Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Algorithms of placing recovery points
Information Processing Letters
Approximation schemes for parallel machine scheduling problems with controllable processing times
Computers and Operations Research
Minimizing the total weighted flow time in a single machine with controllable processing times
Computers and Operations Research
Parallel machine selection and job scheduling to minimize machine cost and job tardiness
Computers and Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Discrete Applied Mathematics
A survey on offline scheduling with rejection
Journal of Scheduling
Computers and Industrial Engineering
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When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well-known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. We also know that scheduling decisions are quite sensitive to the processing times. Therefore, this paper considers minimizing total manufacturing cost (F"1) and total completion time (F"2) objectives simultaneously on identical parallel CNC turning machines. Since decreasing processing time of a job increases its manufacturing cost, we cannot minimize both objectives at the same time, so the problem is to generate non-dominated solutions. We consider the problem of minimizing F"1 subject to a given F"2 level and give an effective formulation for the problem. For this problem, we prove some optimality properties which facilitated designing an efficient heuristic algorithm to generate approximate non-dominated solutions. Computational results show that proposed algorithm performs almost equal with the GAMS/MINOS commercial solver although it spends much less computation time.