On the computational complexity of uncapacitated multi-plant lot-sizing problems

Cunha, Jesus O.; Kramer, Hugo; Melo, Rafael A.

doi:10.1007/s11590-020-01615-x

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Thus, when the proposed fuzzy-GA is used to solve a lot-sizing problem, 𝑃 groups of parameters can be selected. Figures [11][12][13] show the parameters in the case of P c1 , P c2 , and P c3 . When the fuzzy-GA is run many times, the target value changes with the number of iterations.…”

Section: Results and Discussion For Experimentsmentioning

confidence: 99%

“…Depending on whether the planning of the lot size is affected by the production capacity of the production resources, the lot-sizing problem can be divided into two groups: uncapacitated and capacitated. Lot-sizing problems can be divided into single level and multilevel according to the structure of the bill of material (BOM), which consists of subassembly, pieces, raw material, and finished products, and is a structured material list that describes the assembly relationship of components [13][14][15]. Since the single-level uncapacitated lot-sizing problem, known as the Wagner-Whitin problem, was proposed, there have been single-level capacitated lot-sizing problems, multilevel uncapacitated lotsizing problems, and multilevel capacitated lot-sizing problems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Genetic Algorithm Based on Fuzzy Reasoning for the Multilevel Capacitated Lot-Sizing Problem with Energy Consumption in Synchronizer Production

et al. 2022

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The multilevel capacitated lot-sizing problem (MLCLSP) is a vital theoretical problem of production planning in discrete manufacturing. An improved algorithm based on the genetic algorithm (GA) is proposed to solve the MLCLSP. Based on the solution results, the distribution of energy consumption in a synchronous production case is analyzed. In the related literature, the GA has become a much-discussed topic in solving these kinds of problems. Although the standard GA can make up for the defects of the traditional algorithm, it will lead to the problems of unstable solution results and easy local convergence. For these reasons, this research presents an adaptive genetic algorithm based on fuzzy theory (fuzzy-GA) to solve the MLCLSP. Firstly, the solving process of the MLCLSP with the fuzzy-GA is described in detail, where algorithms for key technologies such as the capacity constraint algorithm and the algorithm of solving fitness value are developed. Secondly, the auto-encoding of decision variables for MLCLSPs is studied; within this, the decision variables of whether to produce or not are encoded into a hierarchical structure based on the bill of material; combined with external demand, the decision variables of lot-sizing are constructed. Thirdly, the adaptive optimization process of parameters of the GA for the MLCLSP based on fuzzy theory is expounded, in which membership function, fuzzy rule, and defuzzification of the MLCLSP is mainly presented. Experimental studies using the processed dataset collected from a synchronizer manufacturer have demonstrated the merits of the proposed approach, in which the energy consumption distribution of the optimized production plan is given. The optimal lot-sizing is closer to the average value of the optimal value compared with the standard GA, which indicates that the proposed fuzzy-GA approach has better convergence and stability.

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Section: Results and Discussion For Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Genetic Algorithm Based on Fuzzy Reasoning for the Multilevel Capacitated Lot-Sizing Problem with Energy Consumption in Synchronizer Production

et al. 2022

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“…Several problems involving integrated production and transportation have been studied in the literature. Among these, we can highlight multi-level lot-sizing problems (Eppen & Martin, 1987;Slama, Ben-Ammar, Dolgui, & Masmoudi, 2020), one-warehouse multi-retailer problems (Solyalı & Süral, 2012;Cunha & Melo, 2016) and some of its generalizations (Park, 2005;Melo & Wolsey, 2012;Li & Hai, 2019), problems in the context of production and transportation by third-party logistic companies (Stecke & Zhao, 2007;Melo & Wolsey, 2010), and supply chain optimization problems involving multiple plants in which items can be transferred between the plants (Tanksale & Jha, 2017;Carvalho & Nascimento, 2018;Cunha, Kramer, & Melo, 2021).…”

Section: Introductionmentioning

confidence: 99%

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

Cunha¹,

Mateus²,

Melo³

2021

Preprint

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In this paper, we consider the capacitated three-level lot-sizing and replenishment problem with a distribution structure (3LSPD-C), recently proposed in the literature. In 3LSPD-C, a single production plant delivers items to the warehouses from where they are distributed to their corresponding retailers. There is a capacity on the total amount the plant can produce in each period, whereas there are no capacities on transportation. The goal of this optimization problem consists in determining an integrated three-echelon production and distribution plan minimizing the total cost, which is composed of fixed costs for production and transportation setups as well as variable inventory holding costs. Additionally, we consider a generalization of the problem which also establishes storage capacities (or inventory bounds) on the warehouses and/or retailers, given the importance of such characteristics in practical industrial and commercial environments. Such extension is denoted generalized capacitated three-level lot-sizing and replenishment problem with a distribution structure (G3LSPD-C). We propose a hybrid mixed integer programming (MIP) heuristic consisting of a relax-and-fix approach to generate initial feasible solutions and a fix-and-optimize improvement procedure grounded on varying-size neighborhoods to obtain high-quality solutions. Computational experiments are performed to analyze the potential cost reductions achieved using the new hybrid heuristic when compared with a state-of-the-art MIP formulation. The results show that the proposed hybrid heuristic can match or improve the solution quality obtained by the MIP formulation for the majority of the 3LSPD-C instances within a specified time limit. Additionally, such superior behavior remains valid when the approaches are applied to the more general G3LSPD-C. Furthermore, we investigate the economic impacts of the storage capacities and how they affect the performance of our newly proposed hybrid heuristic.

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A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

Cunha

Mateus²,

Melo³

2022

Computers & Industrial Engineering

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On the computational complexity of uncapacitated multi-plant lot-sizing problems

Cited by 5 publications

References 19 publications

Adaptive Genetic Algorithm Based on Fuzzy Reasoning for the Multilevel Capacitated Lot-Sizing Problem with Energy Consumption in Synchronizer Production

Adaptive Genetic Algorithm Based on Fuzzy Reasoning for the Multilevel Capacitated Lot-Sizing Problem with Energy Consumption in Synchronizer Production

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

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