A Critique on
AN OPTIMIZATION MODEL FOR ANNUAL HARVEST PLANNING
Authors: Jenny Karlsson
, Mikael Rönnqvist
, Johan Bergström
. Journal:
Canadian Journal of Forest Research ; Aug 2004; 34, 8 pg. 1747.
By: Rahmawaty
I. Title of the Study
• As a researcher, the title provided by the authors has the element of simplicity, brevity, specificity and location and subject matter focused. The reader can easily determine what
the study is all about and what it tries to investigate An optimization model for annual harvest planning and what mathematical model? A mixed integer programming MIP. Brief
title but very informative. To more make informative, it would be better if the author mention the location of the study and the MIP on the title, so the reader know the location and the
mathematical model of the study.
• Just going through the title, one can easily understand that the concern of the research study is related to optimization model in forestry. The keywords used such as “annual harvest
planning” clearly indicate that the subject matter is in the field of forestry.
II. Introduction A. Background of the Study:
• According the authors, In Sweden, wood flow planning for forest companies, including harvest and transportation planning, occurs in different stages. Harvest planning includes
decisions on different levels, both spatial and temporal. Prognoses are made for long-time horizons strategic planning, in Sweden typically 100 years. The maximum harvested
volumes are estimated, as well as proportions of thinning and final felling, with respect to requirements on sustainable forestry.
• This stage of harvest planning is usually called the tactical level. Time for thinning and final felling is estimated to maximize the total value. On a medium or annual level, planning is
aimed to identify which areas to harvest in given months to balance supply and demand. On a shorter time horizon, plans are often made for a number of weeks only.
• Larger forest companies in Sweden have an organization whereby operations are divided into smaller regions, which may be composed of one or several districts. Plans at different
levels are continuously updated on rolling planning horizons. The different levels of harvest planning are described in Figure 1.
• The problem we consider in this paper is the annual planning problem at the district level. The annual planning starts from a list or a pool of areas that correspond to 1.5-2 years of
harvesting. The main decisions deal with which areas to harvest and which crew to assign. The selection of harvesting areas strongly affects the production level of different
assortments, as each area has a particular assortment mix. It also affects the choice of crew, as each area has an average tree size and harvest teams have a given capacity and
efficiency depending on this size.
• The planning also includes transportation planning, road maintenance decisions, and control of storage in the forest and at terminals. In a central planning process, the annual demand
for paper-, pulp-, and saw-mills are distributed for each district on a monthly level. Weather conditions vary a lot during the year and this fact needs to be considered. Some roads are
closed and some areas cannot be harvested during thawing in the spring and heavy rainy periods in the autumn.
Universitas Sumatera Utara
• The output from this plan is the distribution of harvest areas over the year, assuring accessibility, as well as assuring that the monthly harvested amount corresponds to the
demand of the wood-processing facilities. The result from the annual plan yields input to short-term, operational planning.
• Currently, planning for harvesting and transportation for each district, both on an annual and operative level, is carried out manually. There are usually a limited number of qualified and
experienced persons that make the short-term harvest plans, and they spend a large amount of time preparing qualitative plans. Coordination between districts is limited and is only
considered in particular situations during the year.
• In short-term planning, the storage level and age of the harvested timber is considered to obtain a better estimate of storage cost. To determine the harvested amount of different
assortments each week, we need to determine the sequence of harvest areas during the planning period.
• There have been many studies dealing with harvesting planning on different levels. The terminology is not uniform; planning on time horizons between 1 and 70 years is sometimes
mentioned as tactical planning. A medium-range, tactical harvest schedule model called OPTIMED is mentioned in Epstein
et al. 1999. This model supports decisions concerning
which stands to harvest, how much timber is needed to satisfy projected demands, and which roads are needed to gain access to the harvest areas for a total planning horizon of 2-
5 years. • Annual harvesting planning is found in Newham 1991, where a version of the system
LOGPLAN II is described. This is a model based on linear programming LP that can be used to schedule timber harvesting and regeneration activities given available equipment,
wood resources, planting stock, and mill demands in order to minimize cost. An annual planning problem within Swedish forestry is described in Gunnarsson
et al. 2004. Here the
problem is to decide where and when forest residues are to be converted into forest fuel and how the residues are to be transported and stored to satisfy demand at heating plants.
• Tactical and operational harvesting planning often includes discrete decisions about specific stands or roads, which create integer or mixed-integer problems. The presence of integer
variables and the size of real-world problems often lead to heuristic methods to achieve practical solution times.
• A long-term, spatially constrained harvest-scheduling problem is studied in Yoshimoto et al.
1994. They developed a heuristic procedure in which the problem is partitioned into a number of subproblems, which are then solved independently. Weintraub
el al. 1995
describes a heuristic algorithm for solving a tactical problem for 2-3 decades, including harvesting decisions and road building.
• The solution procedure iterates between solving relaxed LP versions of the model and applying rules to fix fractional variables to integer variables. A branch-and-price algorithm is
used to obtain optimal integer solutions. To achieve compatible decision made at different levels, different approaches have been used. Hierarchical methods have been developed to
integrate tactical and strategic planning.
• The authors start by developing a mathematical model, which gives a mixed integer problem MIP. To test the model, we have made a case study. The annual planning typically starts
with a large number of areas, which leads to a large number of binary and continuous variables and numerous constraints. According the authors, case study problem
corresponds to planning on a district level.
• This is solvable directly with a commercial MIP solver CPLEX 8.1, within 1 of optimality in a couple of hours, which is a practical time limit for annual planning. When solving larger
instances, a heuristic method is likely needed. The authors propose a feasible approach corresponding to a limited branch-and-bound search. The developed model and methods
are not a production system but is intended to become an important part of a future decision support tool.
Universitas Sumatera Utara
B. Objectives of the Study:
• The main contribution of this paper is a model describing the annual harvesting planning problem, including decisions about harvest areas, simultaneous allocation of harvest teams,
and overall transportation and storage planning. • The case study gives input to a future development of a decision support system. The
remainder of this paper is organized as follows: in the following section, the annual harvesting planning problem is described. We then present the mathematical formulation of
the problem. A case study is then described, followed by Computational Results. Finally, concluding remarks are made.
III. Mixed Integer Programming MIP A. Definition
