Chapter 1.4, Problem I.8E

Oscar’s Bowling, Inc., wants to break into the Phoenix metropolitan market with one of its super-sized 200 lane, 24-hour bowling alleys. It, however, only has enough capital to build one facility. Oscar wants it to be centered by population, as determined by the center of gravity method. The following information is given: City Population x coordinate y coordinate Tempe Scottsdale Chandler Mesa Glendale 250,000 400,000 300,000 700,000 350,000 5 5 5 10 1 5 10 0 1 10 a. Where should Oscar build? b. If Oscar wanted to relocate to the closest city near his new facility, where would he live?

Consider the transportation problem having the following data:   c) write the algebraic formulation of this problem.

Suppose a company with a plant located in Toronto is serving a market in the northeastern United States with many customers located in Boston. If the company ships direct to customers from the Toronto plant, most shipments will be less than truckload. However, if it locates a distribution center in Boston, it can ship truckload (TL) to Boston and distribute bylocal cartage (LTL) to customers in that area. Whether this is economical or not depends on the total cost of shipping direct compared with shipping via the distribution center. Assume the following figures represent the average shipments to the Boston area:Option 1: Plant to customer LTL: $100/cwt. [uses direct dispatch from company to customers]Option 2: Through DCPlant to distribution center TL: $50/cwt.Inventory-carrying cost (distribution center): $10/cwt.Distribution center to customer LTL: $20/cwt.QuestionIs it more economical to establish the distribution center in Boston? If the annual shipped volume is 10,000 cwt., what…

TMA manufactures 37-in. high definition LCD televisions in two separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of televisions to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the two TMA plants to the two Pulsar factories are as follows.       To Pulsar Factories     From TMA City A City B   Location I $5 $3   Location II $6 $9 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x, y)  =…

Three existing facilities are located at (0, 0), (5, 5), and (10, 10). The weights applied to these facilities are 1, 2, and 3, respectively. Find the location of a new facility that minimizes the weighted Euclidean distance to the existing facilities.

Tommy Hilfiger is currently considering to source certain textile goods, Tommy Jeans, from Mexico. The estimated shipping time from Mexico to the U.S. for each shipment of Tommy Jeans is 4 days and the estimated freight cost of each shipment is $800. On the other hand, the current average shipping time from Vietnam to the U.S. for each shipment of Tommy Jeans is 23 days and the average freight cost is $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…

The photocopying business is thriving in Dagupan City. Miss Josefina “ Fina” Datu is the owner and operator of the biggest copying firm in the city. Fina has been in the business for more than 20 years and because of her daring and enterprise, she was able to put up three branches in each of the capital towns of three adjoining provinces, namely Nueva Ecija, Tarlac, and Pangasinan. She is planning to operate in Nueva Vizcaya and Isabela shortly.     This business involves using machines to copy documents, books magazines, and other materials. Fina employs six young ladies per branch. A big dealer in Manila supplies her with the latest copying machines, paper, and ink. Fina has an open credit line with the leader.      Fina personally trains new employees in the firm’s main office in Dagupan. After a month of training, the new employees are deployed in the various branches. New employees are paid daily wages depending on the output. They are also entitled to free board and lodging.…

The photocopying business is thriving in Dagupan City. Miss Josefina “ Fina” Datu is the owner and operator of the biggest copying firm in the city. Fina has been in the business for more than 20 years and because of her daring and enterprise, she was able to put up three branches in each of the capital towns of three adjoining provinces, namely Nueva Ecija, Tarlac, and Pangasinan. She is planning to operate in Nueva Vizcaya and Isabela in the near future.     This business actually involves using machines to copy documents, books magazines, and other materials. Fina employs six young ladies per branch. A big dealer in Manila supplies her with the latest copying machines, paper and ink. Fina has an open credit line with the leader.      Fina personally trains new employees in the firm’s main office in Dagupan. After a month of training, the new employees are deployed in the various branches. New employees are paid daily wages depending on output. They are also entitled to free board…

Suppose there is a transportation model with 4 factories and 6 warehouses. In order to develop an initial solution using the intuitive lowest cost method, do we have to add one or more dummy sources in the transportation matrix, and why?