Production, Manufacturing and Logistics
Supply chain modelling of forest fuel

https://doi.org/10.1016/S0377-2217(03)00354-0Get rights and content

Abstract

We study the problem of deciding when and where forest residues are to be converted into forest fuel, and how the residues are to be transported and stored in order to satisfy demand at heating plants. Decisions also include whether or not additional harvest areas and saw-mills are to be contracted. In addition, we consider the flow of products from saw-mills and import harbors, and address the question about which terminals to use. The planning horizon is one year and monthly time periods are considered. The supply chain problem is formulated as a large mixed integer linear programming model. In order to obtain solutions within reasonable time we have developed a heuristic solution approach. Computational results from a large Swedish supplying entrepreneur are reported.

Introduction

In recent years, the use and importance of bioenergy fuel have increased. In Sweden, its share of the total energy supply increased from 15% to 18% during the first half of the 1990s, see Brunberg et al. [3]. Considering the environmental regulations and taxation on, for example, CO2 emissions, this share is expected to increase even more in the future. Bioenergy fuel is often used by heating plants, which are normally operated by local communities to provide energy for the cities. The number of such heating plants is steadily increasing. The increased demand of bioenergy fuel has led to an increased demand for decision support tools which can help the complex planning of supplying the heating plant with bioenergy fuel. Since it is important to find high quality plans, there is a need to integrate optimisation models and solution procedures in the decision support tools.

Bioenergy fuel consists of several assortments. One important type is wood fuel which can be further divided into forest fuel, energy forest fuel and recycled wood fuel, see Filipsson [7]. The difference between forest fuel and energy forest fuel is that the latter consists of trees planted in order to be used as fuel. Other types of bioenergy fuel are reed fuel, straw fuel and waste paper. The heating plants can use several of these bioenergy fuel types, but in this paper we focus only on forest fuel, and on the problem of satisfying a given demand of forest fuel at a number of heating plants.

The supply of forest fuel is provided by companies which are obliged by contract to deliver a certain amount of bioenergy (forest fuel), specified in MW h, for each time period (normally a month) during the time of the contract. In most contracts there is also a clause that makes it possible for the heating plant to reduce or increase the demanded amount of energy up to 10–15%, incurring a penalty cost for the heating plant. The main reason for including such a clause is for the heating plant to have the possibility to adapt to unexpected cold or warm weather.

The problem we consider in this paper is the problem of the supplying company, which is to minimise the total cost for satisfying the demand given by the contract.

Forest fuel is mainly obtained from forest residues in harvest areas or from byproducts from saw-mills. Both harvest areas and saw-mills can be either owned by the company or available to the company by long-term contracts. Forest residues are branches and tops left in the harvest areas after the logs have been transported to, for example, saw-mills or pulp-mills. The forest residues have to be chipped (converted into small pieces) before they can be used as fuel by the heating plants, and the chipping can be made either directly at the harvest area or at a terminal, before transported to a heating plant. Byproducts from saw-mills consist of bark and sawdust, and they can either be transported directly to the heating plants, or to a terminal for storage and use in a forthcoming period. There is also a possibility to import different types of forest fuel, mainly by boat from Russia and the Baltic states.

Terminals are needed in order to balance the seasonal fluctuation in demand at the heating plants. At terminals we can store non-chipped and chipped forest residues as well as byproducts from saw-mills.

The problem is a true supply chain problem as there are multiple sources (harvest areas, saw-mills and import harbors), several intermediate terminals, several demand nodes (heating plants), different types of forest fuel and several time periods. The supply chain problem of the company contains decisions concerning which type of fuel to use, the timing of forwarding and chipping, the location of chipping, the storage at terminals, and the design of transportation pattern. Main decisions are also whether or not a harvest area or saw-mill should be contracted and if a specific terminal is to be used. In addition we have to consider restrictions on capacities of chipping, forwarding and storage at terminals. An illustration of the possible flows is given in Fig. 1.

Supply chain modelling and supply chain management have received a lot of attention among companies in recent years. It provides a tool for integrated planning of several interrelated planning situations. A driving force to the development of supply chain management systems has been the development of company wide databases for data collection and efficient optimisers to solve the resulting, often large, optimisation models. A basic description of supply chain modelling is found in Shapiro [10]. A more detailed description of industrial cases can be found in Stadtler and Kilger [11]. Examples include a case of computer assembly by Kilger [8] and a case about food and beverages by Wagner and Meyr [12].

With respect to forestry planning we can mention Carlsson and Rönnqvist [4] who give an overview of supply chain modelling in the Swedish forestry industry. The decisions made for the forest fuel in our case are similar to the decisions made by harvest planners in their case. They describe a need for an annual planning where scheduling of harvest areas is made. At the same time there is a need to come up with efficient transportation and storage planning on a monthly basis. One difference is that the supply of timber is unknown to a greater extent. This is so because no detailed information regarding the timber volume at the planned harvest areas, is collected (and if there is, it often includes faulty estimates) and several products or assortment are involved. Storage is also more difficult, as the value of logs decreases as it gets older. The demand at saw-, pulp- and paper-mills are also known to a less extent. There are, for example, no contracts stating the actual amount.

