Development of Production Scheduling Model With Constraint Resources and Parallel Machines

In this paper, a production scheduling model with constraint resources and parallel machines has been investigated. This problem is proposed as a multi-product production problem. Shortage is not allowed and the production horizon is indefinite. The objective is to maximize the level of resource usage and support the management’s standpoint (delays reduction). In this paper, this problem is modeled as the popular Knapsack problem in 0 and 1 programming. Then due to being NP-hard type for this kind of problems to obtain an optimal solution, A heuristic approach has been used to obtain the acceptable solution. By using the branch-and bound method, a near optimal solution is provided. Finally, resultant solutions by the proposed approach have been compared with the optimal solutions of some real-world problems and it has been observed that deviation from the optimal solution is negligible that indicates the accuracy of the proposed approach

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;

Machine Scheduling with Resource Dependent Processing Times

We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource. A given amount of that resource, e.g. workers, can be distributed over the jobs in process at any time, and the more of that resource is allocated to a job, the smaller is its processing time. This model generalizes classical machine scheduling problems, adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied previously by Shmoys and Tardos. On the basis of integer programming formulations for relaxations of the respective problems, we use LP rounding techniques to allocate resources to jobs, and to assign jobs to machines. Combined with Graham''s list scheduling, we thus prove the existence of constant factor approximation algorithms. Our performance guarantee is 6.83 for the most general case of unrelated parallel machine scheduling. We improve this bound for two special cases, namely to 5.83 whenever the jobs are assigned to machines beforehand, and to (5+e), e>0, whenever the processing times do not depend on the machine. Moreover, we discuss tightness of the relaxations, and derive inapproximability results.operations research and management science;

Providing a Suitable Model for Solving Resource Leveling in Project Management

Resource leveling and resource Allocation are main tasks of project management. The aim of project scheduling is allocating resources to activities while faced on minimizing some economic objectives. In particular, in resource leveling problems the objective is to minimize a function of the resource utilization over time. If there is no restriction on the amount of available resources, raised the issue of resource leveling is required to fluctuations in resource utilization decreases without increasing the project duration. In this paper for managing transportation resource leveling problem, especially when based on multiple objective function of NP-hard problems, has been used Genetic Algorithm. This method is inspired from nature, presented as well as the desired resolution and optimal solutions. The results indicated that the genetic algorithm is able to respond very well at a reasonable offer

Hybridizing guided genetic algorithm and single-based metaheuristics to solve unrelated parallel machine scheduling problem with scarce resources

This paper focuses on solving unrelated parallel machine scheduling with resource constraints (UPMR). There are j jobs, and each job needs to be processed on one of the machines aim at minimizing the makespan. Besides the dependence of the machine, the processing time of any job depends on the usage of a rare renewable resource. A certain number of those resources (Rmax) can be disseminated to jobs for the purpose of processing them at any time, and each job j needs units of resources (rjm) when processing in machine m. When more resources are assigned to a job, the job processing time minimizes. However, the number of resources available is limited, and this makes the problem difficult to solve for a good quality solution. Genetic algorithm shows promising results in solving UPMR. However, genetic algorithm suffers from premature convergence, which could hinder the resulting quality. Therefore, the work hybridizes guided genetic algorithm (GGA) with a single-based metaheuristics (SBHs) to handle the premature convergence in the genetic algorithm with the aim to escape from the local optima and improve the solution quality further. The single-based metaheuristics replaces the mutation in the genetic algorithm. The evaluation of the algorithm performance was conducted through extensive experiments

Scheduling problems for parallel dedicated machines under multiple resource constraints

The paper considers scheduling problems for parallel dedicated machines subject to resource constraints. A fairly complete computational complexity classification is obtained, a number of polynomial-time algorithms are designed. For the problem with a fixed number of machines in which a job uses at most one resource of unit size a polynomial-time approximation scheme is offered

Contributions à l'analyse des systèmes industriels et aux problèmes d'ordonnancement à machines parallèles flexibles : application aux laboratoires de contrôle qualité en industrie pharmaceutique

Dans cette thèse, nous abordons deux thématiques très différentes du génie industriel, mises en oeuvre sur un même cas d'application industriel. Tout d'abord, nous nous intéressons à l'analyse des systèmes industriels en intégrant deux courants de pensée : la modélisation d'entreprise d'une part, et l'amélioration des systèmes industriels d'autre part. Nous proposons une grille d'analyse/action basée sur la modélisation d'entreprise et permettant de mettre en évidence les dysfonctionnements du système industriel et les instruments d'amélioration à mettre en oeuvre. Un cas d'application est développé sur notre problématique industrielle. Ensuite, un problème d'ordonnancement original est issu du précédent cas d'application. Il s'agit d'un atelier à machines parallèles flexibles et nécessitant des ressources secondaires (outils et intervention d'opérateurs), avec temps de préparation importants, mais sans contrainte de précédence entre les opérations d'un job. Nous étudions le critère de la somme des retards des jobs. Deux approches sont proposées pour ce problème : par heuristique et par recuit simulé. Pour l'approche heuristique, une règle appelée ATCTRS est développée. Elle cherche à réaliser un compromis entre le retard d'une opération et la bonne occupation de la machine. Pour l'approche par méta-heuristique, nous étudions principalement une structure de voisinage adaptée au problème à résoudre. ABSTRACT : In this PhD thesis, we deal with two axes of industrial engineering, implemented on the same industrial case of study. First of all, we focus on the analysis of industrial systems, using previous work concerning both enterprise modeling and continuous improvement. We propose an analysis/action grid based on enterprise modeling in order to identify the problems of the system and improvement tools to use. An application is presented based on our industrial problem. Furthermore, a new scheduling problem results from the previous application : a shop with parallel flexible machines requiring secondary ressources (tools and operator interventions), with set-up but without precedence constraints between operations of a job. We will study the total job tardiness criterion. Two approaches are proposed to solve this problem : by heuristic and by simulated annealing. For the heuristic approach, a new rule called ATCTRS has been developed. Its aim is to make a compromise between the tardiness of an operation and the occupation of the machine. For the meta-heuristic approach, we mainly study a neighborhood structure fitting the problem to solve