A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. D1 D2 D3 D4 Capacity S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Find initial basic feasible solution for given problem by using column minima method if the object is to minimize the total transportation cost.

A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. D1 D2 D3 D4 Capacity S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Find initial basic feasible solution for given problem by using column minima method if the object is to minimize the total transportation cost.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 80P

See similar textbooks

Similar questions

A product is produced by four factories F1, F2, F3, and F4. Their production capacities are: F1:47 units, F2:67 units, F3:27 units and F4:57 units. These factories supply the product to four stores, demand of which is 22, 32, 102, and 17 units respectively. Unit transportation cost in dollars from each factory to each store is given in the following table. Determine the extent of deliveries from each of the factories to each of the stores so that the total production and transportation cost is minimum. Factories Stores Supply S1 S2 S3 S4 F1 4 6 8 13 47 F2 14 12 10 8 67 F3 11 1 7 10 27 F4 10 12 14 9 57 Demand 22 32 102 17
A product is manufactured by four factories A, B, C and D. The unit production costs in them are ETB 2, ETB 3, ETB 1 and ETB 5 respectively. Their production capacities are 50, 70, 30 and 50 units 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 store is given in the table below. Stores 1 2 3 4 2 4 6 11 10 8 7 5 13 3 9 12 4 6 8 3 A Factories B C D Determine the transportation plan to minimize the total production-cum-transportation cost by using: Vogel’s Approximation Method (VAM)…
Transeast Airlines flies planes on the following route:L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) ofeach segment of this trip is as follows: L.A.–Houston, 1,500miles; Houston–N.Y., 1,700 miles; N.Y.–Miami, 1,300miles; Miami–L.A., 2,700 miles. At each stop, the planemay purchase up to 10,000 gallons of fuel. The price of fuelat each city is as follows: L.A., 88¢; Houston, 15¢; N.Y.,$1.05; Miami, 95¢. The plane’s fuel tank can hold at most12,000 gallons. To allow for the possibility of circling overa landing site, we require that the ending fuel level for eachleg of the flight be at least 600 gallons. The number ofgallons used per mile on each leg of the flight is1 (average fuel level on leg of flight/2,000)Review Problems 123To simplify matters, assume that the average fuel level onany leg of the flight isFormulate an LP that can be used to minimize the fuel costincurred in completing the schedule
Transportation Problem: A semi-products manufacturer has 3 production facilities (X, Y, Z) and distributes its products to 3 various customers (K, L, M) from these production facilities. The daily production capacity of each production facility and the daily distribution costs are given in the below table. Daily demands of customers are 42, 27, and 33, respectively. Namely, in a day, customer K requires 42 units of products, customer L requires 27 units of products, and customer M requires 33 units of products. (a) Formulate a balanced transportation problem that could be used to determine how to minimize the total cost of meeting the demand of customers. The formulation should be in open form and decision variables should be defined as integer amounts. (b) Use LINGO/OPL/EXCEL to solve your model. Write down the results of the decision variables and the objective function. Explain the value of the decision variables. What do they mean? (c) Use the Northwest Corner method to find a…
A manufacturer has two factories, located in Toronto and Winnipeg. Warehouses are located in Moncton, Montreal, and Calgary. Minimum requirements at the three warehouses are for at least 5 000, 8 000, and 7 000 units, respectively. The production capacities of the two factories are 9 000 and 11 000 units, respectively. Shipping costs per unit from each factory to each warehouse are given below: WAREHOUSE Moncton Montreal Calgary FACTORY Toronto $14 $6 $18 Winnipeg $22 $17 $9 The manufacturer wants to determine the optimal shipping schedule that will minimize transportation costs. Formulate the linear programming model for this problem.
General Ford has two plants, two warehouses, and three customers. The locations of these as follows: Plants: Detroit and Atlanta;Warehouses: Denver and New YorkCustomers: Los Angeles, Chicago, and Philadelphia Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. Detroit can produce 142 cars per week, and Atlanta can produce 86 cars per week. Los Angeles requires 50 cars per week; Chicago, 52; and Philadelphia 84. It costs $9500 to produce a car in Detroit and $7500 to produce a car in Atlanta, and the costs of shipping a car between cities are given in the table below. What is the minimal cost of meeting General Ford's weekly demands?
There are three factories located at Arkansas (AR), Indianapolis (IN), and Texas (TX) respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The revenue per commodity item is $18. The weekly demand of the warehouse A and B are respectively 45 and 60 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 24, 28, and 33 units. The cost of transportation per unit is given as below. Cost Warehouse A Warehouse B AR 5 3 IN 6 6 TX 2 4 To maintain a good relationship with all the factories, warehouse A requires that it receives at least 30% of its product from factory in AR. Realize that it is making good profit in warehouse B, TX requires that at least 35% of its product shipped to warehouse B. Formulate (without solving) a linear programming problem to maximize the profit.
General Ford has two plants, two warehouses, and threecustomers. The locations of these are as follows:Plants: Detroit and AtlantaWarehouses: Denver and New YorkCustomers: Los Angeles, Chicago, and PhiladelphiaCars are produced at plants, then shipped to warehouses,and finally shipped to customers. Detroit can produce 150cars per week, and Atlanta can produce 100 cars per week.Los Angeles requires 80 cars per week; Chicago, 70; andPhiladelphia, 60. It costs $10,000 to produce a car at eachplant, and the cost of shipping a car between two cities isgiven in Table 62. Determine how to meet General Ford’sweekly demands at minimum cost.
The logistic company headquartered in New York wants to expand its business in Chicago, Texas, and Las Vegas. They will place 3 branch heads (A, B a, nd C) from several branch offices owned by the company to set-up offices and run operations in these 3 locations. Below are the costs for allocating the 3 branch heads to each location: Chicago Texas Las Vegas A $8,000,000 $11,000,000 $12,000,000 B $5,000,000 $15,000,000 $13,000,000 C $5,000,000 $10,000,000 $23,000,000 a. Create a table using the assignment method.b. Based on the results of your calculations, what advice can you give to the leader of the company for the most optimum companylocation placement of each of the above branch heads? Explain why?c. What is the total optimum cost that must be incurred by the company to allocate all company branch offices?
The Humber Transport Company has expanded its shipping capacity by purchasing 75 trailer trucks from a competitor that went bankrupt. The company subsequently located 25 of the purchased trucks at each of its shipping warehouses in Mississauga, Windsor, and Kingston. The company makes shipments from each of these warehouses to terminals in Montreal, New York, and Chicago. Each truck is capable of making one shipment per week. The terminal managers have each indicated their capacity for extra shipments. The manager in Montreal needs to accommodate 20 additional trucks per week, the manager in New York needs to accommodate 15 additional trucks per week, and the manager in Chicago needs to accommodate 30 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport rates. Terminal Warehouse A B C Montreal New York Chicago…
Luminous lamps have three factories - F1, F2, and F3 with production capacity 30, 50, and 20 units per week respectively. These units are to be shipped to four warehouses W1, W2, W3, and W4 with requirements of 20, 40, 30, and 10 units per week respectively. The transportation costs (in Rs.) per unit between factories and warehouses are given below. Find an initial basic feasible solution.
The Child-fair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distribution centers is given below. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost, where the freight cost for each shipment is $100 plus 50 cents/mile? Formulate this case as a transportation problem (a) algebraically, and (b) on a spreadsheet, then (c) use Solver to obtain the optimal solutions