Programacion lineal

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JULY, 1983


James E. Hotvedt
Forest management and planning is complex, involving the application of many scarce and diverse resources to the production and maintenance of a multitude of products and services from the forest over a relatively long period of time. The forestmanager hopes to produce a balanced mix of products and services, with the mixture depending upon the landowner's objectives. Although many objectives are complementary in nature, others are competitive, with some mutually exclusive. As a result, allocating the resource manager's scarce and diverse resources among the alternative and possibly competitive products and services becomes a complexproblem. Timber management planning is normally an integral part of managing a forest, and two traditional tasks of timber management planning are establishing harvest schedules (cutting budgets) and developing a regulated forest. The harvest-scheduling problem involves determining what, where, when, and how much to cut in order to ensure a smooth transition from an unregulated to a regulated foreststructure, while at the same time meeting short-term requirements, objectives, and constraints. A regulated forest is a forest with age and size classes represented in such a proportion that a stable periodic yield of products and services may be obtained over time (Davis). The regulation problem involves selecting and developing a long-term, steadystate forest structure, the regulated forest (Dress).There are, in general, many ways to manipulate existing and future forest stands to solve the regulation and harvest-scheduling problems. As a result, many forest product companies and public forest management agencies have adopted advanced planning techniques for developing harvest schedules and determining long-term, steady-state forest structures. This has been encouraged by increasedcompetition for available stumpage, anticipated increases in stumpage costs, interest in a stable wood supply, and the potential for increased financial returns from fee and leased lands. Advanced forest management planning techniques developed over the last two decades have incorporated operations research methodologies, with linear programming (LP) the methodology most commonly used. Early linearprogramming applications to timber management planning (e.g., Theiler; Loucks; Kidd et al.; Ware and Clutter; and Navon) were developed, in general, to aid in the systematic selection of optimal sets of forest-stand treatments and harvest schedules. Present net worth maximization, harvest volume maximization, and cost minimization, all over relatively long periods of time, have all been specified inobjective functions. Economic analyses incorporating linear programming are often based, in part, on the implied assumption that economic man has but one objective. Indeed, the classical theory of the firm postulates "rational" economic man as an optimizer (Henderson and Quandt), whether it be output maximization subject to a cost constraint, cost minimization subject to an output constraint, orprofit maximization. This view of economic man has been questioned, however (Arrow; Cyert and March; Lane; Margolis; Simon). Firms do not seek to satisfy a unidimensional goal, but rather seek to satisfy a multidimensional goal set. A problem associated with using linear programming for solving multiobjective problems is that it requires that all incommensurable goals be transformed into a common unitof measure (usually dollars), and this may often be difficult or impossible to achieve. The commonly used approach for resolving this problem has been to select one goal for specification in the objective function, while all other goals are assigned minimal or maximal desired levels of achievement and placed in the constraint set. Since these latter goals are not optimized, however, conflicts...
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