A Flexible Job Shop Scheduling Problem with Controllable Processing Times to Optimize Total Cost of Delay and Processing

In this paper, the flexible job shop scheduling problem with machine flexibility and controllable process times is studied. The main idea is that the processing times of operations may be controlled by consumptions of additional resources. The purpose of this paper to find the best trade-off between processing cost and delay cost in order to minimize the total costs. The proposed model, flexible job shop scheduling with controllable processing times (FJCPT), is formulated as an integer non-linear programming (INLP) model and then it is converted into an integer linear programming (ILP) model. Due to NP-hardness of FJCPT, conventional analytic optimization methods are not efficient. Hence, in order to solve the problem, a Scatter Search (SS), as an efficient metaheuristic method, is developed. To show the effectiveness of the proposed method, numerical experiments are conducted. The efficiency of the proposed algorithm is compared with that of a genetic algorithm (GA) available in the literature for solving FJSP problem. The results showed that the proposed SS provide better solutions than the existing GA.