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Operations Research
What we expect to learn
Formulate managerial problems to optimize decision making
To be able to apply correct OR-techniques to solve such
aproblem
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Operations Research
I. Linear programming
II. Sensitivity analysis
III. Special cases of LPP
IV. Multicriteria decision making
V. Integer programming
VI. Network flow
VII. Queuing theory
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Course coverage
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Operations Research
Linear programming
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Caselet: Indian House works Limited.
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QUESTION 1:
Do you agree with the view of the new trainee ?Support your
decision.
What are the decision variables?
What is the objective? objective function? What are the
Constraints?
What do you mean by non-negativity restrictions?
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Diet Problem
The Central Canteen at Manipal Hospital (KMC) has to prepareat
least 800 kg of a special nutrition-rich dish for surgeonsevery
day. This special dish is a mixture of corn and soya beanpaste,
which in turn contains some proportions of protein and
fiber in them. While corn contains 9% protein and 2% fiber,soya
bean paste contains 60% protein and 6% fiber. It is alsoknown that
corn and soya bean paste cost Rs. 30 and Rs. 90per kg respectively.
The dietary requirements of the specialdish are that it must
contain at least 30% protein and at most
5% fiber.
What would be the mix so that the canteen can minimizecost?
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Optimization Techniques in Graphical
method
End point enumeration method:
Isoprofit (cost) function line:
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Graphical solution to Exercise 1.
Variable x
Variable y
What is the solution space?
What is the Feasibility region?
Feasible solution?
Optimal solution?
D(4,0)
A(0,6)
E(6,0)
G(0,8)
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C(4, 8/3)
B(3/2, 6)
F(10,0)(0, 0)
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Extreme Point Theorem:
If an LPP has a feasible region, then the optimal
solution lies at one or more of the extreme points of
the LPP. It never lies in the interior region.
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Principle of convexity
A convex region is one in which all the points on a
line joining any two points within the region, also lie
within the same region.
Realization:If an LPP has a feasible region, then it is
always
convex
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Infeasibility:
Problem 2:
Max Z= 20x + 30y s.t2x + y 40, 4x - y 20, x 30, x, y
positive.
Unboundedness: Problem 3:
Max Z = 10x +20y s.t
2x +4y 16x + 5y 15
x, y 0
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Class Exercise:
A retired person wants to invest an amount of Rs 30000 in
fixed income securities. His broker recommends investing in
two bonds: Bond L&T yielding 9.5% and bond ABC yielding10%.
After some consideration he decides to invest at most Rs
12000 in Bond ABC and at least Rs 6000 in Bond L&T. He
also
wants the amount invested in Bond L&T to be at least equal
to
the investment in the other Bond. What the broker
recommended if the investor wants to maximize his ROI?
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Scheduling Problem
PERIOD CLOCK TIME (24-HOUR DAY) MINIMUM NUMBER OF
NURSES REQUIRED
1 6 a.m.10 a.m. 2
2 10 a.m.2 p.m. 7
3 2 p.m.6 p.m. 15
4 6 p.m.10 p.m. 8
5 10 p.m.2 a.m. 20
6
2 a.m.6 a.m.
6
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A city hospital has the following minimal daily requirements
for nurses. Nurses report at the hospital at the beginning
ofeach period and work for 8 consecutive hours. The hospital
wants to determine the minimum number of nurses to be
employed so that there will be a sufficient number of nurses
available for each period.
