Single facility scheduling with nonlinear processing times
Computers and Industrial Engineering
Scheduling deteriorating jobs on a single processor
Operations Research
Scheduling jobs under simple linear deterioration
Computers and Operations Research
Parallel machine scheduling with time dependent processing times
Discrete Applied Mathematics
Approximation algorithms for scheduling
Approximation algorithms for NP-hard problems
Scheduling linearly deteriorating jobs on multiple machines
Computers and Industrial Engineering - Special issue: new advances in analysis of manufacturing systems
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
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This article considers two scheduling problems on parallel identical machines with deteriorating jobs, in which the processing time of job is proportional function of its starting times to be processed. Namely, for job j, pj = bjt, where bj 0 is its deterioration rate, t ≥ t0 0 is its starting time and t0 is a given constant. The criteria of optimality are minimising the makespan and maximising the minimum machine completion time. It has been proved that the first problem is NP-hard; we prove that the second problem is also NP-hard. For both problems heuristic algorithms are constructed and their performance is analysed.