A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

doi:10.1080/00207543.2011.649095

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A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

Journal Article•DOI•

A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

Srimathy Mohan¹, Mohan Gopalakrishnan¹, Rahul R. Marathe², Ashwin Rajan³•Institutions (3)

Arizona State University¹, Indian Institute of Technology Madras², Cisco Systems, Inc.³

04 Oct 2012-International Journal of Production Research (Taylor & Francis Group)-Vol. 50, Iss: 19, pp 5538-5543

TL;DR: In this paper, the capacitated lot sizing problem with set-up carryover and setup splitting (CLSP-SCSS) is formulated as a mixed integer linear program.

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Abstract: The capacitated lot-sizing problem with set-up carryover and set-up splitting (CLSP-SCSS) is formulated as a mixed integer linear program. We define set-up carryover as the production of a product that is continued over from one period to another without incurring an extra set-up. Set-up splitting occurs when the set-up for a product is started at the end of a period and completed at the beginning of the next period. We allow product dependent set-ups. Initial experimentation highlights the importance of including set-up splitting in the CLSP model. In 12 out of the 18 problem instances tested, our model yielded better solutions or removed infeasibility when compared with a CLSP model without set-up splitting.

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Journal Article•DOI•

A review of discrete-time optimization models for tactical production planning

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Manuel Díaz-Madroñero¹, Josefa Mula¹, David Peidro¹•Institutions (1)

Polytechnic University of Valencia¹

08 Aug 2014-International Journal of Production Research

TL;DR: In this paper, the authors present a review of optimization models for tactical production planning and identify streams and future research directions in this field based on the different classification criteria proposed by the authors.

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Abstract: This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively...

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97 citations

Cites background from "A note on modelling the capacitated..."

...2009; Grubbstrom and Huynh 2006a), set-up carry-overs (Helber and Sahling 2010; Kaczmarczyk 2011; Nascimento, Resende, and Toledo 2010), set-up sequence-dependents (Goren, Tunali, and Jans 2012; Mohan et al. 2012; Ozturk and Ornek 2010) or set-up groups (Absi and Kedad-Sidhoum 2008)....
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...Product-related limitations appear in those papers addressing the production of only a single product (18 references) or in those that consider only mono-level product structures (Alwan, Liu, and Yao 2008; Degraeve and Jans 2007; Gaglioppa, Miller, and Benjaafar 2008; Ho, Chang, and Solis 2006; Ho, Solis, and Chang 2007; Kim and Xirouchakis 2010; Mohan et al. 2012; Nascimento, Resende, and Toledo 2010)....
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...…nine references (Anily, Tzur, and Wolsey 2009; Clark, Morabito, and Toso 2010; Federgruen, Meissner, and Tzur 2007; Goren, Tunali, and Jans 2012; Mohan et al. 2012; Mula, Peidro, and Poler 2010; Omar and Teo 2007; Pastor, Altimiras, and Mateo 2009; Tempelmeier and Buschkuehl 2008; Toso,…...
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...…or in those that consider only mono-level product structures (Alwan, Liu, and Yao 2008; Degraeve and Jans 2007; Gaglioppa, Miller, and Benjaafar 2008; Ho, Chang, and Solis 2006; Ho, Solis, and Chang 2007; Kim and Xirouchakis 2010; Mohan et al. 2012; Nascimento, Resende, and Toledo 2010)....
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...…et al. 2011; Wu, Lin, and Wu 2010), and in the total production costs (Boudia, Louly, and Prins 2008; Fleischhacker and Zhao 2011; Liu et al. 2007; Mohan et al. 2012; Mula, Poler, and Garcia-Sabater 2008; Pastor et al. 2009; Peidro et al. 2010; Stadtler and Sahling 2013; Van den Heuvel, Borm,…...
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Journal Article•DOI•

Parallel machine, capacitated lot-sizing and scheduling for the pipe-insulation industry

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Jesica de Armas¹, Manuel Laguna²•Institutions (2)

Pompeu Fabra University¹, University of Colorado Boulder²

01 Feb 2020-International Journal of Production Research

TL;DR: A solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon is developed, in the context of the manufacturing of pipe insulation.

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Abstract: We develop a solution procedure for a production problem that involves the optimal lot-sizing and scheduling of multiple products on parallel machines over a long planning horizon. The objective is...

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25 citations

Cites background from "A note on modelling the capacitated..."

