Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

Abstract

We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm.

Optimization for Due-Window Assignment Scheduling with Position-Dependent Weights

“…e proposed model was also extended to the general position-dependent processing time, and the polynomial-time solution was provided. Further extensions are considering the above problems in the setting of m-machine flow-shop and m-identical (unrelated) parallel machines (Hsu and Liao [27]), studying the scheduling with two-agent resource-dependent release time (Liu and Duan [28]), or investigating scheduling with rate-modifying activity under deterioration effect (Xue and Zhang [29]).…”