Abstract: In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.
Abstract: This paper presents optimization of makespan for ‘n’
jobs and ‘m’ machines flexible job shop scheduling problem with
sequence dependent setup time using genetic algorithm (GA)
approach. A restart scheme has also been applied to prevent the
premature convergence. Two case studies are taken into
consideration. Results are obtained by considering crossover
probability (pc = 0.85) and mutation probability (pm = 0.15). Five
simulation runs for each case study are taken and minimum value
among them is taken as optimal makespan. Results indicate that
optimal makespan can be achieved with more than one sequence of
jobs in a production order.
Abstract: This paper suggests a decision tree based approach for flexible job shop scheduling with multiple process plans, i.e. each job can be processed through alternative operations, each of which can be processed on alternative machines. The main decision variables are: (a) selecting operation/machine pair; and (b) sequencing the jobs assigned to each machine. As an extension of the priority scheduling approach that selects the best priority rule combination after many simulation runs, this study suggests a decision tree based approach in which a decision tree is used to select a priority rule combination adequate for a specific system state and hence the burdens required for developing simulation models and carrying out simulation runs can be eliminated. The decision tree based scheduling approach consists of construction and scheduling modules. In the construction module, a decision tree is constructed using a four-stage algorithm, and in the scheduling module, a priority rule combination is selected using the decision tree. To show the performance of the decision tree based approach suggested in this study, a case study was done on a flexible job shop with reconfigurable manufacturing cells and a conventional job shop, and the results are reported by comparing it with individual priority rule combinations for the objectives of minimizing total flow time and total tardiness.
Abstract: During last decades, developing multi-objective
evolutionary algorithms for optimization problems has found
considerable attention. Flexible job shop scheduling problem, as an
important scheduling optimization problem, has found this attention
too. However, most of the multi-objective algorithms that are
developed for this problem use nonprofessional approaches. In
another words, most of them combine their objectives and then solve
multi-objective problem through single objective approaches. Of
course, except some scarce researches that uses Pareto-based
algorithms. Therefore, in this paper, a new Pareto-based algorithm
called controlled elitism non-dominated sorting genetic algorithm
(CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our
considered objectives are makespan, critical machine work load, and
total work load of machines. The proposed algorithm is also
compared with one the best Pareto-based algorithms of the literature
on some multi-objective criteria, statistically.
Abstract: Scheduling for the flexible job shop is very important
in both fields of production management and combinatorial
optimization. However, it quit difficult to achieve an optimal solution
to this problem with traditional optimization approaches owing to the
high computational complexity. The combining of several
optimization criteria induces additional complexity and new
problems. In this paper, a Pareto approach to solve the multi
objective flexible job shop scheduling problems is proposed. The
objectives considered are to minimize the overall completion time
(makespan) and total weighted tardiness (TWT). An effective
simulated annealing algorithm based on the proposed approach is
presented to solve multi objective flexible job shop scheduling
problem. An external memory of non-dominated solutions is
considered to save and update the non-dominated solutions during
the solution process. Numerical examples are used to evaluate and
study the performance of the proposed algorithm. The proposed
algorithm can be applied easily in real factory conditions and for
large size problems. It should thus be useful to both practitioners and
researchers.
Abstract: Flexible Job Shop Problem (FJSP) is an extension of
classical Job Shop Problem (JSP). The FJSP extends the routing
flexibility of the JSP, i.e assigning machine to an operation. Thus it
makes it more difficult than the JSP. In this study, Cooperative Coevolutionary
Genetic Algorithm (CCGA) is presented to solve the
FJSP. Makespan (time needed to complete all jobs) is used as the
performance evaluation for CCGA. In order to test performance and
efficiency of our CCGA the benchmark problems are solved.
Computational result shows that the proposed CCGA is comparable
with other approaches.
Abstract: The performance of schedules released to a shop floor may greatly be affected by unexpected disruptions. Thus, this paper considers the flexible job shop scheduling problem when processing times of some operations are represented by a uniform distribution with given lower and upper bounds. The objective is to find a predictive schedule that can deal with this uncertainty. The paper compares two genetic approaches to obtain predictive schedule. To determine the performance of the predictive schedules obtained by both approaches, an experimental study is conducted on a number of benchmark problems.