the problem of minimizing these objective functions, respectively. We also use these rules as heuristics for the general cases and analyze their worst-case error bounds.