In this paper we study the scheduling of a given set of jobs on several identical parallel machines tended by a common server. Each job must be processed on one of the machines. Prior to processing, the server has to set up the relevant machine. The objective is to schedule the jobs so as to minimize the total weighted job completion times. We provide an approximation algorithm to tackle this intractable problem and analyze the worst-case performance of the algorithm for the general, as well as a special, case of the problem.

Approximation algorithm for parallel machine scheduling with a common server

This paper addresses the problem of scheduling jobs on two identical parallel machines with a single server such that the makespan is minimized. Each job can be processed by either one of the two parallel machines, but before processing, a setup operation must be done by a single server. Two mixed integer programming models for the considered scheduling problem are developed using time indexed variable and sequence indexed variable respectively. To evaluate the performance of the two models, CPLEX is used to test instances generated randomly. The results show that the sequence indexed model outperforms on the number of variables and computational time, which can be used to solve the instance of 20 jobs.

Mixed Integer Programming Models for Two Identical Parallel Machines with a Single Server

Open shop scheduling problem is a typical NP problem with wide engineering background. It is of importance with respect of theory and application. In this paper, a mixed integer programming model was established with the objective to minimize the makespan based on the characteristics of the open shop, and a evolution genetic algorithm(EGA) was proposed. The representation of chromosome used in this paper was composed of two layers: operation layer and machine layer, which can be encoded and decoded easily. In generating initial population, DS/LTRP heuristic was used in order to improve the quality of the population. And particular crossover operation was proposed, which generated multiple offspring at a time, so that the efficiency of the algorithm can be well improved. At last, the proposed algorithm was tested on taillard benchmark, and numerical example showed good result.

Research on Open Shop Scheduling Based on Genetic Algorithm

Open shop scheduling problem was studied, and a dense scheduling algorithm based on semi-matching theory was proposed. Using decomposition strategy, the scheduling problem was converted into iterations of resource assignment. Based on this, dense scheduling was constructed by the construction and optimization of primal solution. To improve computational efficiency, the semi-matching model of the resource assignment problem with the optimal function of load balancing was developed. The optimal semi-matching searching algorithm based on augmenting path was proposed. And a dense scheduling construction method with two steps was proposed, as well as initial solution optimization methods and mechanisms to eliminate interference among machines. At last, the validity of the developed scheduling algorithm was illustrated by benchmarks of Taillard.

Open Shop Dense Scheduling Algorithm Based on Semi-Matching Theory

This paper considers single-stage multi-parallel machines scheduling problems. A fuzzy scheduling model is developed with objective to minimize the makespan. In the scheduling model, the uncertainty of processing time is represented by triangular fuzzy number, and the credibility theory is used to assess fuzzy number. In the optimal scheduling searching process, we introduce matching theory to model the scheduling problem consider in this paper, and two heuristic rules are used to improve searching efficiency. At last, genetic algorithm is developed for solving the scheduling problem, and numerical example shows good result.

Research on Fuzzy Scheduling Problem of Single-Stage Multi-Parallel Machines

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Papers

Mixed Integer Programming Models for Two Identical Parallel Machines with a Single Server

Research on Open Shop Scheduling Based on Genetic Algorithm

Open Shop Dense Scheduling Algorithm Based on Semi-Matching Theory

Research on Fuzzy Scheduling Problem of Single-Stage Multi-Parallel Machines