Abstract
In many real scheduling environments, a job processed later needs longer time than the same job when it starts earlier. This phenomenon is known as scheduling with deteriorating jobs to many industrial applications. In this paper, we study a scheduling problem of minimizing the total completion time on identical parallel machines where the processing time of a job is a step function of its starting time and a deteriorating date that is individual to all jobs. Firstly, a mixed integer programming model is presented for the problem. And then, a modified weight‐combination search algorithm and a variable neighborhood search are employed to yield optimal or near‐optimal schedule. To evaluate the performance of the proposed algorithms, computational experiments are performed on randomly generated test instances. Finally, computational results show that the proposed approaches obtain near‐optimal solutions in a reasonable computational time even for large‐sized problems.
Highlights
Scheduling is a form of decision making that plays a crucial role in manufacturing and service systems
Cheng and Ding 24 studied a piecewise model where the job processing time deteriorates as a step function if its starting time exceeds a given threshold, and presented NP-complete proofs for minimizing makespan, flow time, and weighted flow time in single machine scheduling
We can use the same method to determine the sequence of early jobs and tardy jobs assigned to a given machine for minimizing the total completion time
Summary
Scheduling is a form of decision making that plays a crucial role in manufacturing and service systems. There are many practical situations where the processing times of jobs are not constant but increasing overtime such that the later a job starts, the longer it takes to process The original schedule may become inapplicable under the new environment This motivates the research of the scheduling problem with piecewise-deteriorating jobs. The scheduling problem with step-deterioration jobs is NP-complete even if in single machine environment. As for such a problem over a certain size, it is handicapped to render an optimal schedule within a reasonable run time, depending on exact methods.
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