An analysis of formulations for the capacitated lot sizing problem with setup crossover

Fiorotto, Diego Jacinto; Jans, Raf; Araújo, Silvio Alexandre de

doi:10.1016/j.cie.2016.12.037

Cited by 18 publications

(5 citation statements)

References 23 publications

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“…The setup structure in the capacity constraint is another consideration that affects the problem complexity ( Karimi et al, 2003 ). The setup of a product can be dependent or independent of the previous product in the production sequence ( Guimarães, Klabjan, & Almada-Lobo, 2014 ), or the final setup in a period can be carried over to the next period ( Gopalakrishnan, Ding, Bourjolly, & Mohan, 2001;Sahling, Buschkühl, Tempelmeier, & Helber, 2009 ) or split between two periods ( Fiorotto, Jans, & de Araujo, 2017 ).…”

Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

Classification and literature review of integrated lot-sizing and cutting stock problems

Melega

Araújo

Jans

2018

European Journal of Operational Research

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a b s t r a c tThe aim of this paper is to classify the literature related to the integration between the lot-sizing and cutting stock problem. A deterministic mathematical model, that considers multiple dimensions of integration and comprises several aspects found in practice, is proposed. This model is used as a framework to classify the current literature in this field. The main classification of the literature is organized around two types of integration. In a planning horizon which consists of multiple periods, the inventory provides a link between the periods. This integration across time periods constitutes the first type of integration. The proposed model also considers the production of different types of items at three different levels: objects are fabricated or purchased and next cut into pieces which are then assembled into final products. The integration between these three production levels constitutes the second type of integration. The classification indicates that, even though many papers in the current literature analyze an integrated lot-sizing and cutting stock problem, they vary widely with respect to the level of integration on the time and production level dimensions. Furthermore, our analysis indicates that the current models also consider varying assumptions with respect to the inventory, the production capacities and the setups. Finally, we point out some possible interesting areas for future research. (R. Jans). that might correspond to customer requests, and a decision related to the cutting stock problem is needed. Part of the smaller reels can be cut again into paper sheets, according to some decision related to the lot size for the papers sheets. In the furniture industry, wooden plates are produced or purchased from different suppliers, and a decision about the size of the lots to be produced or purchased from each supplier must be taken. Then, these wooden plates are cut into several wooden parts (in a two-dimensional cutting stock process) to be assembled into the final products. A decision about the size of the lots of final products is also needed, and consequently there are three levels of decisions. Other examples can be found in the fiberglass industry, where fiberglass plates are cut to manufacture printed circuit boards and in the aluminium industry, where aluminium profiles are cut to make several window types. The basic idea of the integrated lot-sizing and cutting stock problem is to consider, simultaneously, the decisions related to both problems so as to capture the interdependency between these decisions in order to obtain a better global solution. Several papers from the literature present computational results showing the benefits of considering an integrated approach instead of taking decisions separately

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Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

Classification and literature review of integrated lot-sizing and cutting stock problems

Melega

Araújo

Jans

2018

European Journal of Operational Research

Self Cite

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“…Ramya et al [7] proposed a formulation for the CLSP with setup carryover and setup-splitting and no backorders or lost sales. Fiorotto et al [12] compared two formulations proposed by Mohan [10] and by Menezes [6] and proposed symmetry braking constraints. With computational experiments, they showed that the proposed constraints are effective for the formulation proposed by Mohan.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Constraints (11) ensure that remaining setup times are allowed only during setup crossover. From Assumption 1, idle time is not allowed during setup operation, this is reflected in constraints (12). First two terms of the left-hand side are added to lift the constraint.…”

Section: Variablesmentioning

confidence: 99%

Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

Kang

2020

Processes

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Since setup operations have significant impacts on production environments, the capacitated lot-sizing problem considering arbitrary length of setup times helps to develop flexible and efficient production plans. This study discusses a capacitated lot-sizing problem with sequence-dependent setup, setup carryover and setup crossover. A new mixed integer programming formulation is proposed. The formulation is based on three building blocks: the facility location extended formulation; the setup variables with indices for the starting and the completion time periods; and exponential number of generalized subtour elimination constraints (GSECs). A separation routine is adopted to generate the violated GSECs. Computational experiments show that the proposed formulation outperforms models from the literature.

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“…(2016); Fiorotto et al. (2017) also studied the capacitated lot‐sizing problem with characteristics of setup carryover, crossover, and splitting. While considering the problem characteristics, they also propose MIP formulations and present their analyses.…”

Section: Literature Reviewmentioning

confidence: 99%

Multi‐level, multi‐stage lot‐sizing and scheduling in the flexible flow shop with demand information updating

Rehman

Wan

Zhan

2019

Int Trans Operational Res

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Motivated by a real‐world problem in an automobile manufacturing firm, we study the multi‐level, multi‐stage lot‐sizing and scheduling problem with demand information updating. The objective is to determine the quantities and sequences of production on different production stages to minimize the total costs of production and inventory. We employ the martingale model for forecast evolution to model the evolving demand over time and build a mixed‐integer programing (MIP) model for the problem using a hybrid period approach (i.e., combining micro‐ and macro‐periods). To solve this NP‐hard problem, we propose three heuristic algorithms based on the idea of “relax‐and‐fix” within the rolling horizon framework. We conduct computational experiments to test the performance of the heuristic algorithms as well as compare the performance of the proposed heuristics with the benchmark procedure (truncated procedure for MIP) for both small‐ and large‐scale problem instances. The computational results show that Heuristic 1 performs the best among the three heuristic algorithms.

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An analysis of formulations for the capacitated lot sizing problem with setup crossover

Cited by 18 publications

References 23 publications

Classification and literature review of integrated lot-sizing and cutting stock problems

Classification and literature review of integrated lot-sizing and cutting stock problems

Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

Multi‐level, multi‐stage lot‐sizing and scheduling in the flexible flow shop with demand information updating

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