APICS Dictionary

Terms Related to Operations Research/Management Science

Several other terms could have been included for areas that are often considered to be an integral part of Operations Management itself, especially terms related to project models (critical path scheduling and PERT), forecasting, inventory models, waiting line (queuing) models, and probability and statistics.

Algorithm - A prescribed set of well-defined rules or processes for solving a problem in a finite number of steps, e.g., the full statement of the arithmetic procedure for calculating the reorder point.

Box-Jenkins model (DBB note - an advanced approach for forecasting often used by OR/MS analysts) - A forecasting approach based on regression and moving average models. The model is based not on regression of independent variables, but on past observations of the item to be forecast at varying time lags and on previous error values from forecasting.

Branch and bound - Operations research models for determining optimal solutions based on the enumeration of subsets of possible solutions, which implicitly enumerate all possible solutions.

Break-even point - The level of production or the volume of sales at which operations are neither profitable nor unprofitable. The break-even point is the intersection of the total revenue and total cost curves.

Constrained optimization - Achieving the best possible solution to a problem in terms of a specified objective function and a given set of constraints.

Constraint - Any element or factor that prevents a system from achieving a higher level of performance with respect to its goal. Constraints can be physical, such as a machine center or lack of material, but they can also be managerial, such as policy or procedure.

Decisions under certainty - Simple decisions that assume complete information and no uncertainty connected with the analysis of decisions.

Decisions under risk - A decision problem in which the analyst elects to consider several possible futures, the probabilities of which can be estimated.

Decisions under uncertainty - Decisions for which the analyst elects to consider several possible futures, the probabilities of which cannot be estimated.

Decision table - A means of displaying logical conditions in an array that graphically illustrates actions associated with stated conditions.

Decision tree - A method of analysis that evaluates alternative decisions in a tree-like structure to estimate values and/or probabilities. Decision trees take into account the time value of future earnings by using a rollback concept. Calculations are started at the far right-hand side, then traced back through the branches to identify the appropriate decision.

Deterministic models - Models where no uncertainty is included, e.g., inventory models without safety stock considerations.

Dynamic programming - A method of sequential decision making in which the result of the decision at each stage affords the best possible means to exploit the expected range of likely (yet unpredictable) outcomes in the following decision-making stages.

Endogenous variable - A variable whose value is determined by relationships included within the model.

Exogenous variable - A variable whose value is determined by considerations outside the model in question.

Fixed cost - An expenditure that does not vary with the production volume; for example, rent, property tax, and salaries of certain personnel.

Heuristic - A form of problem solving in which the results or rules have been determined by experience or intuition instead of optimization.

Incremental analysis - A method of economic analysis in which the cost of a single additional unit is compared to its revenue. When the net contribution of an additional unit is zero, total contribution is maximized.

Incremental cost - 2) Additional cost incurred as a result of a decision.

Linear programming - Mathematical models for solving linear optimization problems through minimization or maximization of a linear function subject to linear constraints. For example, in blending gasoline and other petroleum products, many intermediate distillates may be available. Prices and octane ratings as well as upper limits on capacities of input materials that can be used to produce various grades of fuel are given. The problem is to blend the various inputs is such a way that 1) cost will be minimized profit (will be maximized), 2) specified optimum octane ratings will be met, and 3) the need for additional storage capacity will be avoided.

Management science - Syn: operations research.

Marginal cost - The incremental costs incurred when the level of output of some operation or process is increased by one unit.

Marginal pricing - Pricing products at a markup over the marginal cost of producing the next item. Marginal costs generally include the variable cost of producing and selling an additional item.

Marginal revenue - The incremental sales dollars received when the level of output of some operation is increased by one unit.

Mathematical programming - The general problem of optimizing a function of several variables subject to a number of constraints. If the function and constraints are linear in the variables and a subset of the constraints restricts the variables to be nonnegative, we have a linear programming problem.

Matrix - A mathematical array having one, two, and sometimes more dimensions, into which collections of data may be stored and processed.

Model - A representation of a process or system that attempts to relate the most important variables in the system is such a way that analysis of the model leads to insights into the system. Frequently, the model is used to anticipate the result of a particular strategy in the real system.

Monte Carlo simulation - A subset of digital simulation models based on random or stochastic processes.

Network - 2) A graph consisting of nodes connected by arcs.

Node - One of the defining points of a network - a junction point joined to some or all of the others by arcs.

