Management science is the

application of a scientific approach to solving management problems in order to help managers make better decisions.

___ is a recognized and established discipline in business

Management Science.

Management Science is also referred to

operations research, quantitative methods, quantitative analysis, and decision sciences. It encompasses a logical approach to problem solving.

The steps of the scientific method are

observation, problem definition, model construction, model solution, and implementation.

A management scientist is a

person skilled in the techniques of management science and trained to identify problems and who has been hired specifically to solve problems using management science techniques.

A model is

an abstract mathematical representation of a problem situation. It can be in form of a chart, graph, but most frequently consists of a set of mathematical relationships. It is a functional relationship that includes variables, parameters, and equations.

A variable is a

symbol used to represent an item that can take on any value. The term variable is used because no set numeric value has been specified for these items

Dependent variable

is called so because it is dependent on the number of units sold.

Independent variable

because the number of units sold is not dependent on anything else.

Parameters are

known, constant values that are often coefficients of variables in equations. They usually remain constant. Parameter values are derived from data.

Data

are pieces of information from the problem environment.

A model is a

functional relationship that includes variables, parameters, and equations. A functional relationship is also called function and relationship.

Objective function

is the profit equation in the new model.

The resource equation is a

constraint.

Decision variable

is also known as x.

A management science technique usually applies to a

specific model type.

Some management techniques provide

descriptive results: results that describe the system being modeled.

The final step in the management science process for problem solving is

implementation.

Implementation is the

actual use of the model once it has been developed or the solution to the problem the model was described to solve.

Break even analysis:

or also called profit analysis: it is used to determine the number of units to be produced and sold, as the dollar volume of sales, or as a percentage of total capacity available.

The three components of break-even analysis are

volume, cost, and profit. Volume is the level of sales or production by a company. It can be expressed as the number of units produced and sold, as the dollar volume of sales, or as a percentage of total capacity available.

Fixed costs:

are generally independent of the volume of units produced and sold. They remain constant, regardless of how many units are produced within a given range. They can include such items as rent on plant and equipment, taxes, staff and management techniques.

Variable costs

are determined on a per-unit basis. They depend on the number of units produced. Variable costs include such items as raw materials and resources, direct labor, packaging, material handling, and freight.

Total Cost (TC)=

equals the fixed cost plus the variable cost per unit multiplied by volume.

Profit is the

difference between total revenue (volume multiplied by price) and total cost.

The break even point is the volume that equates total revenue with total cost where

profit is zero.

The study of changes on a management science model is

sensitivity analysis. How sensitive the model is to changes.

In general, an increase in price lowers the break-even point,

all other things constant.

Total variable costs

are a function of the volume and the variable cost per unit.

Sensitivity analysis

sees how sensitive a management model is to changes.

In general an increase in price

lowers the break-even point, all other things held constant.

In general, an increase in variable costs

will increase the breakeven point, all other things held constant.

In general, an increase in fixed costs will

increase the breakeven point, all other things held constant.

A deterministic technique assumes

certainty in the solution. i.e. decision analysis.

A decision support system (DSS)

is a computer based system that helps decision makers address complex problems that cut across different parts of an organization and operations.

Linear programming

is a model that consists of linear relationships representing a firm's decisions, given an objective and resource constraint. We want to maximize profit and minimize costs. The three steps are that the problem must be identified as being solvable by linear programming, the unstructured problem must be formulated as a mathematical model, the model must be solved by using mathematical techniques.

Linear programming consists of

decision variables, an objective function, and model constraints which consist of decision variables and paramaters.

Decision variables

are mathematical symbols that represent levels of activity.

The objective function

is a linear relationship that reflects the objective of an operation. It always consists of maximizing or minimizing some value.

The model constraint is

a linear relationship that represents a restriction on decision making.

Parameters are

numerical values that are included in the objective functions and constraints.

Nonnegativity constraints

restrict the decision variables to zero or positive values.

A feasible solution

does not violate any of the constraints.

An infeasible problem

violates at least one of the constraints.

Graphical solutions are limited

to linear programming problems with only two decision variables.

Multiple optimal solutions

can occur when the objective function is parallel to a constraint line.

A slack variable is added to a <_ constraint to

convert it to an equation (=)

A slack variable represents unused

resources. It also contributes nothing to the objective function value.

A surplus variable is subtracted from a >_ constraint to convert it to

an equation (=).

A surplus variable represents an

excess above an above a certain restraint level.

Alternate optimal solutions

are at the endpoints of the constraint line segment that the objective function parallels.

An infeasible problem has no

feasible solution area; every possible solution solution point violates one or more constraints.

In an unbounded problem,

the objective function can increase indefinitely without reaching a maximum value. The solution space is not completely closed in,

Two components of a linear programming model are an

objective function, decision variables, and constraints.

Proportionality

means the slope of a constraint or objective function line is constant.

The terms in the objective function or constraints are

additive.

The values of decision variables are

continuous or divisible.

All model parameters are assumed to be known with

certainty.

Standard form

requires all variables to be to the left of the inequality and numeric values to the right.

A double sub-scripted variable

is simply another form of variable name.

In a balanced transportation model,

supply equals demand such that all constraints are equalities.

In an unbalanced transportation,

supply does not equal demand, and one set of constraints is <_.

Profit is maximized in the objective function by

subtracting cost from revenue.

Shadow price is the

marginal economic values of one additional unit of a resource.