Management science

● is a scientific approach to solving management problems.

● is the application of a scientific approach to solving management problems to help
managers make better decisions.
● is a recognized and established discipline in business.
● can be used in a variety of organizations to solve many different types of problems.
● science (also referred to as operations research, quantitative methods, quantitative
analysis, decision sciences, and business analytics) is part of the fundamental
curriculum of most programs in business.
● encompasses a logical approach to problem solving.
● can be either a recommended decision or information that helps a manager make a
decision.
Management science is an art.

The steps of the scientific method are

(1) observation,
(2) problem definition,
(3) model construction,
(4) model solution, and
(5) implementation.

(1) Observation
- The first step in the management science process is the identification of a problem that
exists in the system (organization).
- The system must be continuously and closely observed so that problems can be
identified as soon as they occur or are anticipated.
- Management scientist is the person skilled in the techniques of management science
and trained to identify problems.
- They are hired specifically to solve problems using the management science
techniques.
-The system must be continuously and closely observed so that problems can be
identified as soon as they occur or are anticipated.

(2) Definition of the Problem

- Once it has been determined that a problem exists, the problem must be clearly and
concisely defined.
- Improperly defining the problem can easily result in no solution or an inappropriate
solution.

(3) Model Construction

- A management science model is an abstract representation of an existing problem
situation.
- It can be in the form of a graph or chart, but most frequently, it consists of a set of
mathematical relationships.
-A variable is a symbol used to represent an item that can take on any value. In this
example Z is the dependent variable and X is the independent variable.

Parameters
- are known, constant values that are often coefficients of variables in equations.
- The equation as a whole is known as a functional relationship. If only one functional
relationship exists, it is also the model. However, this model does not replicate a
problem.
Data are pieces of information from the problem environment.
(4) Model Solution
- Once models have been constructed, they are solved using the applicable
management science technique. A management science solution technique usually
applies to a specific type of model.
- Some management science techniques do not generate an answer or a recommended
decision. Instead, they provide descriptive results that describe the system being
modeled.

(5) Implementation
- The final step in the management science process for problem solving
- It is the actual use of the model once it has been developed or the solution to the
problem the model was developed to solve.
- This is a critical but often overlooked step in the process.

Business analytics uses large amounts of data with management science techniques
and modeling to help managers makes decisions.

Developing Analytical Career Skills

Critical thinking
- purposeful and goal directed thinking used to define and solve problems, make
decisions and form judgements related to a particular situation.

Collaboration
- The necessary skill for decision scenarios that take place in a project team-based
environment.

Information Technology and Computing Skills

- Important attributes to employers because of the reliance on computer software to
solve decision problems.

Data Literacy
- The ability to access, interpret, manipulate, summarize, and communicate data in a
decision-making situation.

Break-even Analysis or Profit Analysis

- The modeling technique used to determine the number of units to sell or produce that
will result in zero profit (total revenue equals total cost).
- The point where total revenue equals total cost is called the break-even point.
- The break-even point gives a manager a point of reference in determining how many
units will be needed to ensure a profit.

Components of Break-Even Analysis

(1) Volume
- the level of sales or production by a company
- can be expressed as the number of units (i.e., quantity) produced and sold, as the
peso volume of sales, or as a percentage of total capacity available

The break-even point is the volume (v) that equates total revenue with total cost where
profit is zero.
 (2) Cost
Total cost of an operation is computed by summing total fixed costs and total variable
costs.

● Fixed costs
- costs that are generally independent of the volume of units produced and sold (i.e., it
remains constant)
- rent on plant equipment, taxes, staff and management salaries, insurance, advertising,
depreciation, heat and light, and plant maintenance
● Variable costs
- costs that are determined on a per unit basis
- depends on the number of units produced
- raw materials cost, direct labor, packaging, material handling, and freight
-Total variable costs are a function of the volume and the variable cost per unit.

(3) Profit
- the difference between total revenue and total cost
- Total Revenue is the volume multiplied by the selling price per unit

Management Science Modeling Techniques

Linear Programming
- a model that consists of linear relationships representing a firm’s decision(s), given an
objective and resource constraints
- derives its name from the fact that the functional relationships in the mathematical
model are linear, and the solution technique consists of predetermined mathematical
steps—that is, a program.

Probabilistic Techniques
- based on application of statistics for probability of uncontrollable events as well as risk
assessment of decision
- In this technique, “risk” means uncertainty for which the probability of distribution is
known

Network Techniques
- These models offer a pictorial representation of the system under analysis.
- One example is making a network diagram to determine the shortest route among a
number of different routes from a source to a destination

Other Techniques
- Other techniques that overlap several categories or they may be unique

Business Usage of Management Science Techniques

The most frequently used techniques in business are linear and integer
programming, simulation, network analysis (including critical path method/project
evaluation and review technique [CPM/PERT]), inventory control, decision analysis, and
queuing theory, as well as probability and statistics.

Areas of application include the following:

(1) project planning, (2) Capital budgeting, (3) Production planning, (4) Inventory
analysis, (5) Scheduling, (6) Marketing Planning, (7) Quality control, (8) Plant Location,
(9) Maintenance Policy, (10) Personnel Management, (11) Product Demand
Forecasting, and others.
Sensitivity analysis sees how sensitive a management model is to changes.
Sensitivity analysis can be performed on all management science models in one form or
another.

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 break-even point, all
other things held constant.

In general, an increase in fixed costs will increase the break-even point, all other
things held constant.

LINEAR PROGRAMMING

Objectives of a business frequently are to maximize profit or minimize cost.

Linear programming is a model that consists of linear relationships representing a

firm’s decision(s), given an objective and resource constraints.

Decision variables are mathematical symbols that represent levels of activity.

The objective function is a linear mathematical relationship that reflects the objective
of an operation. that describes the objective of the firm in terms of the decision
variables.

A 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.

A linear programming model consists of decision variables, an objective function,

and constraints.

Nonnegativity constraints restrict the decision variables to zero or positive values.

A feasible solution does not violate any of the constraints.The feasible solution
area is an area on the graph that is bounded by the constraint equations.

An infeasible problem violates at least one of the constraints.

Graphical solutions are limited to linear programming problems with only two
decision variables.

The graphical method provides a picture of how a solution is obtained for a linear
programming problem.
The optimal solution is the best feasible solution.

The optimal solution point is the last point the objective function touches as it leaves
the feasible solution area.

Extreme points are corner points on the boundary of the feasible solution area.

Constraint equations are solved simultaneously at the optimal extreme point to

determine the variable solution values.

The slope is computed as the “rise” over the “run.”

Sensitivity analysis is used to analyze changes in model parameters.

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.

A slack variable contributes nothing to the objective function value.

The three types of linear programming constraints are <=, =, >=

In a minimization problem the boundary of the feasible solution area closest to the
origin contains the optimal extreme point.

A surplus variable is subtracted from a >= constraint to convert it to an equation (=).

A surplus variable represents an excess above a constraint requirement level.

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

Multiple optimal solutions provide greater flexibility to the decision maker.

In an unbounded problem the objective function can increase indefinitely without

reaching a maximum value.

The solution space is not completely closed in.

Properties of Linear Programming Models

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.

Summary of the Graphical Solution Steps

The steps for solving a graphical linear programming model are summarized here:
1. Plot the model constraints as equations on the graph; then, considering the
inequalities of the constraints, indicate the feasible solution area.
2. Plot the objective function; then, move this line out from the origin to locate the
optimal solution point.
3. Solve simultaneous equations at the solution point to find the optimal solution values.