a mathematical technique used to determine the optimum allocation of resources to maximize an objective function where the problem involves either a sequence of decisions or a situation that can be treated as if the decisions were sequential in time —note kinds of mathematical programs include the following:

—dynamic programming a generalized approach to solving optimization problems in which a sequence or set of interrelated parts (e.g., multistage problems) is solved before the final solution is developed —note dynamic programming problems often deal with a time-based sequence of decisions (e.g., multiple thinnings, construction of roads) that are decomposed and solved; the problems may involve linear or nonlinear relationships

—goal programming a multicriterion mathematical programming formulation designed to minimize the (usually weighted) deviations from preset management targets

—integer linear programming a special case of linear programming in which some or all of the decision variables are constrained to have positive integer values

—linear programming a mathematical model for representing a decision problem characterized by a set of decision variables, a linear objective function of those decision variables representing the system component that is to be maximized or minimized (e.g., harvest volume, present net worth, sediment pollution, and cost), and a set of linear constraints that satisfy the assumptions of additivity, proportionality, determinism, and divisibility —note 1. linear programming assumes that the contribution of all activities to the objective function is the sum of the contribution of each activity (additivity), that all variables are continuous and can have any positive value (divisibility), that the contribution of any activity to the objective function is directly proportional to the level of that activity (proportionality), and that all coefficients can be represented as known with certainty (determinism); linear programming is used to help decide the most profitable combination of products that a given machine, factory, or forest can yield, or the best combination of factors of production or of machines and equipment to produce a given output —note 2. linear programming is used extensively in scheduling periodic harvests based on management objectives; the objective function (e.g., maximize net present value, minimize cost, maximize timber volume) and constraints (e.g., land area, harvest flow) are formulated and solved as linear equations —see assignment problem

—multiple objective programming a mathematical formulation designed to evaluate trade-offs between two or more objectives

—nonlinear programming a mathematical algorithm in which the objective function (e.g., maximize net present value, minimize cost, maximize timber volume) and the constraints (e.g., land area, harvest flow) are formulated and solved as nonlinear equations —note nonlinear programming helps to decide the most profitable combination of products that a given machine, factory, or forest can yield, or the best combination of factors of production or of machines and equipment to produce a given output; it is used less extensively than linear programming in scheduling periodic harvests based on management objectivesThis definition last updated 10/27/2008