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Pesquisa Operacional
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  1. Pesquisa Operacional Exemplo de Análise de Sensibilidade no Solver

  2. 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.

  3. 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

  4. CARLTON PHARMACEUTICALSNetwork presentation

  5. Destinations Boston Sources 35 Cleveland 30 Richmond 40 S1=1200 32 37 40 Detroit 42 25 S2=1000 Atlanta 35 15 20 St.Louis Greensboro 28 S3= 800 D1=1100 D2=400 D3=750 D4=750

  6. 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: i=1 (Cleveland), 2 (Detroit), 3 (Greensboro) j=1 (Boston), 2 (Richmond), 3 (Atlanta), 4(St.Louis)

  7. The supply constraints Supply from Cleveland X11+X12+X13+X14  1200 Supply from Detroit X21+X22+X23+X24  1000 Supply from Greensboro X31+X32+X33+X34  800 X11 Cleveland X12 X31 S1=1200 X21 X13 X14 X22 X32 Detroit X23 S2=1000 X24 X33 Greensboro S3= 800 X34 Boston D1=1100 Richmond D2=400 Atlanta D3=750 St.Louis D4=750

  8. Total shipment out of a supply node cannot exceed the supply at the node. Total shipment received at a destination node, must equal the demand at that node. CARLTON PHARMACEUTICAL – The complete mathematical model Minimize 35X11 + 30X12 + 40X13 + 32X14 + 37X21 + 40X22 + 42X23 + 25X24+ + 40X31+15X32 + 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

  9. =SUMPRODUCT(B7:E9,B15:E17) =SUM(B7:E7) Drag to cells G8:G9 =SUM(B7:E9) Drag to cells C11:E11 CARLTON PHARMACEUTICALS Spreadsheet

  10. CARLTON PHARMACEUTICALS Spreadsheet MINIMIZE Total Cost SHIPMENTS Demands are met Supplies are not exceeded

  11. CARLTON PHARMACEUTICALS Spreadsheet - solution

  12. 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.

  13. 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.

  14. 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.

  15. 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 doesn´t may decrease up, with no change in the current optimal transportation plan.