tut2 - 2-Dimensional Geometry and Sensitivity Analysis. An...

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Tutorial: 2D Sensitivity Analysis, for 15.053 1 2-Dimensional Geometry and Sensitivity Analysis. An Online Tutorial It is often the case that data is not known accurately. One of the great strengths of modeling is the opportunity to rerun the model with different data or with different assumptions. When one checks the sensitivity of a model to changes in the data, it is usually referred to as “sensitivity analysis.” Sensitivity analysis is widely used throughout all of Management Science and Operations Research, and is common in other fields as well. Normally, when one wants to check the sensitivity of a model to changes in a single datum (singular of data), one reruns the model with the old datum replaced by the new one. In linear programming models, the number of variables (millions of variables), that one could not expect to check the sensitivity to very much data. But one would be wrong!
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Tutorial: 2D Sensitivity Analysis, for 15.053 2 On Sensitivity Analysis in Linear Programming When the simplex algorithm solves a linear program, it simultaneously generates detailed sensitivity analysis for changes in the RHS coefficients and changes in the cost coefficients. The purpose of this tutorial is to describe this type of sensitivity analysis in the case of linear programs with two variables. We first review David’s Tool Company, which we will use as a running example. Cleaver, an MIT Beaver If you think that this tutorial is valuable to you, please send me two shekels, one for each variable. Just joking.
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Tutorial: 2D Sensitivity Analysis, for 15.053 3 Data for the DTC Problem Pack of 10 Slingshot Kits Pack of 10 Stone Shields Resources Stone Gathering time 2 person days 3 person days 10 person- days Stone Smoothing 1 person-day 2 person- days 6 person- days Delivery time 1 person-day 1 person- days 5 person- days Demand 4 packs 3 packs Profit 30 shekels 50 shekels We first investigate changes to the optimal objective function, and to the optimal solution itself, as we change one of the right hand side coefficients. To motivate this, we first consider a managerial question that David wants to answer. Suppose that one of the children in town, say Beth, volunteered to do stone gathering. What would be the extra profit for David, assuming that he does not pay her? Alternatively, what is the maximum amount he could pay her while breaking even? In the original DTC problem, the RHS was measured in hours, and the columns were the number of kits. We have changed the units here to better conform with the 2D geometry used in class. We assume here that each person-day corresponds to 10 hours.
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Tutorial: 2D Sensitivity Analysis, for 15.053 4 Modeling the managerial sensitivity analysis question As is the case with all managerial models, one needs to transform the managerial situation into the mathematical model. Note that we omitted some information from the managerial situation. We did not say how efficient Beth is, or how many hours she is willing to work. So, there is no way that one can give a precise answer without making some additional assumptions.
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This note was uploaded on 01/18/2012 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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tut2 - 2-Dimensional Geometry and Sensitivity Analysis. An...

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