Single facility scheduling with nonlinear processing times
Computers and Industrial Engineering
Scheduling deteriorating jobs on a single processor
Operations Research
V-shaped policies for scheduling deteriorating jobs
Operations Research
Scheduling jobs under simple linear deterioration
Computers and Operations Research
Two machine open shop scheduling problem with bi-criteria
Discrete Applied Mathematics
Scheduling jobs with varying processing times
Information Processing Letters
Parallel machine scheduling with time dependent processing times
Discrete Applied Mathematics
A Greedy Approach for a Time-Dependent Scheduling Problem
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Multicriteria Optimization
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In the paper two problems of a single machine bicriterion scheduling of a set of deteriorating jobs are considered. The jobs are independent, nonpreemptable and are ready for processing at time 0. The processing time pj of each job is a linear function of the starting time Sj of the job, pj = 1 + αjSj, where Sj ≥ 0 and αj 0 for j = 0, 1,...,n.The first problem is to find a schedule which is Pareto optimal with respect to ΣCj and Cmax criteria. The second problem is to find an optimal schedule subject to the minimization of the criterion in the form of λΣCj+(1-λ) Cmax, where λ ∈ [0, 1].There are given necessary and sufficient conditions for a schedule to be Pareto optimal for the first problem. It is proved that there exists 0 0 0] the second problem is solvable in O(n log n) time. It is also proved that an optimal schedule for the second problem has a V-shape for all λ ∈ [λ1, 1], where λ0 1