Given the following nodes from A to G as shown in the diagram, determine the shortest path network from node A to all other nodes in the given cost network graph. 5 km G 5.2 km F D 2.2 km 4.7 km 3.3 km E 2.9 km 6.4 km C 3 km 4.1 km 7 km 4.9 km A 3.2 km B
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Given the following nodes from A to G as shown in the diagram, determine the shortest path network from node A to all other nodes in the given cost network graph.
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- NEED ALL 1. Nodes with only outflows (total outflows <= capcity) 2. Nodes with only inflows (total inflows >= demand) 3. Nodes with both outflows and inflows (total outflows = total inflows) 4. Network structure and flows (List of arcs in the network by (Origin, Destination) 5. Objective to minimizeConsider the network in the following figure. Edges that are not pictured have a length of ∞. Image attatched (a) What is the optimal TSP tour on this network, and what is its total length, z*? What is the optimal 1-tree Tˆ* on this network (“rooted” at node 1), and what is its total length, z(Tˆ*)? (b) Find the best Held-Karp lower bound you can. That is, find weights to add to one or more nodes so that z* and the right-hand side of the following formula are as close as possible. z* ≥ z(Tˆ*) + SUM{i∈N} λi(di(Tˆ*) − 2) Image attatched Here Tˆ* is the optimal 1-tree under the revised distance matrix, z(Tˆ*) is its cost and di(Tˆ*) is the degree of node i in 1-tree Tˆ*.A salesman for Healthproof Pharmaceutical Company travels each week from his office in Atlanta to one of five cities in the Southeast where he has clients. The travel time (in hours) between cities along interstate highways is shown along each branch in the following network: A. Determine the shortest route from Atlanta to each of the other five cities in the network. B. Assume that the network now represents six different communities in a city and that the local transportation authority wants to design a rail system that will connect all six communities with the minimum amount of track. The miles between each community are shown on each branch. Develop a minimal spanning tree for this problem.
- In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and others are city streets, the shortest-distance routes between the office and the construction site may not necessarily provide the quickest or shortest-time route. Shown here is the Gorman road network with travel time rather than distance. Find the shortest route from Gorman’s office to the construction site at node 6 if the objective is to minimize travel time rather than distance.Solve the Least Support Tree Problem There are 6 offices, namely, A,B,C,D,E,F and G (see following figure), how to design the local area network cable so as to connect all offices together with shortest network cable length?Abu Dhabi municipality is given an assignment to ensure provision of enough water for residents of the Abu Dhabi city. The water is purified in a large water treatment plant (node 1) and then is sent via a water supply network to the Abu Dhabi city (node 14). As shown in the below water supply network, the capacity of each water pipeline (arc) is shown in million liters per hour. For example, the hourly water flow from node 1 to node 2 is four million liters, and from node 2 to node 1 is zero million liters. a) The municipality is interested to find out how much water (in million liters per hour) can be sent from the water treatment plant to the Abu Dhabi city via this water supply network. Determine it. b) Due to a maintenance problem both nodes 10 and 11 need to be taken offline. Therefore, these nodes cannot flow any water in and out. How this problem impacts the network maximum flow capacity? Please include algebraic method and excel solver.
- Anderson Watch Company is considering opening four possible distribution centers located in Atlanta, Lexington, Milwaukee, and Salt Lake City with a fixed cost to open of $17,000, $22,000, $35,000, and $25,000, respectively. They currently have ten retail stores located in Seattle, San Francisco, Las Vegas, Tucson, Denver, Dallas, Birmingham, Orlando, Cleveland, and Philadelphia. Lisa, the supply chain VP, wants to minimize the transportation costs of shipping their French down pillows. The per-unit shipping cost from each distribution center to each retail location and the amounts currently in inventory and ordered at each retail location are shown in the following tables. What is the minimum cost solution? What is the minimum cost solution if Lisa wants to use single sourcing?The MidLands Trucking Company based in Louisvillehas eight trucks located throughout the Mideast that havedelivered their loads and are available for shipments. Through their Internet logistics site MidLands has re-ceived shipping requests from 12 customers. The follow-ing table shows the mileage for a truck to travel to a customer location, pick up the load, and deliver it. Determine the optimal assignment of trucks to customersthat will minimize the total mileage. Customers Truck A B C D E F G H I J K L1 500 730 620 410 550 600 390 480 670 710 440 5902 900 570 820 770 910 660 650 780 840 950 590 6703 630 660 750 540 680 750 810 560 710 1200 490 6504 870 1200 810 670 710 820 1200 630 700 900 540 6205 950 910 740 810 630 590 930 650 840 930 460 5606 1100 860 800 590 570 550 780 610 1300 840 550 7907 610 710 910 550 810 730 910 720 850 760 580 6308 560 690 660 640 720 670 830 690 880 1000 710 680The Thor International Company operates four factories that ship products to five warehouses. The shipping costs, requirements, and capacities are shown in the tableau below. Use the transportation method to find the shipping schedule that minimizes shipping cost. Factory Shipping Cost per Case to each Warehouse Capacity W1 W2 W3 W4 W5 Dummy F1 $4 $5 $4 $3 $6 $0 50,000 F2 $3 $4 $4 $5 $7 $0 80,000 F3 $3 $4 $5 $3 $5 $0 90,000 F4 $4 $6 $5 $6 $3 $0 40,000…
- Consider the transportation problem having the cost and requirement table below. Draw a network showing the quantities obtained in the final iteration and the optimal value of z.ASAP PLEASE.. The distribution of goods from the source (factory) to the target (warehouse) will cause problems regarding TRANSPORT, namely how the goods are sent from the factory to the warehouse which produces minimum costs. If it is known that - the capacity of 3 factories is 40000, 30000 and 20000, - the need for 3 warehouses is 20000, 50000 and 30000 respectively. The cost of shipping goods from the factory to the warehouse is shown in the following table Solve the above TRANSPORTATION problems with VAM and MODIThe members of the Vistas Club are planning a month long hiking and camping trip through the Blue Ridge Mountains, from north Georgia to Virginia. There are a number of trails through the mountains that connect at various campgrounds, crossings, and cabins. Thefollowing network shows the different connecting trails and the distance of each connectingbranch, in miles: 1. Determine the shortest path from node 1 in north Georgia to node 13 in Virginia and indicatethe total mileage of the trail. 2. Determine the shortest route a concrete truck would take from the plant at node 1 to node 8and the total distance for this route, using the shortest route method.