| Harvest Scheduling is the decision making process that specifies where to harvest, when to harvest and how much to harvest each year over a many year planning horizon to best achieve some predefined set of objectives. Harvest Scheduling is a subset of the Forest Management Activity Scheduling problems. These problems usually include timber harvest scheduling, but other activities are now common as well. A forest plan includes a harvest schedule.
Early Approaches
Harvest scheduling methodology has evolved from the early 15th century in Europe when people first realized that timber resources needed to be managed in order to insure a sustainable supply of wood (Roise and others 2000). This first attempt evolved into what we call Area Control harvest scheduling. Give a forest area “A” and a desired harvest age for trees, rotation length “R”, the land area of yearly sustainable harvested “a” is equal to (A/R). The per unit area yield of wood at the rotation age multiplied by “a” is the Long Term Sustained Yield (LTSY) of a forest.
The next major advance in harvest scheduling technology occurred in the early 1800s when algebraic formula methods were proposed to calculate the Allowable Cut. Formula methods were based on the sustained yield concept that you should harvest less than you grow. These methods were easy to apply in theory, but the information needed for accurate estimates was difficult to collect and reduce into a usable form.
Linear Programming and Simulation
In the 1950s, when computers started to be used for harvest scheduling and allowable cut calculations, the technology used in harvest scheduling underwent major advances, also at that time forest planning linear programming (LP) formulations were first proposed. With the aid of computers, and new mathematical programming techniques full-scale multiple-use planning became possible. A series of progressively more sophisticated harvest scheduling models were developed using the combination of area control and formula techniques. The first of many forest simulation models was ARVOL (ARea VOLume check method) (Chappelle 1966). This was followed shortly by “Short Run Allowable Cut” (SORAC, Chappelle 1968) which was designed to look beyond the current rotation toward how intensively managing the regenerated stands might affect current harvest levels. The next step in complexity came with Simulating Intensively Managed Allowable Cut (SIMAC, Sassaman and others 1972) which permitted the used of a wide range of intensive management practices. Many other simulation models followed.
By the 1970s linear programming was being used for harvest scheduling. The Timber Resource Allocation Model (Timber RAM, Navon 1971) was an early LP matrix generator and report writer widely used within the U.S. Forest Service. The plans themselves were developed to address the questions of biological sustainability of the cut on a forest wide basis. The questions Timber RAM was designed to address concerned only timber management. At that time planning issues were beginning to shift from harvest scheduling to multiple use questions.
The Multiple Use-Sustained Yield Calculation technique (MUSYC, Johnson and Jones, 1979) was an attempt to improve the limited orientation of Timber RAM and provided for integration of other forest uses into timber planning. Out of this effort emerged the Model I/Model II nomenclature and harvest scheduling formulations (Johnson and Scheurman, 1977). The difference between these two formulations is how the decision variables are defined.
In Model I, a decision variable represents the amount of land allocated to a set of management activities from the present to the planning horizon. The set of management activities may include actions on the existing stand through perhaps several harvests on future regenerated stands. (Roise and others 2000). In Model II, there are decision variables for existing stands and different ones for regenerated stands. Each time a stand gets harvested it gets transferred to another decision variable.
Both Model I and II formulations have advantages for timber harvest and activity scheduling. They are both useful. However, when ecological consideration need to be incorporated the Model I formulation has a slight advantage that a unit of land can be easily tracked from beginning to end of the planning horizon. Both formulations have a fundamental weakness in terms of ecological forest planning and analysis. They both are essentially strata based models and most ecological problems require spatial integrity. The required spatial integrity can be achieved by making the model I formulation an integer program with each stand receiving only one management regime. Using a Model I integer formulation, integer constraints mean that management units can easily be tracked across the planning horizon. A new problem emerged with integer formulations. They are difficult to solve even with the most powerful computers. The way around this problem usually consists of a heuristic procedure to find a good or simply feasible solution. Heuristics also add increased flexibility needed to analytically form harvest blocks from smaller land elements, instead of having to predefine all stands in the present and assume that they remain constant throughout time.
In the late 1970s, a new forest management LP matrix generator/report writer called FORPLAN came into extensive use. Spectrum, which is still in use today, is a graphical user interface version of FORPLAN. They are highly flexible modeling programs, which incorporate both the strata-based information required for per acre yields and an innovative area based formulation required by recreation, wildlife, water and other environmental outputs needing area wide yields. The areas were called Zones and they could receive totally different sets of management prescriptions depending on the type of management emphasis which was assigned to the zone.
