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1. Optimization Techniques

2. What is Operations Research?
• It is a discipline that deals with the application
of advanced analytical methods to help make
better decisions.
• Concerned with determining the maximum
(profit, performance, or yield) or minimum
(loss, risk, or cost) of some real world
objective.

3. Applications
• Manufacturing (determining the product mix)
• Scheduling (airlines, buses)
• Assignment (assigning crew to flights,
employees to projects)
• Facility location (deciding most appropriate
location for factory ware house)
• Health services (information and supply chain
management)

4. Mathematical Operations Research
Models
Identification of three main components:
1. Decision alternatives (decision variables)
2. Restrictions/constraints
3. Objective function

5. Operations Research Techniques
• Linear programming
• Dynamic programming
• Integer programming
• Non-linear programming
• Goal programming
• Network programming

6. Simulation Modeling
• An alternative approach to modeling complex
systems
• Imitates the actual behavior of the real system
• Flexible as compared to mathematical
modeling

7. Principal Phases for Implementing OR
1. Definition of the problem
2. Construction of the model
3. Solution of the model
4. Validation of the model
5. Implementation of the solution

8. Linear Programming (LP)
• A mathematical modeling technique designed
to optimize the usage of limited resources.
• Maximizing or minimizing the linear objective
function subjected to linear constraints

9. Construction of LP Model
• Decision variables that we seek to determine
• Objective that we want to optimize
• Constraints that we need to satisfy

10. Linear Programming Problem 1
Consider a chocolate manufacturing company which
produces only two types of chocolate – A and B. Both the
chocolates require Milk and Choco only. To manufacture
each unit of A and B, following quantities are required:
• Each unit of A requires 1 unit of Milk and 3 units of Choco
• Each unit of B requires 1 unit of Milk and 2 units of Choco
The company kitchen has a total of 5 units of Milk and 12
units of Choco. On each sale, the company makes a profit
of
• Rs 6 per unit A sold
• Rs 5 per unit B sold.
Now, the company wishes to maximize its profit. How
many units of A and B should it produce respectively?

11. Linear Programming Problem 2
• A firm uses lathes, milling machines and grinding
machines to produces two parts. The following
table represents the machining time required for
each part, the machining time available on
different machines, and the profit for each part.

12. Type of Machine Machining time required for
machined parts (minutes)
Max. time
available per
week (minutes)
Part I Part II
Lathe machine 12 6 3000
Milling Machine 4 10 2000
Grinding machine 2 3 900
Profit per unit Rs. 40 Rs. 100
Formulate the linear programming problem to find
the number of parts I and II to be manufactured in
order to maximize profit.

13. Linear Programming Problem 3
• Food X contains 6 units of vitamin A per gram
and 7 units of vitamin B per gram and costs
Rs. 12 per gram. Food Y contains 8 units of
vitamin A per gram and 12 units of vitamin B
per gram and costs Rs. 20 per gram. The daily
minimum requirement of vitamin A and
vitamin B is 100 units and 120 units
respectively. Find the minimum cost of
product mix

14. Problem 4
• Reddy Mikks produces both interior and exterior paints
from two raw materials, M1 and M2.The following table
provides the basic data of the problem:
• A market survey indicates that the daily demand for
interior paint cannot exceed that for exterior paint by
more than 1 ton. Also, the maximum daily demand for
interior paint is 2 tons. Reddy Mikks wants to determine
the optimum (best) product mix of interior and exterior
paints that maximizes the total daily profit.
Tons of raw material per ton of Maximum
daily
availability
(tons)
Exterior Paint Interior Paint
Raw Material, M1 6 4 24
Raw Material, M2 1 2 6
Profit per ton
($1000)
5 4

15. Problem 5
• Ozark Farms uses at least 800 lb of special feed
daily. The special feed is a mixture of corn and
soybean meal with the following compositions:
• The dietary requirements of the special feed are
at least 30% protein and at most 5% fiber. Ozark
Farms wishes to determine the daily minimum-
cost feed mix.
Feedstuff
lb per lb of feedstuff
Cost
($/lb)
Protein Fiber
Corn 0.09 0.02 0.30
Soyabean
meal
0.60 0.06 0.90