Chapter One Summary
Introduction
The key to management science applications is a mathematical
model. A mathematical model is
a quantitative representation, or approximation, of a real problem, and
has the following advantages:
1, it enables an analyst to understand the problem better;
2, It allows the analyst to employ a variety of the mathematical
solution procedures;
3, the modeling itself, if done correctly, can provide
solution to people who must work with the system that is eventually implemented.
A Waiting-Line Example
Descriptive models simply describe a situation, while optimization
or prescription models suggest a desirable course of action.
A Seven
- Eleven store has a single cash register.
The manager is concerned that people are waiting in line too long,
and may be turning away potential customers. The example was used
to illustrate the descriptive and prescriptive models for the purpose
of describing the situation and then recommending a solution to the store’s
waiting line that would maximize profit.
Descriptive Model: This
example is a typical waiting line (queneing)
problem. Input and outputs must
be defined to describe the situation.
There are two inputs and three outputs.
Inputs:
Arrival rate
(customers per minute)
Service rate
(customers per minute)
Maximum customers
(before others go elsewhere)
Outputs
Average number
in line
Average time
(minutes) spent in line
Percentage
of potential arrivals who don’t enter
A mathematical spreadsheet model is developed
to solve for the outputs.
Optimization Model: The
descriptive model fails to reflect any economic solutions, but simply
states the situation. The optimization
model defines three options the manager can take – (1) leave the system
as is, (2) hire a second person to help the first cashier process customers
more quickly, (3) lease a new model of cash register. Based on the three options, a mathematical spreadsheet
model is developed to calculate which option is the most optimal (economically).
Seven-Step Modeling Process
- Problem
Definition The management
scientist fist defines the organization’s problem, including specifying
the organization’s objectives and the parts of the organization that
must be studied before the problem can be solved.
- Data
Collection After
problem definition, the analyst collects data to estimate the value
of parameters that affects the organization’s problem.
- Model
Formulation The analyst
formulates a mathematical model of the problem. The model should, first,
represent the client’s real problem accurately; second, should be simple
enough to allow a mathematical solution; third, should be approximations
of the real world, not mirror images in every last detail.
- Model
Verification Verify
the model and use the model for prediction to test its reliability.
- Selection
of an Alternative Given
a model and a set of alternatives, choose the alternative that best
meets the organization’s objectives.
- Presentation
of the Results Present
the model and the recommendation to the organization.
- Implementation
of the Model Implement
the model and periodically evaluate its reliability.
Successful Management Science Applications
- Citgo Petroleum – A linear programming model was developed
to assist Citgo management not only in optimizing
its refinery operations, but also in improving its supply distribution
marketing system.
- San
Francisco Police – The San Francisco Police Department
(SFPD) developed Police Patrol Scheduling System (PPSS) to assist in
determining schedules that would minimize fatigue and maximize productive
hours for the police force.
- GE
Capital – Models were developed to assist in reducing delinquent accounts
and the costs of processing them.
Why Study Management Science
- Develops
skills in structuring problems and logical thinking
- Increase
quantitative skills
- Master
the use of spreadsheets (Excel)
- Help
develop intuition and indicate where intuition also sometimes falls
short
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