Uses optimization to identify the best alternatives to minimize or maximize some business objectives.

depending on the approach to prescriptive analytics and the type of problem being addressed

indicates that some (or all) of the variables in the formulation must assume only integer values. We refer to such variables as the integer variables in a problem.

are variables that are not required to assume strictly integer values

one approach to finding the optimal integer solution in which you relax, or ignore, the integrality conditions and solve the problem as if it were a standard LP problem where all the variables are assumed to be continuous.

The objective function value for the optimal solution to the ILP problem can never be better than the objective function value for the optimal solution to its LP relaxation.

variables which can assume only two integer values: 0 and 1.

variables which can assume only two integer values: 0 and 1.

All network flow problems can be represented as a

circles in the network flow model

sending nodes

receiving nodes

(can both send to and receive from other nodes in the network)

lines connecting the nodes; indicate the valid paths, routes, or connection between the nodes in a network flow problem

when the lines connecting the nodes in a network flow problem indicate a direction

use to represent the needed net flow (demand) into a given node

use to represent the available net flow (supply) out of a node

NWF problems with each unit that flows from node i to node j incurring some cost, cij.

simple set of rules that applies constructing the constraints for minimum cost network flow problems.

One of the most effective ways to analyze and evaluate decision alternatives.

Set of mathematical relationships and logical assumptions implemented in a computer as a representation of some real-world object, decision problem or phenomenon.

computer model implemented through a spreadsheet.

Field of study that uses computer, statistics, and mathematics to solve business problems. Involves applying the methods and tools of science to management and decision making.

Science of making better decisions” Sometimes referred to as operations research or decision science.

Simplest approach to decision- making

help to illustrate how the various parts of the structure will fit together when it is completed

Assists a driver in analyzing the various routes from one location to another

might use scale models of buildings and bridges to study the strengths of different construction techniques

Uses mathematical relationships to describe or represent an object or decision problem

one that accurately represents the relevant characteristics of the object or decision problem being studied.

There is a gap or disparity between the present situation and some desired state of affairs. Involves gathering a lot of information and talking with many people; sift through all this information and try to identify the root problem/s Requires insight, some imagination, time, and good bit of detective work.

Fundamental differences in the types of problems that a manager may face: Values of the independent variables affecting the problem are under the manager's control; sometimes not. Forms of the functional relationships f(.) relating the variables are well-defined, sometimes not.Fundamental differences in the types of problems that a manager may face: Values of the independent variables affecting the problem are under the manager's control; sometimes not. Forms of the functional relationships f(.) relating the variables are well-defined, sometimes not.

Arise when a seemingly trivial factor serves as a starting point (or anchor) for estimations in a decision-making problem.

How a decision maker views or perceives the alternatives in a decision problem— often involving a win/loss perspective.

constraints that represent a target that a decision- maker wants to achieve

allows us to determine how close a given solution comes to achieving the goal.

represents the level of achievement that the decision maker wants to obtain for the goal

represents the amount by which each goal deviates from its target value

Determine a solution that achieves all the goals as closely as possible

Solution which each goal achieved exactly at the level specified by its target value. All deviational variables in all the goal constraints would equal 0.

sometimes helpful to GP to minimize the maximum deviation from any goal