Consider the following network representation of a transportation problem: Des Moines 25 14 Jefferson City 30 16 Kansas 15 City 10 20 Omaha St. Louis 10 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. What is the optimal (cost minimizing) distribution plan?
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- Jefferson Distributing is analyzing distribution networks with either 4, 5, 6 or 7 warehouses to serve 200 major customers in Europe. Relevant costs include transportation cost from the warehouses to customers, fixed facility costs, and inventory costs in the warehouses. The table below shows the annual transportation cost produced by a facility location software tool for locating 4, 5, 6 or 7 warehouses for this company. Suppose that annual inventory cost for the network can be modeled as $800,000 times the square root of the number of warehouses. Thus, if the network has 4 warehouses, then the annual inventory cost would be $800,000 x √4= $1,600,000. Number of Warehouses Transportation Cost 4 8,000,000 5 6,500,000 6 5,000,000 7 4,400,000 a) If the annual fixed cost per warehouse is $1,000,000, how many warehouses should there be to minimize the total (transportation + warehouse + inventory) cost? b) Now suppose the…consider the following network representation of a transportation problem:(The image provided) The supplies, demands, and transportation costs per unit are shown on the network. The optimal (cost minimizing) distribution plan is given below. Des Moines Kansas City St.Louis Supply Jefferson City 20 0 10 30 Omaha 10 10 0 20 Demand 30 10 10 Total Cost: $530. Find an alternative optimal solution for the above problem. If required, round your answer to nearest whole number and if your answer is zero enter “0” Des Moines Kansas City St.Louis Jefferson City Omaha Total Cost: $ is?In a typical network model representation of the transportation problem, the nodes indicate a. roads b. rail lines c. geographic locations d. rivers For all routes with positive flows in an optimized transportation problem, the reduced cost will be: a. zero b. how much less shipping costs would have to be for shipments to occur along that route c. how much more shipping costs would have to be for shipments to occur along that route d. how much the capacity is along that shipping route The decision variables in transportation problems are: a. profits b. costs c. flows d. capacities Which of the following statements is a type of constraint that is often required in blending problems? a. Integer constraint b. Quality constraint c. Binary constraint d. None of these options When a workforce…
- The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M. Which type of network optimization problem is used to solve this problem? Multiple Choice: Minimum Flow Problem Average-Cost Flow problem Maximum Flow Problem Shortest Path Problem Maximum-Cost Flow problemGeneral Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P05_54.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars.a. Determine how to minimize the cost of meeting demands in Houston and Tampa.b. Modify the answer to part a if no shipments through Atlanta are allowed.A person starting in Columbus must visit Great Falls, Odessa, and Brownsville, and then return home to Columbus in one car trip. The road mileage between the cities is shown. Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- a)Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit.
- A minimum-cost flow problem has 5 supply nodes, 2 transshipment nodes, and 5 demand nodes. Each supply node can ship to each transshipment node but cannot ship to any demand node or to any other supply node. Each transshipment node can ship to each demand node, but cannot ship to any supply node or to any other transshipment node. How many arcs will be included in the model?The optimal solution to the original Grand Prix problem indicates that with a unit shipping cost of $132, the route from plant 3 to region 2 is evidently too expensive—no autos are shipped along this route. Use SolverTable to see how much this unit shipping cost would have to be reduced before some autos would be shipped along this route.In a 3 x 3 transportation problem, let xij be the amount shipped from source i to destination j and let cij be the corresponding transportation cost per unit. The amounts of supply at sources 1, 2, and 3 are 15, 30, and 85 units, respectively, and the demands at destinations 1, 2, and 3 are 20, 30, and 80 units, respectively. Assume that the starting northwest-corner solution is optimal and that the associated values of the multipliers are given us u1 = -2, u2 = 3, u3 = 5, v1 = 2, v2 = 5, and v3 = 10. a) Find the associated optimal cost. b) Determine the smallest value of cij for each nonbasic variable that will maintain the optimality of the northwest-corner solution.
- Fred Block Company has orders for 90 tons of concrete blocks at three suburban locations as follows: Northwood -- 25 tons, Westwood -- 45 tons, and Eastwood -- 20 tons. Fred has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is shown as follows Delivery Cost Per Ton Northwood Westwood Eastwood Plant1 20 30 40 Plant 2 30 40 45 a. Develop a network representation of this distribution problem. b. Develop a linear program model that can be used to determine the plan that will minimize total distribution costs. c. Solve the problem to describe the distribution plan and show total distribution cost.(Submit Excel files).Solve the following problems using Excel Solver or R Studio. A company produces cars in Atlanta, Boston, Chicago, and Los Angeles. The cars are then shipped to warehouses in Memphis,Milwaukee, New York City, Denver, and San Francisco. The number of cars available at each plant is given in Table 1. Eachwarehouse needs to have available the number of cars given in Table 2. The distance (in miles) between the cities is given inTable 3. Assuming that the cost (in dollars) of shipping a car equals the distance between two cities, determine an optimalshipping schedule.A company has three manufacturing plants (in Atlanta,Tulsa, and Springfi eld) that produce a product that is then shipped to one of four distribution centers. Th e three plants can produce13, 18, and 12 truckloads of product each week, respectively. Eachdistribution center needs 10 truckloads of product each week. Th eshipping costs per truckload between the plants and distributioncenters are given in the table. Th e company needs to determinehow much to ship from each plant to each distribution center andwould like to minimize total shipping costs (a) Formulate an LP to minimize the total shipping costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution