this video is by far the best explanation I've seen! Thank you! I have two questions, what steps would you take if you generated a sensitivity report and wanted to remove a constraint? 2nd, if you're adding a new variable (a new decision) but aren't given the profit (you are just given the constraints) how would you figure out the price of that unit?
If the constraint you are removing isn't binding/tight (i.e if the left hand side doesn't match the right hand side), and you are removing only that constraint, then the solution will remain the same. If the constraint is binding, then the sensitivity report does not tell you what will happen if you remove it completely, only what will happen to the value of the objective if you loosen or tighten the constraint (by changing the right-hand side). If you are adding a variable, to tell whether or not it will help the objective get better you compute the reduced cost as I explain. If the profit coefficient of that variable is unknown, you still do the same calculation but treat that profit coefficient as a variable p in the calculation and solve for it. As in, you can deduce what it would have to be for the reduced cost to be positive (assuming you are maximizing profit): p - (stuff in the parentheses) > 0, so p > (stuff in the parentheses), where "stuff in the parentheses" is what goes inside the parentheses of a reduced cost calculation as I explained in this particular video.
this really helped, i had many questions and you literally have answered every single one of them in the video i will come here to update if i get full mark at my midterm...
Because they are only using 40 acres, there's a surplus of 5 acres. This means that losing up to 5 acres won't affect what's happening now (shadow price of zero). However, if you were to lose more than 5 acres, the current solution would not be feasible anymore and they'd need to produce less, which would result in a smaller profit. Therefore, if the land available goes down below 40, that constraint will have a positive shadow price to indicate that "having more of this resource would increase the objective function (i.e. the profit)."
Thanks for your video it really helped. How do you determine if your sensitivity report is reliable without making any changes within the allowable range?
Happy to hear it helped. I don't quite understand your question. How to determine it's reliable without making changes within the range? Do you mean you want to make changes outside the ranges? If that's the case, you can't use the report. You need to make these changes in the Excel model and re-solve the model.
I'd need more context. Is this homework? Maybe your teacher defined what they mean by "reliable" in class. One thing you can do is check to see if the report is consistent with the answer. For example: look at the final solution, is it really feasible? Plug the answer into the constraint formulas. Are the constraints that have zero slack matching the ones the report indicates? Is the shadow price equal to zero when the slack (difference between left-hand side and right-hand side values of a constraint) is not zero? etc. You can also look at the signs of the shadow prices: are they in the right direction? For example: does it make sense for a certain shadow price to have positive or negative sign? Think of the constraint in question. If it's a limited resource, getting more of it should improve your objective (where improve means increase for maximization and decrease for minimization). Is this happening? Etc.
@@TallysYunes it's an assignment. I did replay the class video but that was never said however I like the way you are looking at it. I'll use this approach I think it should help. Many thanks!
Sir when I look the my constraints' of Excel sensivity analysis table, I see the whole RHS numbers equal to 0. But actually all of them have a number. Even in some constraints the LHS and RHS equals to each other. I need to write down the binding and nonbinding constraints but in this case it wouldn't be possible. All my 17 constraints' RHS's equal to 0. Why? How can I change this? Thank you
If you set everything up correctly, the values in the "RHS" column of the constraints table of the sensitivity report should match the right-hand side values of your constraints in the spreadsheet (assuming those were constants, rather than formulas). To check whether or not a constraint is binding, you just need to see if the value in the "Final Value" column of the constraint matches the value in its "RHS" column.
The allowable increase and decrease are computed automatically by the Solver. We don't have to compute it ourselves. There is a calculation that can be done by hand, which is explained in any standard Linear Programming textbook.
No. For variables that are not touching their lower or upper limits (in this case wheat and corn only have a lower limit of zero and neither or them is equal to zero) the reduced cost will always be set to zero by the solver and that zero doesn't really mean anything special.
The questions are from my lecture notes. I have two more examples of sensitivity analysis if you want to practice further: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-UpxFFkRJpWI.html and ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oDu18ESQg9E.html
In the absence of a condition called "degeneracy," if the allowable increase or allowable decrease of the objective function coefficient of one or more variables equals zero, that indicates alternative optimal solutions exist. CAUTION: If the allowable increase or decrease for the right-hand side number of any constraint is zero, then the linear program is degenerate and the rule above (to detect alternative optimal solutions) doesn't work anymore.
There's a final value column for the variable table (top table) and for the constraint table (bottom table). I explain what they mean, respectively, at times 2:39 and 9:04 in the video.
