Pesquisa Operacional

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Pesquisa Operacional

• Exemplo de Análise de Sensibilidade no Solver

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CARLTON PHARMACEUTICALS

• Carlton Pharmaceuticals supplies drugs and other
  medical supplies.
• It has three plants in Cleveland, Detroit,
  Greensboro.
• It has four distribution centers in Boston,
  Richmond, Atlanta, St. Louis.
• Management at Carlton would like to ship cases of
  a certain vaccine as economically as possible.

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CARLTON PHARMACEUTICALS

• Data
• Unit shipping cost, supply, and demand
• Assumptions
• Unit shipping costs are constant.
• All the shipping occurs simultaneously.
• The only transportation considered is between
  sources and destinations.
• Total supply equals total demand.

To
From
Boston
Richmond
Atlanta
St. Louis
Supply
Cleveland
35
30
40
32
1200
Detroit
37
40
42
25
1000
Greensboro
40
15
20
28
800
Demand
1100
400
750
750
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CARLTON PHARMACEUTICALSNetwork presentation
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D11100
D2400
D3750
D4750
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CARLTON PHARMACEUTICALS Linear Programming
Model

• The structure of the model is
• Minimize Total Shipping Cost
• ST
• Amount shipped from a source ? Supply at that
  source
• Amount received at a destination Demand at
  that destination
• Decision variables
• Xij the number of cases shipped from plant i
  to warehouse j.
• where i1 (Cleveland), 2 (Detroit), 3
  (Greensboro) j1 (Boston), 2
  (Richmond), 3 (Atlanta), 4(St.Louis)

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The supply constraints
Boston
D11100
Richmond
D2400
Atlanta
D3750
St.Louis
D4750
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CARLTON PHARMACEUTICAL The complete
mathematical model
Minimize 35X11 30X12 40X13 32X14 37X21
40X22 42X23 25X24 40X3115X32
20X33 38X34
ST
Supply constraints

X11
X12
X13
X14
1200

X21
X22
X23
X24
1000
X31
X32
X33
X34
800
Demand constraints

X11
X21
X31
1100
X12

X22
X32
400
X13
X23
X33
750
X14
X24
X34
750
All Xij are nonnegative
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CARLTON PHARMACEUTICALS Spreadsheet
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CARLTON PHARMACEUTICALS Spreadsheet
MINIMIZE Total Cost
SHIPMENTS
Demands are met Supplies are not exceeded
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CARLTON PHARMACEUTICALS Spreadsheet - solution
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CARLTON PHARMACEUTICALS Sensitivity Report

• Reduced costs
• The unit shipment cost between Cleveland and
  Atlanta must be reduced by at least 5, before it
  would become economically feasible to utilize it
• If this route is used, the total cost will
  increase by 5 for each case shipped between the
  two cities.

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CARLTON PHARMACEUTICALS Sensitivity Report

• Allowable Increase/Decrease
• This is the range of optimality.
• The unit shipment cost between Cleveland and
  Boston may increase up to 2 or decrease up to 5
  with no change in the current optimal
  transportation plan.

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CARLTON PHARMACEUTICALS Sensitivity Report

• Shadow prices
• For the plants, shadow prices convey the cost
  savings realized for each extra case of vaccine
  produced.For each additional unit available in
  Cleveland the total cost reduces by 2.

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CARLTON PHARMACEUTICALS Sensitivity Report

• Shadow prices
• For the warehouses demand, shadow prices
  represent the cost savings for less cases being
  demanded.For each one unit decrease in demanded
  in Richmond, the total cost decreases by 32.

• Allowable Increase/Decrease
• This is the range of feasibility.
• The total supply in Cleveland may increase up to
  250, but doesnt may decrease up, with no change
  in the current optimal transportation plan.