MATHEMATICAL PROGRAMMING
Mathematical programming (MP) refers to a class of analytical (algebraic) methods that can find the best way to achieve a given objective while complying with a set of constraints. MP models determine the optimal allocation of economic resources among competing alternatives within an operational system. Since this task is precisely the sine qua non of professional management, MP constitutes a pivotal element in the study of rational decision making. The term programming as used here means systematic planning. Thus MP stands for “planning a decision mathematically.”
In addition to the obvious practical benefit of generating optimal solutions, MP provides a sound theoretical basis for properly understanding the broader implications inherent to managerial decision making in general. Certain MP models depict the consequences of alternative courses of action by quantifying the opportunity costs of scarce system resources. Managers are thus made aware of the value forgone by not making optimal decisions. In highly competitive, information-rich environments such as contemporary markets, satisficing is simply not good enough. MP offers a way to avoid the pitfalls associated with the satisficing criterion by providing a comprehensive view of the decision problem that can assist managers in attaining a solid competitive advantage.
MP comprises a variety of paradigms (theoretical frameworks) tailored to different kinds of problems. The most widely used variant is linear programming (LP), a form of MP where the objective and all the constraints are expressed as linear functions. Other variants include integer programming (IP), for problems requiring integer solutions; nonlinear programming (NLP), where the objective and/or one or more constraints are nonlinear functions; and goal programming (GP), for problems with multiple objectives.
Advances in computer technology have brought MP to the forefront of the managerial stage. Any personal computer with a full-featured spreadsheet program, such as Excel or Lotus 1-2-3 or Quattro Pro, is quite capable of solving sophisticated constrained optimization problems. Consequently, any manager with a working knowledge of MP is in a position to exploit the power of these normative models and thereby enjoy a decisive advantage over those competitors who refrain from using these methods.
The page System Concepts is recommended as preliminary reading. This Mathematical Programming module consists of the following sections:
LINEAR PROGRAMMING
Terms
Goal programming – a class of optimization methods designed to handle problems with more than one objective.
Integer programming – a class of optimization methods designed for problems where solutions must be integer valued.
Linear programming – a class of optimization methods for solving problems where all model functions (objective and constraints) are linear.
Mathematical programming – a body of theoretically grounded algorithms that seek the optimal (maximum or minimum) value of an objective function while satisfying a set of constraints.
Nonlinear programming – a class of optimization methods intended for problems where one or more model elements (objective function or constraints) are not linear.
Normative model – a formal representation of a system that determines a recommended course of action or norm (often called prescriptive model).
Opportunity cost – net value forgone due to not allocating system resources optimally.
Satisficing – decision-making behavior where, instead of trying to optimize system performance, a level of aspiration is set either subjectively or heuristically and no further effort is expended in exceeding that level of performance once a minimally acceptable solution is found (term coined by Herbert A. Simon).
Operations Research
Optimization Theory
Management Science
Operations Research
Optimization
Opportunity Cost
Satisficing
Systems Analysis
Stochastic Programming
