Single-machine scheduling with piece-rate maintenance and interval constrained position-dependent processing times

This paper investigates single-machine scheduling problems with piece-rate machine maintenance and interval constrained actual processing time. The actual processing time of a job is a general function of the normal job processing time and the position in job sequence, and it is required to restrict in given interval otherwise earliness or tardiness penalty should be paid. The maintenance duration studied in the paper is a time-dependent linear function. The objective is to find jointly the optimal frequency to perform main-tenances and the optimal job sequence to minimize the total cost, which is a linear function of the makespan, total earliness and total tardiness. There is shown that the problem can be optimally solved in O(n 4) time. There is also shown that two special cases of the problem can be optimally solved by lower order algorithms. Recent developments in the field of job scheduling have triggered into a growing interest towards learning or aging effect. In case of the learning effect, the actual processing time of a job will be shorter when it is scheduled later in a sequence. While in case of the aging effect, the actual processing time of a job will be longer when it is scheduled later in a sequence. Some papers discussed time-dependent scheduling problems. The relevant papers include Bachman et al. [1], Cheng et al. [2] and Ji and Cheng [3]. Mosheiov and Oron [4] and Hsu et al. [5] discussed position-dependent scheduling problems. For scheduling problems with position-dependent effect, the position-dependent function as specific linear or exponential function However, all these papers consider learning or aging model with specific processing time function. Only a few papers study general position-dependent processing times. Mosheiov and Sidney [21] and Wang and Wang [22] considered a scheduling problem with a general position-dependent learning function. Mosheiov [23] studied a scheduling problem with position-dependent job processing times which is not restricted to a monotone function. In addition, it is well-known that the production efficiency can be improved by performing maintenance in manufacturing processes. Some scheduling researchers considered that the machine is maintained exactly once during the planning period , and the duration of maintenance is not fixed. Some recent relevant references are: Kubzin and Strusevich [24], Mosheiov and Sidney [25], Cheng et al. [26], Mor and Mosheiov [27] and Cheng et al. [28]. Some scheduling researchers assumed that the duration of each maintenance is given. Liao and Chen [29] …