1. Research Operation / Management science
Introduction
Research Operation / Management science
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Reference
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OR/MS Approach
Operations Research/Management science (OR/MS) uses a scientific approach to solving management problems.
It is used in a variety of organizations to solve many different types of problems.
It encompasses a logical mathematical approach to problem solving.
Management science, also known as operations research, quantitative methods, etc., involves a philosophy of problem solving in a logical manner.
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The OR/MS Process
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5. Definition of the Problem
The OR/MS Process
Identification of a problem that exists (or may occur soon) in a system or organization.
Observation
problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization.
Definition of the Problem
Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.
Model Construction
Models solved using management science techniques.
Model Solution
Actual use of the model or its solution
Model Implementation
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6. Example of Model Construction (1 of 3)
Information and Data:
Business firm makes and sells a steel product  Product costs $5 to produce
Product sells for $20
Product requires 4 pounds of steel to make
Firm has 100 pounds of steel
Business Problem:
Determine the number of units to produce to make the most profit, given the limited amount of steel available.
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7. Example of Model Construction (2 of 3)
Variables: X = # units to produce (decision variable)
Z = total profit (in $)
Model: Z = $20X - $5X (objective function)
4X = 100 lb of steel (resource constraint)
Parameters: $20, $5, 4 lbs, 100 lbs (known values)
Formal Specification of Model:
maximize Z = $20X - $5X
subject to 4X = 100
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8. Example of Model Construction (3 of 3)
Model Solution:
Solve the constraint equation:
4x = 100
x = (100)/4
x = 25 units
Substitute this value into the profit function:
Z = $20x - $5x
= (20)(25) – (5)(25)
= $375
(Produce 25 units, to yield a profit of $375)
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9. Model Building: Break-Even Analysis (1 of 9)
Used to determine the number of units of a product to sell or produce that will equate total revenue with total cost.
The volume at which total revenue equals total cost is called the break-even point.
Profit at break-even point is zero.
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10. Model Building: Break-Even Analysis (2 of 9)
Model Components:
Fixed Cost (cf) - costs that remain constant regardless of number of units produced.
Variable Cost (cv) - unit production cost of product.
Volume (v) – the number of units produced or sold
Total variable cost (vcv) - function of volume (v) and unit variable cost.
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11. Model Building: Break-Even Analysis (3 of 9)
Model Components
Total Cost (TC) - total fixed cost plus total variable cost.
Profit (Z) - difference between total revenue vp (p = unit price) and total cost, i.e.
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12. Model Building: Break-Even Analysis (4 of 9)
Computing the Break-Even Point
The break-even point is that volume at which total revenue equals total cost and profit is zero:
BEP
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13. Model Building: Break-Even Analysis (5 of 9)
Example: Western Clothing Company
Fixed Costs: cf = $10000
Variable Costs: cv = $8 per pair
Price : p = $23 per pair
The Break-Even Point is:
v = (10,000)/(23 -8)
= pairs
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14. Model Building: Break-Even Analysis (6 of 9)
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15. Model Building: Break-Even Analysis (7 of 9)
Break-even model with an increase in price
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16. Model Building: Break-Even Analysis (8 of 9)
Break-even model with an increase in variable cost
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17. Model Building: Break-Even Analysis (9 of 9)
Break-even model with a change in fixed cost
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18. Break-Even Analysis: Excel Solution (1 of 5)
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19. Break-Even Analysis: Excel Solution (2 of 5)
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20. Break-Even Analysis: Excel Solution (3 of 5)
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21. Break-Even Analysis: Excel Solution (4 of 5)
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22. Break-Even Analysis: Excel Solution (5 of 5)
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23. Classification of OR/MS Techniques
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24. Characteristics of Modeling Techniques
clear objective; restrictions on resources and requirements; parameters known with certainty.
Linear Mathematical Programming
results contain uncertainty.
Probabilistic Techniques
model often formulated as diagram; deterministic or probabilistic.
Network Techniques
variety of deterministic and probabilistic methods for specific types of problems including forecasting, inventory, simulation, multicriteria, etc.
Other Techniques
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Business Use of OR/MS
Some application areas:
Interfaces - Applications journal published by Institute for Operations Research and Management Sciences (INFORMS)
Project Planning
Capital Budgeting
Inventory Analysis
Production Planning
Scheduling
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26. Decision Support Systems (DSS)
A decision support system is a computer-based system that helps decision makers address complex problems that cut across different parts of an organization and operations.
Features of Decision Support Systems
Interactive
Use databases & management science models
Address “what if” questions
Perform sensitivity analysis
Examples include:
ERP – Enterprise Resource Planning
OLAP – Online Analytical Processing
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27. Management Science Models Decision Support Systems
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