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 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 FromBostonRichmondAtlantaSt. LouisSupply Cleveland $ Detroit Greensboro Demand CARLTON PHARMACEUTICALS

4 CARLTON PHARMACEUTICALS Network presentation

5 Boston Richmond Atlanta St.Louis Destinations Sources Cleveland Detroit Greensboro S 1 =1200 S 2 =1000 S 3 = 800 D 1 =1100 D 2 =400 D 3 =750 D 4 =

6 –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 X ij = 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) CARLTON PHARMACEUTICALS – Linear Programming Model

7 Boston Richmond Atlanta St.Louis D 1 =1100 D 2 =400 D 3 =750 D 4 =750 The supply constraints Cleveland S 1 =1200 X11 X12 X13 X14 Supply from Cleveland X11+X12+X13+X14  1200 Detroit S 2 =1000 X21 X22 X23 X24 Supply from Detroit X21+X22+X23+X24  1000 Greensboro S 3 = 800 X31 X32 X33 X34 Supply from Greensboro X31+X32+X33+X34  800

8 CARLTON PHARMACEUTICAL – The complete mathematical model Minimize 35X X X X X X X X X31+15X X X34 ST Supply constraints: X11+X12+X13+X X21+X22+X23+X X31+X32+X33+X34800 Demand constraints: X11+X21+X X12+ X22+X32400 X13+ X23+X33750 X14+X24+X34750 All Xij are nonnegative ======== 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.

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

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

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.