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Maximal flow problem.
Determin the Maximal flow from node 1 to 7
Step by step
Solved in 2 steps
- Consider the network diagram given in figure below with the indicated flow capacities along each branch. Determine the maximal flow from source node A to destination node F. (Show your solution) 2 6. 6. 0( E B 8. 4,Q.) Given the following network, with the indicated flow capacities along each branch, determine the maximum flow from source rode 1 to destination node 6 and the flow along each branch: 15 12 20 0 14 11Do problem 2 letter g
- F Source For the network shown below, the arc capacity from node i to node j is the number nearest node i along the arc between these nodes. formulate the maximum flow as a linear programming problem. 1 4 24 3 33 4 4 54 69 7 Sink F Iteration Augmenting path 1 2 3 C*Suppose as many as 300 cars per hour can travelbetween any two of the cities 1, 2, 3, and 4. Set up amaximum-flow problem that can be used to determine howmany cars can be sent in the next two hours from city 1 tocity 4. (Hint: Have portions of the network represent t 0,t 1, and t 2.)The north-south highway system passing through Albany, New York can accommodate the capacities shown in the table below. From To Capacities 1 2 3 1 3 6 1 4 3 2 4 2 2 5 4 3 4 3 3 6 2 4 2 2 4 3 3 4 5 2 4 6 3 5 2 4 5 4 2 5 6 6 How many units go from Node 1 to 3 and 4 to 2, respectively, in order to maximize the flow. a. 5 and 1. b. 5 and 2. c. none of the answers proposed apply d. 6 and 1. e. 6 and 2.
- Describe in your own words assumptions of Maximal Flow Problem by indicating any differences with the assumptions of Transshipment Problem.(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). B C 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route B 1 2 3 4 A 10 11 9 14 Step 1b: Column subtraction. Truck / Route 1 2 3 4 A 10-6=4 = = = = = B = с = C Step 2: Testing for optimal solution (show your lines covering the zero entries). What is the minimum number of lines required to cover all zeros? D 8 14 10 13 D = = D =City Cab Company identified 10 primary pickup and drop locations for cab riders in New York City. In an effort to minimize travel time and improve customer service and the utilization of the company's fleet of cabs, management would like the cab drivers to take the quickest route between locations whenever possible. The travel times in minutes are shown on the arcs of the network. Note that there are two one-way streets and that the direction is shown by the arrows. 1 I 13 10 15 10 2 5 3 2 4 4 5 15 3 5 6 12 2 7 5 8 4 7 9 Using the above network of roads and streets, what is the quickest route a driver beginning at location 1 should take to reach location 10? path = 1, 10
- NETWORK FLOW OPTIMIZATION - EXAMPLE • Distribution network for a single product Two production plants P1 and P2 Plant P1 has unlimited supply capacity, Plant P2 has a supply capacity of 60,000 units/year Production cost is the same at both plants. Two warehouses W1 and W2 with identical warehouse handling costs and both having unlimited capacity. • Three market areas C1, C2 and C3 with demand of 50000, 100000 and 50000 units/year. • Unit transportation costs: W1 W2 Plant →→ Warehouse P1 P2 $0 $4 $5 $2 Warehouse →→ Market Center C1 C2 C3 $3 $4 $5 $2 $1 $2Problem #3 A, B, CDraw the precedence diagram