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Modify the RedBrand example so that all flows must be from plants to warehouses and from warehouses to customers. Disallow all other arcs. How much does this restriction cost RedBrand, relative to the original optimal shipping cost?

Modify the RedBrand example so that all flows must be from plants to warehouses and from warehouses to customers. Disallow all other arcs. How much does this restriction cost RedBrand, relative to the original optimal shipping cost?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Modify the RedBrand example so that all flows must be from plants to warehouses and from warehouses to customers. Disallow all other arcs. How much does this restriction cost RedBrand, relative to the original optimal shipping cost?

Inputs Common arc capacity 200 Shrinkage factor 90% Network formulation Node balance constraints %3D Origin Destination Unit Cost Flow Arc Capacity Plant constraints 1 2 200 Node Plant net outflow Plant capacity 1 180 <= 200 1 180 <= 200 1 4 200 300 <= 300 1 <= 200 3 100 <= 100 1 6 20 <= 200 1 7 20 200 Warehouse constraints 2 1 200 Node Warehouse net outflow Required 2 200 4 10 %3D 2 4 1 100 200 28 %3D 2 1 <= 200 8. 200 200 Customer constraints 2 7 15 <= 200 Node Customer net inflow Customer demand 1 0.4 <= 200 400 >= 400 3 2 8 <= 200 7 180 180 4 1 <= 200 0.5 280 200 10 200 Here is one more version of the basic logistics model, where the amount 7 12 200 that comes out of a warehouse node is less than what goes in. One question you might ask is whether this shrinkage invalidates the guarantee of integer flows we saw in the basic logistics models. Unfortunately, there is no longer any such guarantee. The culprit, as you'd probably expect, is the decimal shrinkage factor. The changing cells in this particular problem turn out to be integers (aside from minor roundoff), but this isn't true in general. Try an 87% shrinkage factor, for example. 4 5 1.2 200 4 2 100 <= 200 7 12 <= 200 5 4 0.8 200 5 6 2 280 <= 200 5 7 12 <= 200 7 1 180 <= 200 7 6 7 200 Objective to minimize Total cost $3,320 O o O O o O O O
Transcribed Image Text:Inputs Common arc capacity 200 Shrinkage factor 90% Network formulation Node balance constraints %3D Origin Destination Unit Cost Flow Arc Capacity Plant constraints 1 2 200 Node Plant net outflow Plant capacity 1 180 <= 200 1 180 <= 200 1 4 200 300 <= 300 1 <= 200 3 100 <= 100 1 6 20 <= 200 1 7 20 200 Warehouse constraints 2 1 200 Node Warehouse net outflow Required 2 200 4 10 %3D 2 4 1 100 200 28 %3D 2 1 <= 200 8. 200 200 Customer constraints 2 7 15 <= 200 Node Customer net inflow Customer demand 1 0.4 <= 200 400 >= 400 3 2 8 <= 200 7 180 180 4 1 <= 200 0.5 280 200 10 200 Here is one more version of the basic logistics model, where the amount 7 12 200 that comes out of a warehouse node is less than what goes in. One question you might ask is whether this shrinkage invalidates the guarantee of integer flows we saw in the basic logistics models. Unfortunately, there is no longer any such guarantee. The culprit, as you'd probably expect, is the decimal shrinkage factor. The changing cells in this particular problem turn out to be integers (aside from minor roundoff), but this isn't true in general. Try an 87% shrinkage factor, for example. 4 5 1.2 200 4 2 100 <= 200 7 12 <= 200 5 4 0.8 200 5 6 2 280 <= 200 5 7 12 <= 200 7 1 180 <= 200 7 6 7 200 Objective to minimize Total cost $3,320 O o O O o O O O
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