When it first appeared, FORPLAN was unique among planning models within the U.S.A. It could handle a wide variety of problems in forest management. It could evaluate area specific projects. It could evaluate groups of projects connected in space and time. For the first time it gave forest planners the opportunity to shift the focus of planning away from functional concerns toward truly integrated planning (Inverson and Alston, 1986).
Modern Methods
By the late 1980s it became apparent that temporal scheduling alone was not sufficient and that spatial arrangement of activities on the forests (mainly harvesting) was an important issue that could not be addressed with linear formulations. Integer formulations of the forest planning problem were proposed that incorporated adjacency constraints and eventually a variety of spatial arrangement constraints (i.e. connectivity, adjacency, proximity and edge).
Integer formulations were difficult, sometimes imposable, to solve using closed form mathematical programming techniques, such as branch and bound methods. Several heuristic methods were proposed and successfully utilized to find “good” solutions to the spatially constrained harvest scheduling problem. The methods have name such as Taboo Search, Simulated Annealing, and Genetic Algorithms. With these nonlinear methods extremely complex forest planning problems could be analyzed.
Today, it is recognized by forest analysts that the methods of forest planning have far out paced the basic scientific information about forest systems. Forest planners can predict the outcomes of management activities on the growth and yield of trees, but are less able to predict future forest conditions such as desired ecological characteristics, biodiversity, habitat for specific species, occurrence of desired understory species and other desired outcomes and conditions. In addition there is recognition that the future is uncertain and we do not know what events will change our prediction about forest conditions.
Modern harvest scheduling tools have incorporated much from modern information technology. They incorporate and integrate geographic data through GIS, forest inventory data, ecosystem data, environmental data, market data and socioeconomic data through decision support systems. Today forest managers can get a timely understandable synthesis of information if they have the forest inventory, economic, ecologic and societal information needed to run the models.
Conclusion
Overall, we have become more sophisticated in harvest scheduling approaches, the activities and constraints that they include, and mathematical sophistication that they employ. Despite the sophistication of modern harvesting scheduling, it should be noted that it is not uncommon for foresters to check the reasonableness of computer harvest scheduling results using quick estimates of area control (A/R). Thus harvest scheduling will continue to make elegant advances to solve increasingly complex problems, and utilize more powerful computer hardware and software. At the same time, it will continue to rely on managers to implement its outcomes, and adapt those outputs on the ground as practical consideration, public opinions, and budget realities occur.
References
Chappelle, D.E. 1966. A Computer Program for Calculating Allowable Cut Using the Area-Volume Check Method. U.S.D.A. Forest Service Research Note PNW-44, 4p.
Chappelle, D.E. 1968. A Computer Program for Scheduling Allowable Cut Using Either Area or Volume Regulation During Sequential Planning Periods. U.S.D.A. Forest Service Research Note PNW-93, 9 p.
Iverson, D.C. and R.M. Alston. 1986. The Genesis of FORPLAN: A Historical and Analytical Review of Forest Service Planning Models. U.S.D.A. Forest Service Gen. Tech. Rep. INT-214, p.32
Johnson, K.N. and D.B. Jones. 1979. A user’s guide to multiple use sustained yield resource scheduling calculation (MUSYC). U.S.D>A. Forest Service Timber Management, 242 p.
Johnson, K.N. and H.L. Scheurman. 1977. Techniques prescribing optimal timber harvest and investment under different objectives-discussion and synthesis. Forest Science Monograph No. 18, 31p.
Navon, D.I. 1971. Timber RAM.A long-range planning method for commercial timber lands under multiple-use management. U.S.D.A. Forest Service Res. Paper PSW-70, 22p.
Roise, J.P., F.W. Cubbage, R.C. Abt, and J.P. Siry. 2000. Regulation of Timber Yields For Sustainable Management of Industrial Forest Plantations – Theory and practice. Chapter in, Sustainable Forest Management, Ed. Gadow, Pukkala and Tomé, Kluwer Academic Publishers, pp:217-256.
Sassaman, R.W., E. Holt and K Bergsvik. 1972. User’s Manual for a Computer Program for Simulating Intensively Managed Allowable Cut. U.S.D.A. Forest Service Gen. Tech. Rep. PNW-1, 50 p.
Posted 1 October 2007
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