GEOG 3LT3 Lecture Notes - Lecture 14: Simplex Algorithm, Shadow Price
2 May 2018
School
Department
Course
Professor
November 9, 2016
- So there are 2 different warehouses that have to ship goods to different stores,
there may be a different cost to ship goods to different stores and we can assign
a cost of shipping 1 individual good to each store
C = 16 Xii
- Basically if we ship 1 unit from I to A we will have to pay 16 dollars per good 32
dollars to ship 2 goods and so on
- I to Xii, Xi2 and Xi3 we can ship less than or equal to 800 units – this is a supply
constraint
- For II to X2i, x2ii, and x2III we can ship less than or equal to 600 units
- These are supply constraints because we cannot ship more than we have
- But there are also demand constraints which say that the amount of an item at a
store should equal the demand
oXii + X2i is say greater than 500
- There are also non-negativity constraints that say that the flow moves in 1
direction because you don’t want to send goods back to the warehouse
Simplex Method
- This is a method for solving the problems presented with the previous data (From
Evan: I don’t know what the problem is, but I believe it has to do with some of the
constraints faced? He didn’t say what the problem was)
- For the supply constraint if we multiply by -1 on both sides then we change the
transportation problem to have negative values (I am not sure what he wanted us
to get from this, it is still basically the same function is it not?)
- The Dual – imagine that there is a mirror image between 2 functions (he said this
will have significance later but we might not get it now lol)
- To convert the dual we take the situation that we described and (then he just
started to write out the table that he wrote under the primal (see photo)
- This table incorporates the constraints as well as the costs
- Now we will make the dual
oHere we will impose a set of artificial variables (these are the U’s he is
putting at the top of the matrix)
oNotice how the primal table is just transcribed into the dual table
find more resources at oneclass.com
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Document Summary
Basically if we ship 1 unit from i to a we will have to pay 16 dollars per good 32 dollars to ship 2 goods and so on. I to xii, xi2 and xi3 we can ship less than or equal to 800 units this is a supply constraint. For ii to x2i, x2ii, and x2iii we can ship less than or equal to 600 units. These are supply constraints because we cannot ship more than we have. But there are also demand constraints which say that the amount of an item at a store should equal the demand: xii + x2i is say greater than 500. There are also non-negativity constraints that say that the ow moves in 1 direction because you don"t want to send goods back to the warehouse. This is a method for solving the problems presented with the previous data (from.
