Sustained forests; sustained profits
Sustained forests; sustained profits
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based in part on a paper by C.J. Cowles, PhD, Virginia Tech, July, 1979
Webster's New International Dictionary (Unabridged) defines heuristic as an adjective meaning "serving to discover or reveal - applied to argument and methods of demonstration which are persuasive rather than logically compelling or which lead a person to find out for himself." This definition suggests, but fails to pinpoint, the meaning of heuristic as it applies to mathematical programming. Wensink and Sowell (1978), quoting Wagner (1970), stated that heuristic programming is a problem solving approach which employs both simple and sophisticated rules of thumb, as well as partially corrective trial and error procedures, to produce feasible, and, hopefully, near optimal solutions. They asserted that heuristic techniques have little theoretical foundation and are of an ad hoc nature, relying primarily on the modeller's intuition of the system.
According to the former authors, the primary advantage of heuristic techniques are that they often require minimal computational time relative to theoretical models. Also, certain standard techniques may not be tractable for specific problems due to violation of assumptions. If there is no standard technique (such as LP) robust enough to accomodate the problem needs, then a heuristic approach is advantageous. A major disadvantage of heuristic methods is that their answers cannot be compared to the unobtainable theoretical optimum. Levin and Kirkpatrick (1978) stated that a heuristic rule is a "rule of thumb", a heuristic program is a system using a collection of heuristic rules. Thus, their definition is somewhat more restricted than that adopted by Wensink and Sovell (1978) or Wagner (1970).
Taha (1911) stated that heuristic models are mainly used to explore alternative strategies which have been overlooked previously. By applying some intuitive rules or guidelines, the analyst can generate new solutions which may yield an improved result.
In short, a heuristic approach can be viewed to be either a rejection of standard theoretical models replaced by an intuitive model or a means by which several standard models are used interdependently, resulting in one model without a standard name. Within Lasting Forests, the objective is improved decisions that are timely and cost effective. To achieve this we unify the two concepts and say that our work is heuristic optimization, a procedure using intuitive models in combination with several known or standard models to produce a limited range of optimum alternatives (with aids) to the decision maker. It is a procedure seeking to at least achieve the same or better optimization that would be achieved by the best decision maker today.
Examples of heuristic approaches in problem solving are widespread. Levin and Kirkpatrick (1978) used a heuristic method for rescheduling work to meet personnel constraints. Pinto et al. (1978) discussed an extension of heuristic approaches to assembly line balancing, of which there are at least four popular heuristics. Wensink and Sovell (1978) discussed a heuristic method of optimizing the location and marketing volume of tobacco facilities. The latter authors' approach was developed in order to arrive at solutions to a problem which, due to the tremendous number (in the trillions) of feasible solutions, was impossible to solve using modern computational equipment. They also were able to compare results of their heuristic model to a theoretical model for solutions of small problems, thus verifying the heuristic's ability to approximate the optimum. However, their approach to reducing the decision space of an optimization problem is probably one of relatively few methods which can be used to validate a heuristic approach.
The Process
Our concept of doing (or as some prefer) using heuristic programming includes
A Comparison of Normative Models
Models can generally be classified into two major categories, descriptive and normative. Normative models are models used to seek solutions to decision problems where the analyst uses the model to identify an optimum. Descriptive models, on the other hand, are representative of systems with the primary intent to predict system outputs or states. Quening models, population models, input-output models, and most types of simulations can be considered descriptive models. Table 1 shows the major models used in normative situations and the capabilities of each in terms of problem characteristics which can be handled by each.
It is possible to weight the various problem characteristics in terms of importance in maintaining agricultural decision problem realism. For example, based on our knowledge of agricultural systems, it would be safe to state that much of the agricultural complex is of probabilistic nature. Prices, fuel supplies, weather, yields, etc. are rarely predicted with certainty. Therefore, models capable of dealing with probabilistic situations are more applicable than those which cannot. Most agricultural problems deal with resource limitations, are associated with non-linear relationships, have both continuous and integer variables, and are of a multistage nature. Whether agricultural problems require exact solutions is, like the previous generalizations,debateable. We tend to hold that most such decisions do not require exact solutions, that objectives are often unclear, and that many desired bnefits for the rural environment are substitutable. Near-exact solutions at low cost would seem more useful than exact solutions at high cost. For the sake of simplicity, arbitrary weights of 0 or 1 representing model requirements of agricultural problems have been assigned as shown in Table 1.
