Solution of a Transportation Problem Example. Determine an initial basic feasible solution of a transportation problem using Least cost method or matrix minima method. From D E F To 300 Requirement 5 8 9 B 200 0. 4 4 7 C 100 JOD 3 5 Capacity 1000V 300 260 300 O M = 8 n=3 700 3060 2000 2006 Total Cost: (300 * 9) + (200 x 4) + (100 x3) + (100 x 3) = 4,100 (MAN)- =(3+3). S
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- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.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…The Heartland Distribution Company is a food warehouse and distributor that has a contractwith a grocery store chain in several Midwest and Southeast cities. The company wants toconstruct new warehouses/distribution centers in some of the cities it services to serve thestores in those cities plus all the other stores in the other cities that don’t have distributioncenters. A distribution center can effectively service all stores within a 300-mile radius. Thecompany also wants to limit its fixed annual costs to under $1,200,000. The company wants tobuild the minimum number of distribution centers possible. The following table shows thecities within 300 miles of every city and the projected fixed annual charge for a distributioncenter in each city.City Annual fixed charge ($1ks) Cities within 300 miles1. Atlanta 270 1, 2, 72. Charlotte 250…
- Shortest path problem A company sells seven types of boxes, ranging in size from 17 to 33 cubic feet. The demand and size of each box is given in the table below. The variable cost ($) of producing each box is equal to the box’s size. A fixed setup cost of $1000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size. Formulate a shortest path model to minimize the cost of meeting the demand for boxes. Box 1 2 3 4 5 6 7 Size 33 30 26 24 19 18 17 Demand 400 300 500 700 200 400 200 The unit cost (in dollars) of producing each box is equal to the box’s size, for example, $24 per box of type 4 (with size 24). A fixed setup cost of $1000 is incurred to produce a particular size of boxes. For example, if you produce at least one box of type 5, there is a fixed setup cost of $1000, no matter how many boxes of type 5 to produce; the setup cost for type 5 is zero, if no boxes of type 5 are produced. Only formulate…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.Mad Max wants to travel from New York to Dallas bythe shortest possible route. He may travel over the routesshown in Table 8. Unfortunately, the Wicked Witch canblock one road leading out of Atlanta and one road leadingout of Nashville. Mad Max will not know which roads havebeen blocked until he arrives at Atlanta or Nashville. ShouldMad Max start toward Atlanta or Nashville? Which routesshould the Wicked Witch block? Route (Miles)New York–Atlanta 800New York–Nashville 900Nashville–St. Louis 400Nashville–New Orleans 200Atlanta–St. Louis 300Atlanta–New Orleans 600St. Louis–Dallas 500New Orleans–Dallas 300
- 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?General 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.Solve using the duality linear programming method of the following problem:Object Function: F = X1+X2+4X3Subjected to:X1+2X2+3X3 ≥ 1152X1+X2+8X3 ≥ 200X1+X3 ≥ 50X1,X2, X3 ≥ 0 Note: Please make sure to use the duality linear programming method.
- 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 problemPlease use excel for this problem A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table: Machine Country Contemporary Total Machine Time Available Per Week Router 3.5 4.0 1,000 Sander 4.5 6.5 2,000 Polisher 3.0 2.0 1,500 Country tables sell for $395 and contemporary tables sell for $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution?