Solving a multi-period supply chain problem for a pulp company using heuristics—An application to Södra Cell AB

Abstract

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 analyzed which shows that the proposed solution approach is simple and provides high quality solutions.

Regional energy wood logistics – optimizing local fuel supply

“…One way to track down the needed and also optimal feedstock at terminal or plant will be to extend the objective function by a time factor. This can be done in such a way that demand and resource availability on a monthly basis are incorporated into the model (Eriksson andBjörheden 1989, Gunnarsson andRönnqvist 2008).…”

Planning production and supply chain in energy intensive process industries

“…As such, a real problem situation for the case company has been conceptualized and modelled into a scientific mathematical model, in line with Mitroff et al (1974). This model is partly based on a previous model developed by Gunnarsson et al (2007) and modified by Gunnarsson and Rönnqvist (2008). In this dissertation the previous model is referred to as the Mill Mission model, which in a modified form is currently in use at the case company for supply chain planning purposes.…”

“…This study had a starting point in the Mill Mission model previously developed by Helene Lidestam (see e.g. Gunnarsson et al, 2007;Gunnarsson and Rönnqvist, 2008). Thus, Helene Lidestam has partly been involved in the modelling phase as well as in the writing process of Paper 2 and Paper 3.…”

“…The whole supply chain is later on considered by Gunnarsson et al (2007) that also present a model (Mill Mission) with a one year planning period. The Mill Mission model is further developed by Gunnarsson and Rönnqvist (2008) by also considering multiple time periods and the use of heuristics. The same authors, Lidestam and Rönnqvist (2011), later on study the same supply chain and develop a mixed integer linear programming model, for which a Lagrangian heuristic method based on Lagrangian decomposition is used to solve the supply chain planning problem.…”

“…The production and the supply chain of the case company Södra Cell, has previously been studied numerous times (e.g. Carlsson and Rönnqvist, 2005;Gunnarsson et al, 2006;Gunnarsson et al, 2007;Gunnarsson and Rönnqvist, 2008;Lidestam and Rönnqvist, 2011), but none of these studies have taken the energy issues into special consideration as done with Energy Mission in Paper 2 and Paper 3. Plenty of modelling opportunities, where the energy system interacts with the production processes in many different ways, have also been found for the case company involved in the third study presented in Paper 4 and Paper 5.…”