Use of (max,+) algebra for scheduling and optimization of HVLV systems subject to preventive maintenance

Nasri, Imed; Habchi, Georges; Boukezzoula, Reda

doi:10.1016/j.simpat.2014.04.005

Cited by 3 publications

(5 citation statements)

References 27 publications

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“…where the objective function is 12) is solvable, and (1 e − 2) ⊺ is a globally optimal solution of problem (12).…”

Section: Example 3 Consider the Global Optimisation Problem Minmentioning

confidence: 99%

“…Example 4. Find all globally optimal solutions of problem (12). It has been calculated in Example 3 that…”

Section: Theorem 7 If Problem (3) Is Solvable Then the General Formula Of Globally Optimal Solutions Ismentioning

confidence: 99%

“…refs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). Global optimisation is to find the global minimiser of a function or a set of functions over a given set, which has been a basic tool in all areas of engineering, medicine, economics, and so on (see, e.g.…”

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confidence: 99%

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Locally and globally optimal solutions of global optimisation for max‐plus linear systems

Wang

Tao

2021

IET Control Theory & Appl

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This paper considers the locally and globally optimal solutions of the global optimisation problem whose objective function is a max-plus vector-valued function and constraint function is a real affine function. The formulas about global optimisation in the existing work are further explained and simplified. The necessary and sufficient conditions for the existence and uniqueness of locally optimal solutions of a single objective are established, which are then used to deduce these of globally optimal solutions. Furthermore, the general formulas of locally and globally optimal solutions are presented, respectively. The local optimisation is then applied to solve the load distribution problem of distributed systems with no globally optimal solution, and the optimal allocation scheme is proposed to complete the overall task at the earliest time. The proposed method is constructive, and the obtained results are illustrated by the numerical examples. INTRODUCTIONMax-plus linear systems can describe some nonlinear timeevolution systems with synchronisation but no concurrency, such as manufacturing systems, flow shop scheduling, traffic managements, communication networks (see, e.g. refs.[1-4]).Many researches have been made on control and optimisation of max-plus linear systems (see, e.g. refs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]).Global optimisation is to find the global minimiser of a function or a set of functions over a given set, which has been a basic tool in all areas of engineering, medicine, economics, and so on (see, e.g. refs. [23, 24]). The global optimisation of maxplus linear systems has been considered in refs. [25] and[26], whose objective function is a max-plus vector-valued function and constraint function is a real affine function. This paper will further address the global optimisation problem considered in ref. [26]. The global optimisation problem involves some operations between infinity elements and real numbers, which are not clearly defined in ref. [26]. This paper will explain these operations definitely, and simplify the formula of the greatest lower bound and the discriminant of the existence of globally optimal solutions given in ref. [26]. In addition, the zero coefficient in the constraint function is neglected when it discusses the uniqueness of globally optimal solutions (see refs. [26] and [27]), and a sufficient condition for the uniqueness is presented.

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“…where the objective function is 12) is solvable, and (1 e − 2) ⊺ is a globally optimal solution of problem (12).…”

Section: Example 3 Consider the Global Optimisation Problem Minmentioning

confidence: 99%

“…Example 4. Find all globally optimal solutions of problem (12). It has been calculated in Example 3 that…”

Section: Theorem 7 If Problem (3) Is Solvable Then the General Formula Of Globally Optimal Solutions Ismentioning

confidence: 99%

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Locally and globally optimal solutions of global optimisation for max‐plus linear systems

Wang

Tao

2021

IET Control Theory & Appl

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“…Imed Nasri considers a number of N job production load that have been scheduled for N equipment in job-shop industry. The purpose is optimization schedule between maintenance schedule and implementation of production schedule by considering time equipment failure [23]. Laggoune (2009) using opportunistic policy in the implementation of the replacement component, it obtain the components replacement timing in groups to minimize MTTR (Mean Time To Repair) and maximize equipment availability [12].…”

Section: Maintenance Optimizationmentioning

confidence: 99%

Maintenance on Job Shop Industry: Review and Analysis

Harja

Prakosa

Martawirya

2016

AMM

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This paper presents overviews about reliability and maintainability of equipment especially for job-shop manufacturing systems. The job shop industry has the characteristics of a more dynamic production than flow shop industries, where products with a variety of great but small amounts. Its dynamic condition certainly contributes directly to the failure rate and reliability growth of equipment. Therefore, proper maintenance should be done as the reliability improvement. Stages of reliability improvement are reliability modeling, reliability analysis and maintenance optimization. This stage is based on reliability growth of equipment that is indicated the deterioration process of failure components, it can be build from maintenance data history or condition data monitoring.. Cost is often considered in points of a maintenance schedule. This cost was affected by minimizing the negative effects of maintenance and maximizing the benefit of production. The attention at reliability and maintenance optimization is a well researches area until now. This paper presents a brief review of existing reliability and maintenance research. Several reliable methods in this area are discussed and maintenance on job-shop industry as future prospects is investigated. It is shown in this paper that some aspect in the area of maintenance on job-shop industry steel needs to be deeply developed.

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“…In the work of I. Nasri et al [1], HVLV systems are characterized by a wide variety of products using shared machines, a weak and personalized demand, relatively long processing times and frequent change over and set-up times. In the work of S. Wilson [2], HVLV consept refers to the variability of the orders, they propose a classification based on a coefficient defined as the standard deviation of weekly demand divided by the average of the weekly demand.…”

Section: Introductionmentioning

confidence: 99%

HVLV Manufacturing System Controlled with Heijunka-Kanban: A Simulation Study of Dead Time and Delay Constraints

2022

Proceedings of WCSE 2022 Spring Event: 2022 9th International Conference on Industrial Engineering and Applications

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In this work, we treat the Hight Variety Low Volume (HVLV) problematic using Heijunka lean manufacturing tool. In a manufacturing system, the principal objective is to satisfy the customer with quality and also by respecting the delivery delay. In this paper, we tackle the problem of sizing a Heijunka-Kanban production control system in order to cope with SLA delays. Unexpected delays that arise due to a variety of orders and dead time in the production loop are compensated with a suitable sizing of the Heijunka-Kanban control. Unfortunately, because of stock level constraints, unexpected delays may remain. Our work presents a typical case study of the automotive industry, a provider of rubber hoses.

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Use of (max,+) algebra for scheduling and optimization of HVLV systems subject to preventive maintenance

Cited by 3 publications

References 27 publications

Locally and globally optimal solutions of global optimisation for max‐plus linear systems

Locally and globally optimal solutions of global optimisation for max‐plus linear systems

Maintenance on Job Shop Industry: Review and Analysis

HVLV Manufacturing System Controlled with Heijunka-Kanban: A Simulation Study of Dead Time and Delay Constraints

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