3. A product is manufactured by four factories A, B, C and D. The unit production costs in them areETB 2, ETB 3, ETB 1 and ETB 5 respectively. Their production capacities are 50, 70, 30 and 50units respectively. These factories supply the product to four stories, demands of which are 25,35, 105, and 20 units respectively. Unit transportation cost in ETB for each factory to each storeis given in the table below.FactoriesBCD1210134Stores2483636798HUSES4115123Determine the transportation plan to minimize the total production-cum-transportation cost byusing:a. Vogel's Approximation Method (VAM) for initial basic feasible solutionb. North West Corner Method (NWCM)c. Least Cost Method (LCM)

The transportation model is used to calculate the minimum cost of the route by selecting different…

Answered: a. Vogel's Approximation Method (VAM)…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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i ABC A.Ş., which produces white goods, has sales centers (X, Y, Z) in 3 cities and production centers (A, B, C) in 3 cities. White goods orders of sales centers200, 100 and 300, respectively; The capacities of the production centers are 150, 175 and 275, respectively. The transportation cost of one product sent from each production center to each sales center is given in the table below. X Y ZA 6 8 10B 7 11 11C 4 5 12In order to meet the demands of each sales center in line with the capacities with the least cost;Build the linear programming model of the problem.(Hint: You can define the decision variable as xij: the amount of product sent from the i. Production center to the j. Consumption center.)
Suppose the company has received a proposal for setting up another warehouse(Warehouse E) with a capacity of 900 units. The location of the warehouse is such thatthe unit costs of transporting to the six cities are as follows: Hyderabad–45, Mysore–75, Chennai–30, Kochi–65, Pune–90 and Vizag–80. The company would like to knowhow the allocation will change if the warehouse is made operational and the likely costimpact on the operation of the system. After balancing above table by which method we should solve this problem
1.10 Adirondack Paper Mills, Inc. operates paper plants in Augusta, Maine, and Tupper Lake, New York. Warehouse facilities are located in Albany, New York, and Portsmouth, New Hampshire. Distributors are located in Boston, New York, and Philadelphia. The Augusta plant has a capacity of 300 units, and the Tupper Lake plant has a capacity of 100 units. Boston has a demand of 150 units, New York has a demand of 100 units, and Philadelphia has a demand of 150 units. The unit transportation costs (in dollars) for shipments from the two plants to the two warehouses are presented in Table 4 and those from the two warehouses to the three distributors are presented in Table 5. Draw the network representation of the Adirondack Paper Mills problem. Formulate the Adirondack Paper Mills problem as a linear programming problem. Solve the linear program to determine the minimum cost shipping schedule for the problem.
Problem 7-17 (pg 279) Using the following equations, graph the constraints and solve using the corner point approach ONLY. X1 = number of benches produced X2 = number of tables produced Maximize profit = $9X1 + $20X2 subject to 4X1 + 6X2 <= 1,200 hours 10X1 + 35X2 <= 3,500 feet X1, X2 >= 0
We have three Suppliers and four Demanders. the Suppliers have inventory of 61 , 49, 29 respectively, and the Demanders require 54, 37, 4, 44 respectively. Shipping costs from S1 to D1, D2, D3 , D4 are 103, 30, 68, 54from S2 to D1, D2, D3 , D4 are 16, 95, 84, 35from S3 to D1, D2, D3 , D4 are 40, 44, 46, 101. Check that this is a balanced transportation problem. Find the optimal mimimal shipping cost:
1. Transportation Problem: The Navy has 9,000 pounds of material in Albany, Georgia that it wishes to ship to three installations: San Diego, Norfolk, and Pensacola. They require 4,000, 2,500, and 2,500 pounds, respectively (Destination or Demand amounts). Government regulations require equal distribution of shipping among the three carriers (Supply nodes). Note: This means the supply is the same for each type of transportation. The shipping costs per pound for truck, railroad, and airplane transit are shown below. Formulate and solve a linear program to determine the shipping arrangements (mode, destination, and quantity) that will minimize the total shipping cost.DestinationMode San Diego Norfolk PensacolaTruck $12 $ 6 $ 5Railroad 20 11 9Airplane 30 26 28 2. Transshipment Problem The Northside and Southside facilities of Zeron Industries supply three…
