Abstract
The Pulp and Paper industry in North Europe is continuously making strategic decisions for investments. A modern paper mill is a significant long-term investment, and companies are searching for methods for making good investment decisions. In this paper, a method based in mixed integer linear programming (MILP) for decision support in the Pulp and Paper Industry is proposed. It is shown how an MILP formulation can be used for optimising revenues on investments based on forecasts on demand, raw material costs, transportation costs, labour costs and energy costs. In addition, a case study illustrating how the methodology works is presented.
Background One major decision for any industrial activity is where to locate the production units. In the pulp and paper industry, a production unit often is an integrated pulp mill and a paper mill. Moreover, even paper-converting units or saw-mill activities may be run on the same site. Large-scale pulp and paper mills are major investments, and the life time for these facilities is long. The companies are hence looking for reliable decision support mechanisms for their strategic planning. The main objective of any company is to produce profits and return on investments (ROI). Using computational tools, the optimal profit and ROI can be obtained for varying scenarios. The profit of a pulp and paper mill is dependent on various factors, such as raw material costs, labour costs, transportation costs, energy costs, demands, paper prices, interest rates etc. Some of these factors vary regionally more, some less. For instance, the labour costs have a strong relation to the local economy, whereas interest rates do not. Hence, the investment decision is actually a geographical decision, the big questions being where to invest, when and how much.
Related work Even if the pulp and paper industry is a large industry, and only in the Nordic European countries Norway, Sweden and Finland the turnover is US$ 50 billion, and investments are around US$ 400-500 million for one pulp line (Bergman et.al, 2002), there is not very much literature on the area. On a general level Heidenberger(1996) apply MILP to project selection problem, which can be seen as a investment problem, and show similar problem statements. In process synthesis there is a long trend in applying mathematical optimisation, an overview given by Grossmann (1996). In the case of supply chain optimisation, there are numerous examples of applying mathematical optimisation. Applying optimisation to varying scheduling problems the chemical industry has been rather popular (Floudas and Lin, 2004), and the methodology is often reusable for other industries. The development of more sophisticated decision support systems is a general trend shown by Shim et. al (2002). Here has also mathematical programming approaches been used, and the proposed formulation here is a addition to this work. Problem formulation In this paper we present a MILP model for optimising the profits and return on investments based on given forecasts for production costs, paper prices and demands. Even if most of the formulation is LP, the actual investment decisions are discrete, and thus an MILP formulation is used.
Illustrative example In the case study presented in this paper, the task is to supply five geographical areas in Europe with different paper qualities. Each area has a forecasted demand for five different paper qualities. The market is supposed to increase according to a growth plan. Costs for raw materials, labour, and logistics are given as forecasts. Using the optimisation methods proposed in the paper, optimal solutions to support the strategic planning are obtained. A solution provides information on where to produce each paper qualities, where the investments should be done, and how the logistic should be arranged.
Results and conclusion An MILP-formulation for optimising investments in pulp and paper mills was presented. Using this formulation and forecasts for costs, demands and prices, by optimising for profit or return on investment, strategic investment plans can be generated. This work is very An obvious shortcoming of the current formulation is however that forecasts, demands, and prices etc. are uncertain. Hence, the formulations could be developed to also handle optimisation under uncertainty. This could further help the decision makers, not selecting strategic plans that easily fail due to high sensitivity to uncertainty.
Many industries depend on the same key variables for the profitability. The proposed MILP formulations can be easily tuned to meet the requirements of other businesses than just the pulp and paper industry. Literature
Mats A. Bergman, Per Johansson and M.A. Bergman, Large investments in the pulp and paper industry: a count data regression analysis, Journal of Forest Economics, Volume 8, Issue 1, 2002, Pages 29-52. Christodoulos A. Floudas and Xiaoxia Lin, Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review, Computers & Chemical Engineering, Volume 28, Issue 11, 15 October 2004, Pages 2109-2129. Ignacio E. Grossmann and Mark M. Daichendt, New trends in optimization-based approaches to process synthesis, Computers & Chemical Engineering, Volume 20, Issues 6-7, June-July 1996, Pages 665-683. Kurt Heidenberger, Dynamic project selection and funding under risk: A decision tree based MILP approach, European Journal of Operational Research, Volume 95, Issue 2, 6 December 1996, Pages 284-298. J. P. Shim, Merrill Warkentin, James F. Courtney, Daniel J. Power, Ramesh Sharda and Christer Carlsson, Past, present, and future of decision support technology, Decision Support Systems, Volume 33, Issue 2, June 2002, Pages 111-126.