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Preventive Maintenance Modeling
Published in Mangey Ram, Reliability Engineering, 2019
Sylwia Werbińska-Wojciechowska
The main maintenance models focus on optimization of the cycle length T between performance of preventive maintenance actions. A number of research works also deal with the problem of cyclically scheduling maintenance activities assuming a fixed cycle length. In [154], the authors formulate a maintenance scheduling problem to maintain a set of machines for a given determined T. The study presents the completely deterministic approach to decide for each period t ∈ T which machine to service (if any) such that total servicing costs and operating costs are minimized. The solution is obtained with the use of a branch and price algorithm. Another interesting maintenance problem applies to investigation of uncertain lifetime of system units (see [155]), introduction of repairable and non-repairable failures of a system (see [156]), lives of heterogeneous components of a system (see [157]), implementation of a ergodic Markov environment (see [158], or nearly optimal and optimal PM assessment for real-life systems (see [128,159]). The quick overview of the given BRPs is presented in Table 1.2.
Introduction to Coverage Optimization in Wireless Sensor Networks
Published in Huynh Thi Thanh Binh, Nilanjan Dey, Soft Computing in Wireless Sensor Networks, 2018
Huynh Thi Thanh Binh, Nguyen Hai Nam
From the previous discussion, the most challenges in WSN systems are formulated as combinatorial optimization problems and are classified as NP-hard problems (Bang Wang, 2011; Anju and Rishi, 2015). There exist two approaches to solve NP-hard problems: exact solutions and approximate solutions. The first approach includes branch and bound, branch and cut, branch and price, dynamic programming, linear and integer programming, Lagrange relaxation and so on. Meanwhile, the second approach consists of simulated annealing, tabu search, iterated local search, variable neighborhood search, genetic algorithm, memetic algorithm, etc.
A column generation-based approach for proportionate flexible two-stage no-wait job shop scheduling
Published in International Journal of Production Research, 2020
Zhi Pei, Xuefang Zhang, Li Zheng, Mingzhong Wan
Column generation(CG) is a well-recognised optimisation technique first proposed in 1958 by Ford and Fulkerson (Barnhart et al. 1998). This method is mainly applied to solve special structured integer programming problems, such as cutting stock (Gilmore and Gomory 1961) and identical parallel machine scheduling (Xu and Nagi 2013; Mellouli 2013). Meanwhile, a trend to employ CG to solve other practical problems emerges in the recent literature, for instance, Daya and Rishi (2017) presented a set covering formulation for the cumulative VRP problem using column generation. The pricing problem within the CG-based procedure was handled by a dynamic programming method. Recently, an increase in the CG-based research papers has been observed, and this approach could be used to tackle actual complex applications, which can be represented by large-scale mixed integer programming, such as patient admission (Range, Lusby, and Larsen 2014) and logistics assistants task scheduling (Volland, Fügener, and Brunner 2017). Besides, Jose, Harwin, and Dennis (2016) introduced a novel, set-partitioning type of formulation to locate a given number of new roadside wellness centres based on three optimisation criteria. Since the formulation involved a large number of variables, a CG-based algorithm was developed. Numerical experiments showed that the integrality gap for the formulation is very small. Gokhan and Ozgur (2016) studied the pharmacy duty scheduling with column generation. The results showed that the branch-and-price algorithm outperformed the state-of-art general purpose solver.
A column generation based approach for an integrated production and transportation scheduling problem with dual delivery modes
Published in International Journal of Production Research, 2023
Kunpeng Li, Peiyang He, P. N. Ram Kumar
The branch-and-price algorithm combines column generation and branch-and-bound algorithm (Desrochers, Desrosiers, and Solomon 1992). The procedure typically begins by forming a master problem and a sub-problem (Dantzig and Wolfe 1960). Instead of explicitly enumerating all the columns (variables), the Restricted Linear Master Problem (RLMP) considers only a subset of columns and is solved by relaxing the integrality restrictions on the variables. A sub-problem called the pricing problem is solved to find columns with a negative reduced cost that can enter the basis and improve the objective function value. Branching happens only when no columns can enter the basis, and the solution to the relaxation does not satisfy the integrality conditions.