Abstract
This study focuses on identical parallel machine scheduling of jobs with deteriorating processing times and rate-modifying activities. We consider non linearly increasing processing times of jobs based on their position assignment. Rate modifying activities are also considered to recover the increase in processing times of jobs due to deterioration. We also propose heuristics algorithms that rely on ant colony optimization and simulated annealing algorithms to solve the problem with multiple RMAs in a reasonable amount of time. Finally, we show that ant colony optimization algorithm generates close optimal solutions and superior results than simulated annealing algorithm.
Highlights
IntroductionYechiali [8] introduced the concept of deteriorating jobs of which their processing time in-
Yechiali [8] introduced the concept of deteriorating jobs of which their processing time in-In the last two decades, time-dependent processing times of jobs in scheduling literature have received increasing attention
We developed an integer programming model for parallel machine scheduling with deteriorating jobs and rate modifying activities
Summary
Yechiali [8] introduced the concept of deteriorating jobs of which their processing time in-. Mosheiov and Sidney [23] developed an efficient polynomial algorithm that minimizes makespan for sequencing tasks with both learning and a RMA All these studies have considered rate modifying activities on a single machine scheduling without consideration of the deteriorating jobs. The single machine scheduling problem with deteriorating jobs and multiple RMAs is modeled under different objectives, such as minimizing makespan and total completion time [12,24,25,26] In these studies, researchers applied position dependent, non-linear function of processing times for jobs. Wang and Wei [30] showed that an identical parallel machine scheduling problem with linear deterioration and rate-modifying activities can be solvable in polynomial time even the objectives are minimization of total absolute differences in both completion and waiting times. Ijkmαq pj pji xijkm ykm Cim the position number of scheduled jobs at machines the index number of jobs the position number where an RMA is given before processing a job at the kth position the index number of machines constant deterioration rate of processing time of jobs, 0 < α ≤ 1 fixed period of time to perform an RMA the initial (base) processing time of job j at identical machines is the processing time of deteriorated job j at position i 1, if job j is assigned to the ith position after an RMA at the kth position on machine m, otherwise 0 1 if an RMA is assigned at position k on machine m completion time of the job in position i on machine m
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