Introduction
Management Science is the study of how analytical thinking and scientific method can be used to help decision-making. The key to management science application is a mathematical model, which is a quantitative representation, or approximation, of a real problem.
Advantages of mathematical models:
- It helps to define the scope of the problem, the possible solutions, and the data requirements
- It allows the analyst to employ a variety of the mathematical solution procedures
- Correct modeling process often helps to “sell” the solution to the people who must work with the system
Simple Waiting-Line Example
Descriptive model: mathematical relationships that represent a real situation
à Relationships between the inputs and outputs
|
Inputs |
|
|
Arrival rate (customers per minute) |
0.5 |
|
Service rate (customers per minute) |
0.4 |
|
Maximum customers (before others go elsewhere) |
5 |
|
|
|
|
Outputs |
|
|
Average number in line |
2.22 |
|
Average time (minutes spent) in line |
6.09 |
|
Percentage of potential arrivals who don't enter |
27.10% |
Optimization model: a model that suggests desirable course of action (alternatives are presented)
|
Inputs |
Decision 1 |
Decision 2 |
Decision 3 |
|
Arrival rate (customers per minute) |
0.5 |
0.5 |
0.5 |
|
Service rate (customers per minute) |
0.4 |
0.556 |
0.8 |
|
Maximum customers (before others go elsewhere) |
5 |
5 |
5 |
|
|
|
|
|
|
Outputs |
|
|
|
|
Average number in line |
2.22 |
1.41 |
0.69 |
|
Average time (minutes spent) in line |
6.09 |
3.22 |
1.42 |
|
Percentage of potential arrivals who don't enter |
27.10% |
12.60% |
3.80% |
Modeling vs. Models
Model: more of memorizing the detail of a particular model. For example, the simplest of all models is linear or straight line model, which describes the relationship between two variables.
Modeling: a process where we abstract the essence of a real problem into a model.
7-Step Modeling Process
-
Define the problem
For example, minimizing the total costs associated with the operation of the store’s cash register
-
Observe the System and Collect Data to estimate the value of parameters that affect the problem
-
Formulate a Model
Analytic model can be used as an equation to relate parameters or inputs, while Simulation model can be to approximate the behavior of the actual system
-
Verify the Model and Use the Model for Prediction
Determine whether the model developed is an accurate representation of reality
-
Select a Suitable Alternative that best meets the objectives
- Present the Results of the Study to the Organization
-
Implement and Evaluate Recommendations
Implemented system must be monitored constantly to ensure that the model meets the objectives
Why study Management Science
· Modeling approach forces us to think logically about the relationships between variables
· Management Science is all about the quantitative skills can be sharpened immensely
· Spreadsheets can be used in the management science to understand the problem, as represented by the models, better. Proficient spreadsheet skill is a plus for solving large and complex problems faced by the business world
· By studying many models and examining their solutions, one can sharpen one’s intuition considerably
Management Science Software
- Premium Solver: Can be used to solve problems with genetic algorithm that is different from the algorithms used by the built-in Solver
- Palisade Decision Tools Suite
a. @Risk: Probability functions that can be used to perform simulation
b. Precision Tree: Add-in that can be used to analyze decision problems with uncertainty
c. Top Rank: What-if Analysis that determines the values in a model that has greatest impact on output.
d. BestFit: A program that finds the distribution that best fits the data
e. RiskView: Tool that can be used for viewing, creating and assessing probabilities graphically
f. StatPro: Statistics add-in that enhances the statistical capabilities of Excel
