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Solving a multi-period supply chain problem for a pulp company using heuristics—An application to Södra Cell AB
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
Department of Finance and Management Science, Norwegian School of Economics and Business Administration.
2008 (English)In: International Journal of Production Economics, ISSN 0925-5273, Vol. 116, no 1, 75-94 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the integrated planning of production and distribution for a pulp company is considered. The tactical decisions included regard transportation of raw materials from harvest areas to pulp mills; production mix and contents at pulp mills; inventory; distribution of pulp products from mills to customers and the selection of potential orders and their levels at customers. The planning period is one year and several time periods are included. As a solution approach we make use of two different heuristic approaches. The main reason to use heuristics is the need for quick solution times. The first heuristic is based on a rolling planning horizon where iteratively a fixed number of time periods is taken into consideration. The second heuristic is based on Lagrangian decomposition and subgradient optimization. This provides optimistic bounds of the optimal objective function value that are better than the LP relaxation value, which can be used as a measure of the heuristic (pessimistic) solution quality. In addition, we apply the proposed rolling horizon heuristic in each iteration of the subgradient optimization. A number of cases based on real data is analysed which shows that the proposed solution approach is simple and provides high quality solutions.

Place, publisher, year, edition, pages
Elsevier, 2008. Vol. 116, no 1, 75-94 p.
Keyword [en]
Supply chain modelling, Production planning, Heuristics, Lagrangian decomposition
National Category
Social Sciences
URN: urn:nbn:se:liu:diva-14850DOI: 10.1016/j.ijpe.2008.07.010ISI: 000261007900006OAI: diva2:25349

Original publication: Helene Gunnarsson and Mikael Rönnqvist, Solving a multi-period supply chain problem for a pulp company using heuristics—An application to Södra Cell AB, 2008, International Journal of Production Economics. Copyright: Elsevier B.V.,

Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2014-03-07Bibliographically approved
In thesis
1. Supply chain optimization in the forest industry
Open this publication in new window or tab >>Supply chain optimization in the forest industry
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The scope of this thesis is modelling and solving large-scale planning problems in the supply chain within the forest industry. Five research papers are included, the first three of which focus on the modelling, and the last two on the solution methods. All problems included are tactical multi-commodity problems expressed as mixed integer programming (MIP) models. The work has been done in collaboration with two Swedish companies within the forest industry.

In Paper I, a problem concerning the supply chain of forest fuel for Sydved Energileveranser AB is modelled and solved. We study the problem of deciding when and where forest residues are to be converted into wood chips, and how the residues and chips are to be transported and stored in order to satisfy energy demand at heating plants. The company has long-term contracts with forest owners and saw mills. Decisions in the model include whether or not additional harvest areas and saw mills are to be contracted and which terminals to use. The planning horizon is one year and monthly time periods are used.

Papers II--V are based on planning problems at Södra Cell AB. The planning horizon is normally one year. Papers II--III consider only one time period. In Paper II the supply chain from pulp mills to customers is modelled and the combined problem of deciding terminal locations and which ship routes to use is studied. Shipping vessels chartered on short or long term are used to transport products to terminals in Europe. From each terminal, the products are transported to customers by truck, train, or a combination of both. In addition, trains and trucks can be used for transports directly to customers from mills. In Paper III the entire supply chain, from harvest areas to customers, is considered. Decisions included are transportation of raw materials, production mix, the distribution of pulp products, and the selection of potential orders and their quantities at customers. The ship routes are considered as flow links.

In Papers IV--V the problems in Papers II--III are combined into one model and several time periods are used. Lagrangian heuristics based on Lagrangian decomposition are used as solution methods in both papers. In Paper IV, the approach leads to subproblems for each time period, whereas in Paper V, another approach that results in subproblems for different parts of the supply chain is developed.

All models are based on real data from the companies. The models are detailed and describe the problems accurately. The solution methods are developed such that the solution time is kept within practical limits. Results from Papers II--III have been used by Södra Cell AB to support the change of the terminal structure as well as in budget planning.

Abstract [sv]

Denna avhandling presenterar matematiska modeller och lösningsmetoder för optimering av olika logistikproblem inom skogsindustrin. Vi studerar försörjningskedjor för skogsbränsle och massaproduker, och beaktar den årliga planeringen i syfte att optimera flödet.

Det första problemet behandlar skogsbränsle och är ett samarbete med Sydved Energileveranser AB. Råmaterial i form av grenar och toppar från avverkningsplatser ska flisas och transporteras till värmeverk, eventuellt via terminaler. Det finns möjlighet att flisa både i skogen och på terminaler. Biprodukter från sågverk kan också användas som råmaterial. Vid behov kan utbudet av råmaterial utökas genom att fler avverkningsplatser och sågverk kontrakteras. Värmeverken har en efterfrågan, angiven i kWh per månad, som ska uppfyllas. Exempel på beslut som ska tas är var flisning ska ske, om nya avverkningsplatser ska kontrakteras, var lagring ska ske, samt hur och när skogsbränslet ska transporteras.

Nästföljande problem behandlar massaprodukter och är ett samarbete med Södra Cell AB. Olika sorters massaved från skogen och biprodukter från sågverk utgör råmaterial för produktion av massaprodukter. Råmaterialet transporteras till massabruk för tillverkning enligt specificerade recept. De färdiga produkterna transporteras sedan med fartyg till terminaler i Europa. Från terminalerna transporteras produkterna vidare till pappersbruk, vilka är företagets slutkunder. Massaprodukterna transporteras i vissa fall med lastbil eller tåg direkt från massabruken till kunderna. Efterfrågan är angiven inom vissa gränser i olika order. Vissa order är fasta, vilket innebär att dess efterfrågan måste uppfyllas, medan andra order är fria. Exempel på beslut som ska tas är vilka bruk olika produkter ska produceras på, hur många och vilka terminaler som ska användas, samt hur transporterna ska utföras för att ge bästa resultat.

Utifrån ovanstående beskrivningar har matematiska modeller formulerats. Ge-nom att lösa dessa kan vi få svar på logistik- och transportfrågorna och ett optimalt flöde kan hittas. För att lösa modellerna har kommersiell programvara använts. Heuristiker och mer avancerade optimeringsmetoder har också utvecklats i syfte att producera bra lösningar snabbare.

Place, publisher, year, edition, pages
Matematiska institutionen, 2007
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1105
Supply chain, logistics, forestry, optimization, modelling, transportation, mixed integer programming models, försörjningskedjor, logistik, optimering, modellering, transportplanering, blandade heltalsproblem, skogsindustrin
National Category
Computational Mathematics
urn:nbn:se:liu:diva-8856 (URN)978-91-85831-85-2 (ISBN)
Public defence
2007-06-01, C3, C-huset, Linköpings universitet, Linköping, 10:15 (English)
Article 4 was a manuscript entitled "Solving a multi-period supply chain problem for a pulp industry using Lagrangian heuristics based on time periods" at the time of the thesis defence. Available from: 2007-05-14 Created: 2007-05-14 Last updated: 2009-04-28

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