| Table 1. Importance-weighted normative model requirements | |
| Model Requirement | Requirement Weight |
|---|---|
| Knowlwdge Deterministic Probabilistic |
0 1 |
| Resources Constrained Unconstrained |
1 0 |
| Functions Linear Nonlinear |
0 1 |
| Variables Continuous Linear |
1 1 |
| Problem Single-stage Multi-stage |
0 1 |
| Solution Exact Inexact |
0 1 |
Assuming Cij = 1
if an element ij in Table 1 is checked and
Cij = 0
if unchecked, then for each model i, a Model Capability (MC) Factor can be computed as:
| MC= |  |
CijWj |
| Table 2. Capabilities of Mathematical Techniques Based on Criteria in Table 1. | |
| Technique | MC |
| Classical Calculus |
2 |
| Linear Programming |
2 |
| Integer Programming |
2 |
| Non-Linear Programming |
3 |
| Dynamic Programming | 6 |
| Optimum Search |
5 |
| Heuristic Procedures |
7 |
| Simulation | 1 |
| Queuing | 1 |
Heuristic Models in Agricultural Systems
According to Swartzman and Van Dyne (1972), management of ecosystems leads to the need for dynamic optimization when dealing specifically with long range planning objectives. This conclusion corresponds to the relatively high MC Factor of dynamic programming found herein (Table 1). However, Swartzman and Van Dyne (1972) stated that dynamic programming is generally too unwieldy for all but the simplest of real-life problems. In complex situations with many variables, most dynamic programming approaches are insoluble. Thus, in an attempt to obtain a planning aid useful for accomodating ecosystem complexity, they developed a heuristic model of recursive simulation and static optimization (linear programming). The heuristic nature of their approach was underscored by the statement (Swartzman and Van Dyne 1972:348) "With this interactive combination we seek a good (although not necessarily optimal) planning strategy."
In their heuristic model initial conditions were provided to the simulation model which, by use of differential equations, computed values of state variables at 10 day intervals for a 1 year simulation. Values for these state variables (such as shrub yield, livestock weight, soil water yield, range condition indices, etc.) at the end of the 1-year period were then supplied to the optimization model to represent constraints, objective function coefficients, and other technical coefficients. Execution of the optimization model provided an annual plan for maximizing profits and prescribing appropriate strategies of marketing livestock and controlling wild species. The performance of these strategies (such as removal of livestock from the planning unit) was then supplied as new input to the simulator for computing the dynamic changes of the following year. This process was repeated as desired for a long term simulation-optimization.
At the time of its development (1972), the authors believed their simulator-optimizer was the largest such model developed in the natural resource area. The simulator included 94 state variables, 234 flows (couplings) between the state variables, and 754 parameters. Major dynamic processes modeled in the simulator included variation in precipitation, temperature, soil water, herbage biomass, steer forage, steer weight, wild and domestic animal populations, and animal energetics.
The optimization model contained 34 decision variables related to domestic herbivore sales and wild herbivore kills, and 47 constraints requiring 214 non-zero coefficients. The coupling of the simulator to the optimizer required 84 more parameters. In developing the model, they performed no detailed literature review, validation of flow functions, or validation of the total model. An estimated one scientist man-year was spent in discussing the field problem, reviewing the field problem, and developing the initial equations. Compared to other modeling efforts, Swartzan and Van Dyne (1972) stated that their optimization portion was far less complex than others in agricultural decision making, but there had been little or no coupling of simulation to optimization in agricultural research as of 1972. Workers in econometrics, however, were known to combine linear programming with time-series regression, and Van Dyne (1966) had experimented with the heuristic coupling of multiple linear regression with linear programming.
In the latter study, multiple linear regression equations were developed to predict five different vegetative yield and composition variables from data on eleven independent soil and topographic variables. These equations were then used as objective functions or constraints in linear programming models to determine site characteristics for production of maximum protein yield. Research was shown to be needed regarding the use of probabilistic regression equations in a deterministic mode, but, Van Dyne (1966) speculated that the impact of these procedures could be evaluated using Monte Carlo sinulation.
In discussing applications of their approach, Swartzman and Van Dyne (1972) reiterated their opinion that it had definite advantages over dynamic programming and stated that the approach could be used in planning for the individual agricultural enterprise, or on regional or national levels. They listed several evaluative points, summarized below:
Heuristic Programming in Lasting Forests
For unique, developing, dynamic rural systems it is difficult to visualize a specific mathematical modeling approach necessary to accomplish the major project goals. Questions regarding the level of model realism as related to decision needs, whether to produce decision aids from state or regionally- based models, what the final relevant objective functions will be for most land owners, plan book contents, and a host of other items need to be resolved before, or simultaneous with, the specification of necessary equations, simulation models, or optimization techniques. As Van Dyne reported, it takes time to develop such systems, but then they can be used with minor adjustments and changed data for landowners. A systems perspective on design mandates that a major activity to be accomplished relatively early is the establishing owner objectives, both short and long term. Once established, means to the ends can then be identified and related to specific goals.
| Current Interest Rate minus 0.5 | Current Interest Rate | Current Interest Rate plus 0.5 |
|
|---|---|---|---|
| Current Conditions | |||
| Proposed Conditions | |||
| Optimum Conditions |
Using the gross analogy of the region as a factory, sustained profits from almost any factory require a clean, orderly, well-managed place of production. By analogy, high quality outdoor recreation and satisfactory tourism requires a safe, clean, beautiful, stable or improving, non-threatening environment. The region has that now, and it can be improved, then stabilized with intensive management. We are of a notion, somewhat like that of the farmer who "ain't farmin' half as good as I know how." We know of few places where advanced techniques of natural resources are abundantly applied in a sophisticated manner backed by high technology and literally millions of dollars of past studies and research. We do know of special applications of pieces of knowledge and excellent demonstration areas for single phenomena and processes, but we know of no place where modern, sophisticated, decision-making is widely applied, where total systems management attempted. We know of the monumental needs in land and water improvement efforts. We cannot find where cost-effectiveness rules; we see merely efforts in achieving single-minded efficiencies and expenditures.