Noise - The unpredictable or random difference between the observed data and the "true process."

Nonlinear programming - Programming similar to linear programming but incorporating a nonlinear objective function and linear constraints or a linear objective function and nonlinear constraints or a nonlinear objective function and nonlinear constraints.

Objective function - The goal or function that is to be optimized in a model. Most often it is a cost function that should be minimized subject to some restrictions or a profit function that should be maximized subject to some restrictions.

Operations research - 1) The development and application of quantitative techniques to the solution of problems. More specifically, theory and methodology in mathematics, statistics, and computing are adapted and applied to the identification, formulation, solution, validation, implementation, and control of decision-making problems. 2) An academic field of study concerned with the development and application of quantitative analysis to the solution of problems faced by management in public and private organizations. Syn: management science.

Optimization - Achieving the best possible solution to a problem in terms of a specified objective function.

Parameter - A coefficient appearing in a mathematical expression, each value of which determines the specific form of the expression. Parameters define or determine the characteristics of behavior of something, as when the mean and standard deviation are used to describe a set of data.

Path - The physically continuous, linear series of connected activities throughout a network.

Probabilistic demand models - Statistical procedures that represent the uncertainty of demand by a set of possible outcomes (i.e., a probability distribution) and that suggest inventory management strategies under probabilistic demands.

Random - Having no predictable pattern. For example, sales data may vary randomly about some forecast value with no specific pattern and no attendant ability to obtain a more accurate sales estimate than the forecast value.

Random numbers - A sequence of integers or group of numbers (often in the form of a table) that show absolutely no relationship to each other anywhere in the sequence. At any point, all values have an equal chance of occurring, and they occur in an unpredictable fashion.

Risk analysis - A review of the uncertainty associated with the research, development, and production of a product. D.B. Bandy's definition: Risk Analysis Simulation - a synonym for Monte Carlo simulation.

Search models - Operations research models that attempt to find optimal solutions with adaptive searching approaches.

Sensitivity analysis - A technique for determining how much an expected outcome or result will change in response to a given change in an input variable. For example, given a projected level of resources, what would be the effect on net income if variable costs of production increased 20%?

Simplex algorithm - A procedure for solving a general linear programming problem.

Simulation - 1) The technique of using representative of artificial data to reproduce in a model various conditions that are likely to occur in the actual performance of a system. It is frequently used to test the behavior of a system under different operating policies. 2) Within MRP II, using operational data to perform "what-if" evaluations of alternative plans to answer the question, Can we do it? If yes, the simulation can then be run in the financial mode to help answer the question, Do we really want to? See: what-if analysis.

Stochastic models - Models where uncertainty is explicitly considered in the analysis.

Suboptimization - A problem solution that is best from a narrow point of view but not from a higher or overall company point of view. For example, a department manager who would not have employees work overtime to minimize the department's operation expense may cause lost sales and a reduction in overall company profitability.

Sunk cost - 1) The unrecovered balance of an investment. It is a cost, already paid, that is not relevant to the decision concerning the future that is being made. Capital already invested that for some reason cannot be retrieved. 2) A past cost that has no relevance with respect to future receipts and disbursements of a facility undergoing an economic study. This concept implies that since a past outlay is the same regardless of the alternative selected, it should not influence the choice between alternatives.

Time series analysis - Analysis of any variable classified by time in which the values of the variable are functions of the time periods.

Transportation method - A linear programming model concerned with minimizing the costs involved in supplying requirements at several locations from several sources with different costs related to the various combinations of source and requirement locations.

Uncertainty - Unknown future events that cannot be predicted quantitatively within useful limits; e.g., an accident that destroys facilities, a major strike, or an innovation that makes existing products obsolete.

Variable - A quantity that can assume any of a given set of values. Ant: constant.

Variable cost - An operating cost that varies directly with a change of one unit in the production volume, e.g., direct materials consumed, sales commissions.

Wagner-Whitin algorithm - A mathematically complex, dynamic lot-sizing technique that evaluates all possible ways of ordering to cover net requirements in each period of the planning horizon to arrive at the theoretically optimum ordering strategy for the entire net requirements schedule. See: discrete order quantity, dynamic lot sizing.

What-if analysis - The process of evaluation alternate strategies by answering the consequences of changes to forecasts, manufacturing plans, inventory levels, etc. See: simulation.