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Pesquisa Operacional Exemplo de Análise de Sensibilidade no Solver
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.
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
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
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)
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
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
=SUMPRODUCT(B7:E9,B15:E17) =SUM(B7:E7) Drag to cells G8:G9 =SUM(B7:E9) Drag to cells C11:E11 CARLTON PHARMACEUTICALS Spreadsheet
CARLTON PHARMACEUTICALS Spreadsheet MINIMIZE Total Cost SHIPMENTS Demands are met Supplies are not exceeded
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.
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.
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.
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.