...…thereby increasing production capacity (Sox and Gao 1999; Gopalakrishnan et al. 2001; Porkka, Vepsäläinen, and Kuula 2003; Gupta and Magnusson 2005; Suerie 2006; Mohan et al. 2012; Belo-Filho, Toledo, and Almada-Lobo 2014; Ramya, Rajendran, and Ziegler 2016; Fiorotto, Jans, and de Araujo 2017)....
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Posted Content•

Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic

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Florian Sahling¹, Lisbeth Buschkühl², Horst Tempelmeier², Stefan Helber¹•Institutions (2)

Leibniz University of Hanover¹, University of Cologne²

01 Jun 2008-Research Papers in Economics

TL;DR: A new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs is presented.

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Abstract: This paper presents a new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last product produced in a period are determined by the model. We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs. Our algorithm solves a series of mixed-integer linear programs in an iterative so-called Fix-and-Optimize approach. In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.

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22 citations

Journal Article•DOI•

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

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Diego Jacinto Fiorotto, Raf Jans, Silvio Alexandre de Araujo

01 Apr 2017-Computers & Industrial Engineering

TL;DR: A computational study is presented to determine which is the best formulation to model a setup crossover and ideas indicating that in one of the formulations from the literature it is not necessary to impose binary conditions on the crossover variables are explored.

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18 citations

Cites background or methods from "A note on modelling the capacitated..."

...Mohan et al. (2012) include the possibility of setup crossover for the formulation proposed by Suerie and Stadtler (2003) that handles the problem with setup carryover and compare the improvement obtained by adding the crossover in the formulation with setup carryover....
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...Model Proposed by Mohan et al. (2012) (F2) The second formulation is based on the ideas proposed by Mohan et al. (2012) and the main difference is the way to limit the time for the setup crossover (constraints (10) and (11) of the previous formulation)....
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...Next, we present two formulations for the problem with setup crossover based on the ideas proposed by Menezes et al. (2010) and Mohan et al. (2012)....
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...The computational tests indicate that the symmetry breaking constraints are very effective for the formulation proposed by Mohan et al. (2012), but not for the formulation proposed by Menezes et al. (2010)....
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...Although setup crossover is a natural extension of the standard assumption, just a few studies have considered it, due to the difficulty in dealing with the underlying problems (Mohan et al., 2012; Belo-Filho et al., 2014)....
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Journal Article•DOI•

Capacitated lot-sizing problem with production carry-over and set-up splitting: mathematical models

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Ravi Ramya¹, Chandrasekharan Rajendran¹, Hans Ziegler²•Institutions (2)

Indian Institute of Technology Madras¹, University of Passau²

17 Apr 2016-International Journal of Production Research

TL;DR: In this article, the authors proposed a mathematical model for capacitated lot sizing with production carryover and set-up splitting, which can handle two scenarios, namely (1) situation/scenario where the setup costs and holding costs are product dependent and time independent, and with no backorders or lost sales, and (2) situation where the setting costs and hold costs are not product dependent but time dependent.

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Abstract: This work proposes mathematical models (MMs) for the capacitated lot-sizing problem with production carry-over and set-up splitting, which can handle two scenarios, namely (1) situation/scenario where the set-up costs and holding costs are product dependent and time independent, and with no backorders or lost sales, and (2) situation where the set-up costs and holding costs are product dependent and time dependent, and with no backorders or lost sales. Previously, in an existing study the authors had developed a MM for the same problem and situation where the set-up costs and holding costs are product dependent and time independent, i.e. our Scenario 1. We compare our proposed models with the model in the existing study that appears to be incorrect.

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14 citations

Cites background or methods or result from "A note on modelling the capacitated..."

...This CLSP with production carry-over and set-up splitting (with no backorders or lost sales) was addressed by Mohan et al. (2012)....
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...Mohan et al. (2012) addressed the CLSP with production carry-over and set-up splitting (with no backorders or lost sales)....
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...In this paper, we address the CLSP with production carry-over and set-up splitting by developing mathematical models (called MM and alternate mathematical model [AMM] in our paper) with the consideration of a possible production carry-over over successive periods (see Mohan et al. 2012)....
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...…carried between adjacent periods for a product; and binary variable indicating whether a production of an item is continued from period t − 1 to t. Mohan et al. (2012) were the first to develop a model for the CLSP with production carry-over across periods, with the consideration of a possible…...
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...The basic assumptions are the same as those presented in Mohan et al. (2012)....
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References

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Journal Article•DOI•

A review of scheduling research involving setup considerations

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Ali Allahverdi¹, Jatinder N. D. Gupta², Tariq Aldowaisan¹•Institutions (2)

Kuwait University¹, Ball State University²

01 Apr 1999-Omega-international Journal of Management Science

TL;DR: A comprehensive review of the literature on scheduling problems involving setup times (costs) classifies scheduling problems into batch and non-batch, sequence-independent and sequence-dependent setup, and categorizes the literature according to the shop environments of single machine, parallel machines, flowshops, and job shops.

