Scheduling parallel CNC machines with time/cost trade-off considerations

Abstract

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. ᭧

Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

“…, n, respectively. We note that this result can be extended to the more general case of m identical parallel machines in which the sum of completion times is given by (see, e.g., [16])…”

Minimizing total tardiness and earliness problem with controllable processing times using an effective heuristic

“…Constraints (6) and (7) limit the amount of compression and expansion for each job. Constraints (8) and (9) state that only one of the variables x j and x ' j can be positive simultaneously. Constraint (10) shows non-negativity of variables as well as being binary of λ j .…”

“…For instance, Gupta et al [7] worked on hybrid flow shop environment with controllable processing time as well as assignable due dates. Also, Gurel and Akturk [8] surveyed the identical parallel CNC machines with controllable processing time which a time/cost trade-off consideration is conducted. In this study, our objective is determining a set of amount of compression/expansion of processing times as well as a sequence of jobs simultaneously, so that total earliness and tardiness penalties and compression/expansion cost of jobs are minimized.…”

Predictive Approach on Flexible Job Shop Scheduling Problem Considering Controllable Processing Times

“…Flexible job shop scheduling problem (FJSP) extends classical job shop scheduling problem by assuming that each machine is flexible and able to offer more than one particular capability [1], resulting in needs of jobs assignment considering specific variables, such as cost. When the processing times of jobs are controllable, selected processing times affect both of manufacturing cost and scheduling performance [2].…”