An integrated column generation and lagrangian relaxation for flowshop scheduling problems

Nishi, Tatsushi; Isoya, Yukinori; Inuiguchi, Masahiro

doi:10.1109/icsmc.2009.5346159

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…The convergence of the bounds in the conventional CG algorithm is very slow (Nishi et al., 2011). To accelerate the process and identify better lower bounds, the methodology starts with relaxing constraints () using an LR procedure.…”

Section: Methodsmentioning

confidence: 99%

Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

Atik

Hajibabai

2023

Computer aided Civil Eng

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Incident response operations require effective planning of resources to ensure timely clearance of roadways and avoidance of secondary incidents. This study formulates a mixed‐integer linear program to minimize the total expected travel time and maximize the demand covered. The model accounts for the location, severity, frequency of incidents, dispatching locations, and availability of incident respondents. An integrated methodology that includes column generation and Lagrangian relaxation with a density‐based clustering technique that defines incident hot spots is proposed. The hybrid approach is applied to an empirical case study in Raleigh, NC. A network instance with 10,672 incident sites, clustered with a search distance (ε) of 5 min, is solved efficiently with an optimality gap of 1.37% in 2 min. A Benders decomposition technique is implemented to conduct benchmark analyses. The numerical results suggest that the proposed algorithm can solve the problem efficiently and outperform the benchmark solutions.

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Section: Methodsmentioning

confidence: 99%

Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

Atik

Hajibabai

2023

Computer aided Civil Eng

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“…Finally, in order to avoid the confliction of the decoupled constraints, a feasible solution is obtained from the relaxed solution by the use of the different heuristic-based algorithm. The combination of SG or SSG with FDP or BDP under the LR frame has been used in different SCC scheduling problem, such as static scheduling problems [7,15,16,22,23] or dynamic scheduling problems with different objectives and under different conditions [19,31,37]. As for the rescheduling problems with LR algorithm, Xiong et al [36] proposed a dynamic scheduling algorithm with constant processing times in the rescheduling problems without considering the processing time and the other disturbance factors.…”

Section: (Communicated By Adil Bagirov)mentioning

confidence: 99%

Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm

Luan¹,

Mao²

2017

Journal of Industrial &Amp; Management Optimization

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This study investigates a challenging problem of rescheduling a hybrid flow shop in the steelmaking-continuous casting (SCC) process, which is a major bottleneck in the production of iron and steel. In consideration of uncertain disturbance during SCC process, we develop a time-indexed formulation to model the SCC rescheduling problem. The performances of the rescheduling problem consider not only the efficiency measure, which includes the total weighted completion time and the total waiting time, but also the stability measure, which refers to the difference in the number of operations processed on different machines for the different stage in the original schedule and revised schedule. With these objectives, this study develops a Lagrangian heuristic algorithm to solve the SCC rescheduling problem. The algorithm could provide a realizable termination criterion without having information about the problem, such as the distance between the initial iterative point and the optimal point. This study relaxes machine capacity constraints to decompose the relaxed problem into charge-level subproblems that can be solved using a polynomial dynamic programming algorithm. A heuristic based on the solution of the relaxed problem is presented for obtaining a feasible reschedule. An improved efficient subgradient algorithm is introduced for solving Lagrangian dual problems. Numerical results for different events and problem scales show that the proposed approach can generate high-quality reschedules within acceptable computational times.

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“…The dual theory guarantees that the solution of the LD problem can provide the lower bound of the primal problem, whereas the best feasible solution offers an upper bound of the primal problem [2]. The LR approach has emerged as a practical approach for various scheduling problems such as single machine scheduling problem [3], parallel machine scheduling [4], flowshop scheduling [5], jobshop scheduling [6], [7], hybrid flowshop [8], [9], etc. Some researchers such as [10] and [11] applied the LR approach to the SCC scheduling problem under different production environments based on the machine capacity relaxation.…”

Section: Introductionmentioning

confidence: 99%

An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process

Mao

Pan

Chai

et al. 2015

IEEE Trans. Automat. Sci. Eng.

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The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The relaxed problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling. Note to Practitioners-Efficient and effective SCC schedule is vital for the manufacturing system of iron and steel production.Unfortunately, the scheduling is extremely difficult because of its combinatorial nature and practical complex constraints such as job grouping constraints, precedence constraints, different transport time, and setup times. To obtain high-quality solutions within an acceptable computational time, we can use a problem-oriented approach, which can be the LR. However, there are two deficiencies in this approach: its empirical termination criteria, such as maximal iteration number or running time, which make it difficult to find a golden rule for various problems, and the inefficiency, which is caused by the so-called zigzagging phenomena. To overcome these deficiencies, this paper develops an effective subgradient method for SCC scheduling based on the machine capacity relaxation. This method gives an objective termination criterion based on the convergence condition of the method, and improves the efficiency based on a new search direction or a new subgradient. Then, the work shows how this method can be applied to solve an SCC scheduling problem. The computational results confirm their effectiveness and efficiency. The approaches can also be applied to other similar production scheduling problems.

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An integrated column generation and lagrangian relaxation for flowshop scheduling problems

Cited by 3 publications

References 14 publications

Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

Joint column generation and Lagrangian relaxation technique for incident respondent location and allocation

Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm

An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process

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