In this paper, we address the problem of finding a permutation schedule of n jobs in an m machine flow-shop environment that minimizes the maximum completion time Cmax (Makespan) of all jobs. The jobs are available at time zero and have sequence-dependent setup times on each machine. All parameters, such as processing and setup times, are assumed to be known with certainty. This problem is clas...

this paper presents a new mathematical model for a hybrid flow shop scheduling problem with multiprocessor tasks in which sequence dependent set up times and preemption are considered. the objective is to minimize the weighted sum of makespan and maximum tardiness. three meta-heuristic methods based on genetic algorithm (ga), imperialist competitive algorithm (ica) and a hybrid approach of ga a...

This paper presents a new mathematical model for a bi-objective job shop scheduling problem with sequence-dependent setup times that minimizes the weighted mean completion time and the weighted mean tardiness time. For solving this multi-objective model, we develop a fuzzy multi-objective linear programming (FMOLP) model. In this problem, a proposed FMOLP method is applied with respect to the o...

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is Θ(log n). Moreover, we prove that the same result also holds for graphic, euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the ClarkeWright savings heuristic for the metric Traveling Salesman Problem is Θ(log n). keywor...

this paper considers identical parallel machines scheduling problem with past-sequence-dependent setup times, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of the processing times of the jobs already processed and its scheduled position on the corresponding machine. in addition, the setup time of a job on each machin...

Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time O(n2·2n) where n is the number of nodes in the graph. The branch-and-cut algorithm has been applied to solve the problem with a large number of nodes. However,...

We present a very simple family of traveling salesman instances with n cities where the nearest neighbor rule may produce a tour that is Θ(log n) times longer than an optimum solution. Our family works for the graphic, the euclidean, and the rectilinear traveling salesman problem at the same time. It improves the so far best known lower bound in the euclidean case and proves for the first time ...

We present a genetic algorithm for solving the traveling salesman problem by genetic algorithms to optimality for traveling salesman problems with up to 442 cities. Mlihlenbein et al. [MGK 88], [MK 89] have proposed a genetic algorithm for the traveling salesman problem, which generates very good but not optimal solutions for traveling salesman problems with 442 and 531 cities. We have improved...