Linear Programming - Sensitivity Analysis

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A useful property of Linear Programming Models is the ability to carry out Sensitivity Analysis, for example: how sensitive is the optimum solution to changes in the model parameters?

This is sometimes referred to as “What If?” analysis (using Example of Linear Programming: A Minimisation Problem as an example) , examples might be:

• What would happen to the optimum solution if the RZ45 aircraft could be modified to carry eight extra passengers?
• What would happen if the XJ100 aircraft could be modified to carry five extra tons of cargo?
• What would happen if the cost of operating the RZ45 rose from £600 to £1000 per journey?

The purpose of Sensitivity Analysis is to answer these questions. In regard to the first two questions this is equivalent to moving the constraints out to the right in a parallel fashion. This clearly will alter the feasible region and therefore the optimum solution. The third question does not alter the feasible region but will certainly alter the slope of the objective function. Whether this changes the optimum solution will depend on the degree of change.

The effect of the third question is shown in Figure 40 below:

The slope of the ISO-Profit line will change from –5/6 to –5/10.

This gives a new optimum solution. To minimise costs, the firm should operate 12 flights a day of the XJ100 aircraft only. Thus the new minimum cost becomes £500 x 12 = £6,000.

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Reference(s)
	Book		Anderson, D. R., Sweeney, D. & Williams, T. (2002) An Introduction to Management Science: A Quantitative Approach to Decision Making. 10th Edition. South-Western College Publishing: United States of America (USA), California (CA), San Diego. [ISBN: 9780324145632]. [Available on: Amazon: https://amzn.to/3DrQjUY].
	Book		Campbell, D. J. & Craig, T. (2005) Organisations and the Business Environment. 2nd Edition. Elsevier: Netherlands, North Holland, Amsterdam. [ISBN: 9780750658294]. [Available on: Amazon: https://amzn.to/3VHJupz].
	Book		Pfaffenberger, B. (2002) Computers in Your Future 2003. 5th Edition. Prentice Hall: United States of America (USA), New Jersey (NJ), Bergen, Upper Saddle River. [ISBN: 9780139227820]. [Available on: Amazon: https://amzn.to/3gv8n7D].
	Web		Wacha, D. M. (2007) Using Microsoft Excel to Graph Optimization Problems [Online]. Monmouth University: United States of America (USA), New Jersey (NJ), Monmouth, West Long Branch. [Accessed on: 2013-02-07]. [Available on: Monmouth: http://zorak2.monmouth.edu/~dwacha/E07h-LinearProgramming.pdf].

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Reference (or cite) Article
	Kahlon, R. S. (2013) Linear Programming: Sensitivity Analysis [Online]. dkode: United Kingdom, England, London. [Published on: 2013-02-07]. [Article ID: RSK666-0000099]. [Available on: dkode | Ravi - https://ravi.dkode.co/2013/02/linear-programming-sensitivity-analysis.html].

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