Question

During a recent War, Operation Strike Force required large amount of military material and supplies to be shipped daily from supply depots in France to bases in the location of the conflict. The critical factor in the movement of these supplies was speed. The following tables shows the number of planeloads of supplies available each day from each of six supply depots and the number of daily loads demanded at each of five bases. The demands are firm. (Each planeload is approximately equal in tonnage). Also included are the transport hours per plane, including loading and fueling, actual flight time, and unloading and refueling.

Military Base Supply Depot a bd Supply 36 40 32 43 29 2 3 4 34 35 41 29 31 41 42 35 27 36 5 25 28 40 34389 31 30 43 38 40 28 27 29 40 3810 8 6 6 Demand9 Answer the following questions in determining minimal (optimal) transportation.

1.) What is the minimum hours for total transportation times?

2.)How many hours are logged from planes leaving depot-2?

3.)How many hours are logged from planes leaving depot-4?

4.)How many hours are logged from planes leaving depot-6?

5.)How many planes depart depot-1 and arrive at base-e?

6.) How many planes depart depot-3 and arrive at base-e?

7.) How many planes depart depot-5 and arrive at base-a?

8.) How many planes depart depot-6 and arrive at base-b?

9.)How many planes actually depart depot-3?

10.)How many planes actually depart depot-5?

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During a recent War, Operation Strike Force required large amount of military material and supplies to be shipped daily from supply depots in France to bases in the location of the conflict. The critical factor in the movement of these supplies was speed. Objective function: Minimize Z 36x1, t 40хів + 32x,c+ 43x,D+ 29x,E 6A Subject to constraints: Supply constraints at 1, 2, 3, 4, 5, 6 will be as shown below: Demand constraints at A, B, C, D, E will be as shown below: Non-negative Constrain Х,20Formulate the problem as Step 1 Enter the values of different variables, constraints and objective in Excel and use the formulas as shown below shown below: Unit cost matrix From 43 31 35 From Total 12 26 Total costStep 2 Use the formulas for each row and column as shown below 36 41 25 31 28 10 t matrix To 13 14 15 17 18 19 -SUM C18 G18 SUM CI9 G19) SUM(C20:G 21 23 M(C16 C11 SUM D16:021) 25 Total cost -SUMPRODUCTİCS:G10.C16:G21Step 3 Enter the value of the variables, constraints and objective function in Excel Solver, as shown below Solver Pa Set Objective: To: O Max By Changing Variable Cells: o Min Yalue Of SC$16:$G$21 Subject to the Constraints: SC$23:$G$23 $C$25:$G$25 SI$16:SI$21 SK$16:SK$21 Add Change Delete Reset Al Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evoutionary engine for Solver problems that are Help Solve CoseStep 4 After putting the values of objective function, constraints and variables in the above window, click on Solve tab. Solver Results Solver could not find a feasible solution. Reports Feasibility Feasibility-Bounds OKeep Solver Solution O Restore Original Values Return to Solver Parameters Dialog Outline Reports Cancel Save Scenario... Solver could not find a feasible solution. Solver can not find a point for which all Constraints are satisfied.The resultant optimal solution for the given problem is as shown below: From 36 32 27 41 35 41 27 31 43 13 15 Total 17 21 12 10Therefore, the optimal daily flight schedule will be as shown below: Shipment matrix To From 4. 4. 4. 0 1 will supply units to C and units to D. 2 will supply units to B and units to C. will supply units to A and units to B. will supply 5units to A 5 will supply Eunits to E 6will supply units to D and unit to E At this schedule the cost will be minimum that is $ 1.598

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