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, flexibl...

In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial...

We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job has a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. We present the first known polynomial time approximation schemes for the ...

We study the single machine scheduling problem with controllable job processing times to minimize a linear combination of the total weighted job completion time and the total weighted processing time compression. We show that this scheduling problem is a positive half-product minimization problem. Positive half-products make up an interesting subclass of half-products and are introduced in this...

In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial...

In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the problem of scheduling n jobs on a single machine with controllable processing times. Each job has a release date when it becomes available for processing, and, after completing its processing, requires an additional delivery time. Feasible sc...

Most scheduling models assume that the jobs have xed processing times. However, in real-life applications the processing time of a job often depends on the amount of resources such as facilities, manpower , funds, etc. allocated to it, and so its processing time can be reduced when additional resources are assigned to the job. A scheduling problem in which the processing times of the jobs can b...

Most of the applied and interesting problems in industry and real world are difficult to solve. These problems are often NP-hard and the problem in this paper is strongly NP-hard. Approximation and metaheuristic algorithms are used to find a solution to these problems. In this paper we have used a polynomial time approximation algorithm, this algorithm is a suboptimal approach that provably wor...