Abstract
We consider two single‐machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum of completion times minimization problems remains polynomially solvable under the agreeable conditions.
Highlights
IntroductionThe scheduling models routinely assume that job processing times are known and fixed throughout the period of job processing
In classical scheduling problems, the scheduling models routinely assume that job processing times are known and fixed throughout the period of job processing
We investigate the sum of completion times minimization problem under the same model as Lee and Wu 24
Summary
The scheduling models routinely assume that job processing times are known and fixed throughout the period of job processing. We consider the single-machine group scheduling problem with deterioration to minimize the sum of completion times of all jobs. For the 1/GT , pij aij bit, si θi δit/ Cij problem, the optimal schedule is obtained by sequencing the jobs in each group in nondecreasing order of ai j , that is, ai 1 ≤ ai 2 ≤ ai 3 ≤ ai 4 ≤ · · · ≤ ai ni , i 1, 2, 3, . For the 1/GT , pij aij − bit, si θi − δit/ Cij problem, the optimal schedule is obtained by sequencing the jobs in each group in nondecreasing order of basic processing time ai j , that is, ai 1 ≤ ai 2 ≤ ai 3 ≤ ai 4 ≤ · · · ≤ ai ni , i 1, 2, 3, . It is easy to show that the total time for Algorithm 3.3 is O n log n
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