We'll not likely do research(for at least 5 years) because there are already more findings that need to be used than can be used in that period. Herein is a system design that can work. 
I propose to rely heavily upon geographic information systems of the Conservation Management Institute of Virginia Tech which has produced the above vegetation map of Virginia. Every county has access to other GIS service. We will use satellite-based locations (GPS) in our fieldwork, and these, along with field computers and new forest inventory software, can result in major forest resource development economies. We will use combined simulations and heuristic optimization for the diverse tasks encountered on different Pivotal Tracts.
Above all, we have the clarifying objective of profit maximization (but we hasten to repeat a major difference from typical business practice ... profit from the total land and entrepreneurial system over a 150-year planning period). We have new algorithms for vegetation transitions ("ecological succession") and for scheduling land treatments and timber harvests. We have watershed models, ways to map the upland soils, and ways to estimate and map changing "biodiversity."
Many objectives can be achieved by issuing a single directive to an individual. Others can be achieved by simple communication links, such as preparing for emergencies. Some can be achieved by education and notations about where needs can be met.
We tend to use linear or goal programming because it is now well understood and most decisions are made based on simple linear projections. Of course we will use the best models available that justify their cost, and do not require more information than the answers are likely to be worth or that can be gained in the time available until the decision is to be made.
We employ feedback at most nodes, probably matching well with the much-discussed "adaptive management." We work at the regional scale, but have data about the conditions in very small land units throughout the region. We use the Internet to provide land-use plans to individual landowners, plans that contain the results of computer optimization. We provide analyses of populations of animals as pests (e.g., deer) or as much-sought hunted species. We have access to a vast local as well as international library system and knowledge base. Working with premises of general systems theory, we are building a database about the region as the enterprise matures in concept and application. Waste of information is reduced; "re-discovering" is inefficient. We use advanced prognostic or forecasting software and procedures, even improvements for local conditions and processes. We can exploit the resources of Virginia Tech and other colleges and universities as they may relate to the area, for now we have a clear quantifiable objective (unlike public resource areas), a format, and a process.
We have noticeable payoffs (described above) for individuals as well as the region. As stated several times, there is a belief that "money talks." In Lasting Forests we have designed a system that will provide money and many benefits to citizens. We have designed a means to stop begging for grants and gifts, for ethical concerns, for donations from owners of large land units to restore and preserve the environment. We have dodged the tendency to ask for tax funds. In fact with maturity of the project, funds are provided the County and region. We have found a means to support and perpetuate the benefits from lands if they are placed under technical land easements within existing programs. We can thereby encourage land being productive, land taxes being stable or decreasing, and land not being clearcut and sold to pay the taxes and "get out." Herein we are not advocating creating protective easements, simply the sophisticated management of rural and "wildlands" of the region. We have found a financial base for assuring benefits from regional beauty for families and land owners, as well as from its commodities.
Literature Cited
Hennemuth, R.C. and G.P. Patil. 1983. Implementing statistical ecology initiatives to cope with global resource impacts. p. 374-378 in J.F. Bell, ed. Renewable resource inventories and monitoring changes and trends, Proc. International Conf., Corvallis, Oreg, August (SAF 83-14)
Pinto, P. A., D. G. Dannerbrig, and B. N. Khuaavala. 1978. A heuristic network procedure for the assembly line balancing problem. May. Res.. Log.. 25 (2) :299-307.
Levin, B. I. and C. A.Kirkpatrick. 1978.Quantitative approaches to management. McGraw- Hill, Inc. Nev York. 625 pp.
Swartzman, G. L. and G. N. Van Dyne. 1972. An ecologically based simulator-optimization approach to natural resource planning. Annual Rev. Ecol. and System. 3:347-398.
Taha, H. A. 1971.Operations research. An introduction. MacMillan Publishing Co., Inc. New York. 703 pp.
Van Dyne, G. N. 1966. Application and integration of multiple linear regression and linear programming in renewable resource analyses. J. Range Manage. 19:356-362.
Wagner, H. N. 1970. Principles of management science with applications to executive decisions. Prentice-Hall, New York. 562p.
Wensink, B. B. and R. S.Sovell. 1978. Optimizing tobacco market locations: Part II- Heuristic nodels. Agric. Systems 3: 183-194.
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