We formulate an optimisation model describing the planning problem for the supplying company. The model is a mixed integer programming model and we show that the problem can be solved in reasonable time using a heuristic solution procedure. The model can be used both as a tool for tactical planning, and as a strategic tool to analyse the effects on the current planning in various situations.

Typical strategic planning situations are, for example, when

  • the company is competing on a new contract and needs to submit competitive contract prices;

  • the company is analyzing the sensitivity of a solution to variations in demand (within the contract specification), for example an increase in demand during a particular month due to cold weather;

  • a new terminal is available, or the capacity of an existing terminal may be changed, and the potential impact is to be found;

  • chipping or transportation capacity is changed;

  • chipping technology is changed, hence also the chipping cost;

  • a haulage contractor is negotiating the transportation costs.

We have found very few examples dealing with fuel transportation in the literature. In Eriksson and Björheden [6], a linear programming model for solving a fuel transportation problem is presented. One conclusion in that paper is that the transportation costs constitute the most essential part of the total costs. It is also concluded that, contrary to practice, the optimal solution often included the use of flows with mobile chippers and direct transportation to the heating plants. A drawback with the model is that it contains no binary variables. Decisions regarding whether or not to contract a harvest area or saw-mill, and decisions about the time period for forwarding and chipping, cannot be analysed with the model. These decisions are essential in our problem. Our model also includes capacity constraints on storage.

Our mathematical model includes several components from traditional optimisation models. The basis of the model can be considered as a version of a two level facility location problem. Here, the upper level is represented by the harvest areas or saw-mills, the middle level by the terminals, and the lower level by the heating plants. In our application, the heating plants can be viewed as customers defining the demand and the harvest areas or saw-mills as facilities to be opened or not. Furthermore, the problem can be given a natural network representation for the different flows. Finally, we also have a time expanded model as we deal with a multi-period problem.

The outline of the paper is as follows. In Section 2 we describe the supply chain problem from harvest areas to heating plants. Then, in Section 3, we formulate the mathematical model for the problem. In Section 4 we describe the solution method and present computational results using data from a real-life case study. The case is obtained from Sydved Energileveranser AB, which is one of the largest Swedish companies delivering forest fuel to heating plants, and the results include an analysis of a number of different scenarios. Finally, in Section 5, we make some concluding remarks.

Section snippets

Supply of forest fuel

The supplying company obtains forest fuel from several sources, namely harvest areas, saw-mills, and import sources.

The harvest areas can be classified into two groups; self-owned harvest areas and contracted harvest areas. At harvest areas that are owned by the company, the forest residues have to be removed during the planning period, but the products are available without extra cost. The forest residues in contracted harvest areas can be made available by entering into a contract with a

Mathematical model

In this section we present the mathematical model of the forest fuel supply chain problem. We first describe the sets of variables, then follows the constraints and the objective function. The full model is given in the Appendix A.

Let I be the set of supply sources, J the set of terminals, P the set of products, K the set of heating plants and T the set of time periods. The set of supply sources contains subsets for self-owned harvest areas (IH), harvest areas with a potential to be contracted (

Solution methods and computational results

In this section we present a solution procedure for the proposed supply chain model, and we show that the model can be solved in reasonable time using data from a real-life case.

The test problem is given from the Swedish entrepreneur of Sydved Energileveranser AB. Sydved is one of the largest suppliers of bioenergy fuel in Sweden with an annual turnover of about $US 37 million. The company is fully owned by two major forest companies, StoraEnso and Munksjö, and it has therefore a large number

Concluding remarks

The main purpose with this paper is to present a model and solution approach that can be used as a decision support tool for strategic analysis as well as tactical planning of the supply of forest fuel. The mathematical model developed gives a detailed description of the supply chain problem considered. The resulting IP-problem will become very large. However, by using a heuristic approach based on sequential LP solving or the direct use of a commercial IP solver, i.e., CPLEX, it is possible to

Acknowledgements

We are grateful to Sydved Energileveranser AB for providing us with all data and information in the test case. This project was initiated through the graduate school of Energy Systems at Linköping University and financed through the Center for Industrial Information Technology at Linköping University.

References (12)

  • L.O Eriksson et al.

    Optimal storing, transport and processing for a forest-fuel supplier

    European Journal of Operational Research

    (1989)
  • J. Arlinger, B. Brunberg, M. Eriksson, M. Thor, Kvalitetskrav, råvaruutnyttjande och kostnader vid kraftigt ökad...
  • C Barnhart et al.

    Branch-and-price: Column generation for solving huge integer programs

    Operation Research

    (1998)
  • B Brunberg et al.

    SkogForsk, Redogörelse nr

    (1998)
  • D. Carlsson, M. Rönnqvist, Wood flow problems in Swedish forestry, in: G. Frumerie (Ed.), Report No. 1, The Forestry...
  • ...
There are more references available in the full text version of this article.

Cited by (0)

View full text