The present paper extends the idea of job shop Scheduling problem with resting constraints to the train Scheduling problem with the Muslim praying considerations. For this purpose, after proposing the new mathematical model, a heuristic algorithm based on the Electromagnetism-Like algorithm (EM) which is well adjusted to Scheduling problems is employed to solve the large-size practical cases. The effectiveness of the proposed algorithm is then validated by comparing with optimum solution using small-size instances and simulated annealing algorithm, and Particle swarm Optimization (PSO) using medium and large-size instances. At the end, a practical case from Iranian railway network is studied and the results are reported. The results indicate that in the case of considering the Muslim praying constraint, the ratios of total tardiness of trains, and the total praying times are 14.5%, and 3.5%, respectively, while in the case of relaxing this constraint; the first ratio reduces to 12.3%. This result demonstrates that the proposed algorithm is able to schedule the praying times so that in many cases the trains with different directions meet each other during the praying times.

Flow shop Scheduling problem has a wide application in the manufacturing and has attracted much attention in academic fields. From other point, on time delivery of products and services is a major necessity of companies’ todays; early and tardy delivery times will result additional cost such as holding or penalty costs. In this paper, just-in-time (JIT) flow shop Scheduling problem with preemption and machine idle time assumptions is considered in which objective function is minimizing the sum of weighted earliness and tardiness. A new non-linear mathematical model is formulated for this problem and due to high complexity of the problem meta-heuristic approaches have been applied to solve the problem for finding optimal solution. The parameters of algorithms are set by Taguchi method. Each parameter is tested in three levels. By implementation of many problems with different sizes these levels are determined. Genetic algorithm, imperialist competitive algorithm and hybrid of these algorithms are applied to solve the problem and the performance of the proposed algorithms are evaluated by many test problems. The Computational results indicate the superiority of the performance of hybrid approach than GA and ICA in finding the best solution in reasonable computational time.

This paper deals with a multi-agent-based interval type-2 fuzzy (IT2F) expert system for Scheduling steel continuous casting. Continuous caster Scheduling is a complex and extensive process that needs expert staff. In this study, a distributed multi-agent-based structure is proposed as a solution. The agents used herein can cooperate with each other via various communication protocols. To facilitate such communication, an appropriate negotiation protocol (i.e., contract net protocol) is proposed. The due dates specified by expert staff are represented by IT2F membership functions (MFs). As a part of the objective functions, a simple procedure is proposed to calculate the total earliness and tardiness penalty when the due date’s MFs are IT2F. The proposed hybrid multi-agent-based system combines the multi-agent systems with type-2 fuzzy concepts which conforms to the real-world continuous casting problem.

Railway crew Scheduling problem is a substantial part of the railway transportation planning, which aims to find the optimal combination of the trip sequences (pairings), and assign them to the crew complements. In this problem, each trip must be covered by at least one pairing. The multiple-covered trips lead to impose useless transfers called “transitions”.In this study, a new mathematical model to simultaneously minimize both costs of trips and transitions is proposed. Moreover, a new mathematical model is suggested to find the optimal solution of railway crew assignment problem. This model minimizes the total cost, including cost of assigning crew complements, fixed cost of employing crew complements and penalty cost for short workloads. To evaluate the proposed models, several random examples, based on the railway network of Iran are investigated.The results demonstrated the capability of the proposed models to decrease total costs of the crew Scheduling problem.

This paper considered the cost constrained vehicle Scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a di, erent time processing cost. The goal of this problem is to , nd a feasible minimum cost schedule for vehicles. A mathematical formulation of the problem is developed and the complexity of the problem when there are more than two depots is investigated. It is proved that in this case, the problem is NP-complete. Also, it is showed that there is not any constant ratio approximation algorithm for the problem, i. e., it is in the complexity class APX.

A multi-agent single machine Scheduling problem with transportation constraints is studied. We assume that there are several independent agents placed in different geographical locations, each of them has several orders and each order includes different types of products. We use a simple and effective model to obtain maximum profit of the products. To have desired on-time deliveries, the minimization of the transportation costs and total tardiness costs are considered as objective functions. The main idea of this research is to develop a simple and integrated Scheduling and transportation model which can be applied in many factories, chain stores, and so on. In order to solve this problem, a mixed integer linear programming (MILP) model is presented. Moreover, since solving large instances of the proposed MILP model is very time-consuming, a heuristic algorithm is presented. Implementing of two approaches on a variety of datasets show that the heuristic algorithm can provide good-quality solutions in very short time.

Remarkable efforts are made to develop the job shop Scheduling problem up to now. As a novel generalization, the stage shop can be defined as an environment, in which each job is composed of some stages and each stage may include one operation or more. A stage can be defined a subset of operations of a job, such that these operations can be done in any arbitrary relative order while the stages should be processed in a predetermined order. In other words, the operations of a stage cannot be initiated until all operations of the prior stage are completed. In this paper, an innovative lower bound based on solving the preemptive open shop (using a linear programming model in polynomial time) is devised for the makespan in a stage shop problem. In addition, three metaheuristics, including firefly, harmony search and water wave optimization algorithms are applied to the problem. The results of the algorithms are compared with each other, the proposed lower bound, and a commercial solver.