given the transportation problem, assume that the demands at the 4 destinations are 5, 5, 7, and 8 units, respectively, and the supplies at the 4 sources are 7, 3, 7 and 8 units, respectively.C₁₁=7ㅤ C₁₂=9ㅤ C₁₃ = 1ㅤ C₁₄ = 10 C₂₁= 22ㅤ C₂₂ = 25ㅤ C₂₃ = 16ㅤ C₂₄ = 26 С₃₁ = 28ㅤ C₃₂ = 32ㅤ C₃₃ = 24ㅤ Сз₄ = 32 C₄₁ = 12ㅤ C₄₂ = 14ㅤ C₄з = 6ㅤ C₄₄ = 16where m=4, n=4what is the optimal solution using vogel's approximation method, least-cost method, and northwest-corner rule?
Mo. A company needs to make deliveries on 10 different routes. The time (in minutes) to complete each route and the delivery amount (i.e., the load in number of units) are as follows. Route RO1 R02 R03 R04 R05 R06 R07 R08 R09 R10 Time 29 35 15 35 20 23 35 40 45 50 Load 200 240 110 90 65 135 80 170 150 270 The company is considering 6 carriers to make these deliveries. The vehicle capacities of these carriers are as follows. Carrier C01 C02 C03 C04 C05 C06 Capacity 600 720 450 510 660 550 The problem is to assign routes to the minimum number of carriers in such a way that all routes are completed within a time limit of two hours. For instance, routes 5, 9, and 10 could be assigned to carrier C04 because the total time to complete the routes is 115 minutes and the total load is 485. Create a spreadsheet model and use solver for optimized route?
The network in the figure, shows the routes for shipping cars from three (3) plants (nodes, 1,2 and 3) to three (3) dealers (nodes, 6, 7, 8) by way of two (2) distribution centers (nodes 4and 5). The shipping costs per car (in $100) are shown on the arcs. Solve the problem as a transshipment model.1. Formulate the Linear Programming model 2. Choose one among the three methods for the starting/initial basic solution 3. Solve for the optimal solution using Method of Multipliers
Solve the following problem: The Krampf Lines railway company specializes in coal handling. On Saturday, Krampf had empty cars at the following towns in the quantities indicated: Town Supply of cars Morgantown 35 Youngstown 60 Pitsburg 25 By Monday, the following towns will need cars as follows: Town Demand for cars Coal Valley 30 Coal town 45 Coal junction 25 Coalsburg 20 The result is shown in the table below. To From Coal Valley Coal town Coal junction Coalsburg Morgantown 50 30 60 70 Youngstown 20 80 10 90 Pitsburg 100 40 80 30 Required: Minimize total miles over which cars are moved to new locations regarding the following: Formulate as a linear programming. Use North-West corner method to obtain the total shipment cost of coal cars.
FiberTech makes newsprint for newspapers at three mills, A,B, and C. Th e cost of producing newsprint is estimated to be $210 atmill A, $225 at B, and $220 at C. Five primary geographical marketsare served from these mills. Th e monthly demand at each market,the shipping cost (per ton) between each mill and market, and themonthly production capacity of each mill are given in the table FiberTech would like to assign production responsibilities tothe mills, and also specify how much should be shipped fromeach plant to each market, so as to minimize total production anddistribution costs.(a) Formulate an LP to minimize total production anddistribution costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.
the Problem. The DISTRIBUTION UNLIMITED CO. will be producing the same new product at two different factories, and then the product must be shipped to two warehouses, where either factory can supply either warehouse. The distribution network available for shipping this product is shown in Fig. 3.13, where F1 and F2 are the two factories, W1 and W2 are the two warehouses, and DC is a distribution center. The amounts to be shipped from F1 and F2 are shown to their left, and the amounts to be received at W1 and W2 are shown to their right. Each arrow represents a feasible shipping lane. Thus, F1 can ship directly to W1 and has three possible routes (F1 → DC → W2, F1 → F2 → DC → W2, and F1 → W1 → W2) for shipping to W2. Factory F2 has just one route to W2 (F2 → DC → W2) and one to W1 (F2 → DC → W2 → W1). The cost per unit shipped through each shipping lane is shown next to the arrow. Also shown next to F1 → F2 and DC → W2 are the maximum amounts that can be shipped through these lanes. The…

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a. Vogel's Approximation Method (VAM) for initial basic feasible solution b. North West Corner Method (NWCM) c. Least Cost Method (LCM)