In this paper an ant colony optimization algorithm is developed to solve the permutation flow shop scheduling problem. In the permutation flow shop scheduling problem which has been vastly studied in the literature, there are a set of machines and a set of jobs. All the jobs are processed on all the machines and the sequence of jobs being processed is the same on all the machines. Here this pro...

We are interested here in new sub cases for which permutation flow shop schedules are dominant while considering the classical flow shop scheduling problem and the makespan criterion. To obtain these sub cases, we introduce conditions on the lower and upper bounds of the processing times. These conditions can be quite realistic when the corresponding line is balanced.

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probab...

Flow-shop scheduling problem (FSP) deals with the scheduling of a set of jobs that visit a set of machines in the same order. The FSP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To meet the requirements on time and to minimize the make-span performance of large permutation flow-shop scheduling problems in which there are sequence dep...

In flow shop scheduling there are m machines and n jobs, such that every job has to be processed on the machines in the fixed order 1, . . . , m. In the permutation flow shop problem, it is also required that each machine processes the set of all jobs in the same order. Formally, given n jobs along with their processing times on each machine, the goal is to compute a single permutation of the j...

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem ...