ms lecture021 sensitive analysis1 sem2 2011

7/29/2019 MS Lecture021 Sensitive Analysis1 Sem2 2011

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OPIM101 Management Science

Suggested Reading Material:

Taylor 10th Ed, Chapter 3


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Semester 2, 2011/2012 OPIM 101 Management Science 2

Sensitivity analysis determines the effect on the optimal

solution ofchanges in parameter values of the objective

function and constraint equations.

Changes may be reactions to anticipated uncertainties in the

parameters or to new or changed information concerning

the model.


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How sensitive are the optimal solution and objective functionvalue to changes in problem data?

Why should we be interested in changes in problem data?

changing business conditions

problem data are often estimated

evaluate impact of management policies


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In sensitivity analysis, we usually consider the impact of changes

to one parameter while keeping the rest of the problem

unchanged.

We will use the graphical approach to study sensitivity analysis

of

Objective function coefficients (covered in Part I)

RHS values (covered in Part II)


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A company produces two products that are processed on a assembly line with 100

available hours. Each product requires 10 hours on the assembly line. The profitfor product 1 is $6 per unit and profit for product 2 is $4 per unit.

We have learnt how to solve graphically.

What happens if the profit of product 1 increases to $10 per unit, what isthe effect on our ordering policy?

What happens if the profit of product 2 increases to $10 per unit, what isthe effect on our ordering policy?


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Maximize Z = $40x1

+ $50x2

subject to: x1 + 2x2 40

4x1 + 3x2 120

x1, x2 0

Figure 3.1

Optimal Solution Point

Beaver Creek Pottery Example


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Maximize Z = $100x1

+ $50x2


4x1 + 3x2 120

x1, x2 0

Figure 3.2 Changing the x1 Objective Function Coefficient

Change x1 Objective Function Coefficient


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Maximize Z = $40x1

+ $100x2


4x1 + 3x2 120

x1, x2 0

Change x2 Objective Function Coefficient


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The sensitivity range for an objective function coefficient is the range of

values over which the current optimal solution point will remain optimal.

The sensitivity range for the xi coefficient is designated as ci.

Objective Function Coefficient

Sensitivity Range


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objective function Z = $40x1 + $50x2sensitivity range for:

x1: 25 c1 66.67

x2: 30 c2 80

Objective Function Coefficient

Sensitivity Range for c1 and c2


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Produces solvents: CS-01 and CS-02.

Profit margins: $0.30 per gallon for CS-01

$0.50 per gallon for CS-02

Demand for CS-02 is at most 120,000 gallons per week.


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x1= no. ofthousands of gallons ofCS-01 to produce

x2 = no. ofthousands of gallons ofCS-02 to produce

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Intuitive Analysis:

When profit margin increase, objective value will increase.


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Summary:


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We consider the same objective function with the same

constraints.

Slope of objective function is now -3/c2


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We can show that as long as

, optimal solution remain the same.


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Sensitivity Analysis

In our analysis, we only considered varying oneparameter at a time (either c1 or c2) while holdingeverything else constant.

Although the graphical analysis is good for explainingconcepts, it is not practical.

Most LP software (including Excel Solver) can performsensitivity analysis.


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What we have covered

Know what is sensitivity analysis

What happens if objective function changes

What is left to be covered?

Changes in RHS

Using Excel to generate insights. Graphical analysis is too

tedious and restrictive.

ms lecture021 sensitive analysis1 sem2 2011

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