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Abstract: The majority of scheduling research assumes setup as negligible or part of the processing time. While this assumption simplifies the analysis and/or reflects certain applications, it adversely affects the solution quality for many applications which require explicit treatment of setup. Such applications, coupled with the emergence of production concepts like time-based competition and group technology, have motivated increasing interest to include setup considerations in scheduling problems. This paper provides a comprehensive review of the literature on scheduling problems involving setup times (costs). It classifies scheduling problems into batch and non-batch, sequence-independent and sequence-dependent setup, and categorizes the literature according to the shop environments of single machine, parallel machines, flowshops, and job shops. The suggested classification scheme organizes the scheduling literature involving setup considerations, summarizes the current research results for different problem types, and finally provides guidelines for future research.

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899 citations

"A note on modelling the capacitated..." refers background in this paper

...Allahverdi et al. (1999), Jans and Degraeve (2008) and Buschkühl et al. (2010) present comprehensive reviews of lot sizing models with set-up time considerations. Jans and Degraeve (2008) describe how these models also incorporate scheduling, while Buschkühl et al....
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...Allahverdi et al. (1999), Jans and Degraeve (2008) and Buschkühl et al. (2010) present comprehensive reviews of lot sizing models with set-up time considerations. Jans and Degraeve (2008) describe how these models also incorporate scheduling, while Buschkühl et al. (2010) provide a comprehensive review of the solution approaches for the capacitated multi-item lot sizing problem (CLSP) and its variants....
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...Allahverdi et al. (1999), Jans and Degraeve (2008) and Buschkühl et al. (2010) present comprehensive reviews of lot sizing models with set-up time considerations....
[...]
...Allahverdi et al. (1999), Jans and Degraeve (2008) and Buschkühl et al....
[...]
...Allahverdi et al. (1999), Jans and Degraeve (2008) and Buschkühl et al. (2010) present comprehensive reviews of lot sizing models with set-up time considerations....
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Journal Article•DOI•

Capacitated lot sizing with setup times

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William W. Trigeiro, L. Joseph Thomas, John O. McClain

01 Mar 1989-Management Science

TL;DR: In this paper, a Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems, which are solved by dynamic programming.

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Abstract: This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solve...

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444 citations

"A note on modelling the capacitated..." refers background in this paper

...While later models have directly modelled set-up times as consumed capacity (Trigeiro et al. 1989, Armentano et al. 1999, Jans and Degraeve 2004), they do not address the issue of preserving or carrying a set-up across adjacent periods....
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Journal Article•DOI•

Modeling Industrial Lot Sizing Problems: A Review

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Raf Jans¹, Zeger Degraeve²•Institutions (2)

Erasmus University Rotterdam¹, London Business School²

03 Jan 2008-International Journal of Production Research

TL;DR: In this article, the authors give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems, focusing on the modeling of various industrial extensions and not on the solution approaches.

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Abstract: In this paper we give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems. The focus of this paper is on the modeling of various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research.

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350 citations

Journal Article•DOI•

Dynamic capacitated lot-sizing problems: a classification and review of solution approaches

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Lisbeth Buschkühl¹, Florian Sahling², Stefan Helber², Horst Tempelmeier¹•Institutions (2)

University of Cologne¹, Leibniz University of Hanover²

01 Apr 2010-OR Spectrum

TL;DR: A review of four decades of research on dynamic lot-sizing with capacity constraints shows that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice.

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Abstract: This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.

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270 citations

Journal Article•DOI•

Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic

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Florian Sahling¹, Lisbeth Buschkühl², Horst Tempelmeier², Stefan Helber¹•Institutions (2)

Leibniz University of Hanover¹, University of Cologne²

01 Sep 2009-Computers & Operations Research

TL;DR: In this paper, a fix-and-optimize algorithm for the dynamic multi-level capacitated lot sizing problem with setup carry-overs (MLCLSP-L) is presented.

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166 citations