Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. Using this information and other relevant information obtained from Eve, demonstrate how the centre of gravity location technique can be used to determine the best location that will minimize total travel distance.

Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. Using this information and other relevant information obtained from Eve, demonstrate how the centre of gravity location technique can be used to determine the best location that will minimize total travel distance.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 100P

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Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. Using this information and other relevant information obtained from Eve, demonstrate how the centre of gravity location technique can be used to determine the best location that will minimize total travel distance b. Using a numerical example, demonstrate how break-even analysis (graphical approach) can be used to determine the…
Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. b. Using a numerical example, demonstrate how break-even analysis (graphical approach) canbe used to determine the best of three locations.
A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scattered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by a team of workers, who will drive from the central office to the site. Houma will be visited five times a year. Which coordinates represent a good central location for this office? What other factorsmight influence the office location decision? Where would youplace this office? Explain.
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
A chain of home health care firms in Louisiana needsto locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scat-tered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by ateam of workers, who will drive from the central office to the site. Houma will be visited five times a year. Which coordinates rep-resent a good central location for this office? What other factors might influence the office location decision? Where would youplace this office? Explain. PXCITY MAP COORDINATESx yCovington 9.2 3.5Donaldsonville 7.3 2.5Houma 7.8 1.4Monroe 5.0 8.4Natchitoches 2.8 6.5New Iberia 5.5 2.4Opelousas 5.0 3.6Ruston 3.8 8.5
Mitch just built 4 franchise locations for his newest pizzerias and wants to decide where to put his headquarters. He makes 1 weekly visit to his Northside store (X = 3, Y = 10), 2 visits to his Eastside store (X = 4, Y = 6), 3 visits to his Southside store (X = 2, Y = 5) & 4 visits to his Westside store (X = 1, Y = 4). __________ 1. Using the store visits as weights, compute the coordinates of the center of gravity to help him with his location decision.
Hardgrave Machine Company produces computer components at its factories in Cincinnati, Kansas City, and Pittsburgh. These factories have not been able to keep up with demand for orders at Hardgrave’s four warehouses in Detroit, Houston, New York, and Los Angeles. As a result, the firm has decided to build a new factory to expand its productive capacity. The two sites being considered are Seattle, Washington, and Birmingham, Alabama. Both cities are attractive in terms of labour supply, municipal services, and ease of factory financing. Table 1 presents the production costs and monthly supplies at each of the three existing factories, monthly demands at each of the four warehouses, and estimated production costs at the two proposed factories. Transportation costs from each factory to each warehouse are summarized in Table 2. In addition to this information, Hardgrave estimates that the monthly fixed cost of operating the proposed facility in Seattle would be $400,000. The…
A company wants to expand its offices to different cities in the future which might cost them alot and will lower their companies revenue suggest three alternatives with advanatges and disadvanatges they can opt for instead of building offices in different cities
The FAA has granted a license to a new airline, Omniair, and awarded it several routes between Los Angeles and Chicago. The flights per day for each route are shown in the following network: Determine the maximum number of flights the airline can schedule per day from Chicago to Los Angeles and indicate the number of flights along each route.
Frieda Millstone and her family live in Roanoke, Virginia, and they are planning an auto vacation across Virginia, their ultimate destination being Washington, DC. The family has developed the following network of possible routes and cities to visit on their trip: The time, in hours, between cities (which is affected by the type of road and the number of intermediate towns) is shown along each branch. Determine the shortest route that the Millstone family can travel from Roanoke to Washington, DC.
The MidLands Trucking Company based in Louisvillehas eight trucks located throughout the Mideast that havedelivered their loads and are available for shipments. Through their Internet logistics site MidLands has re-ceived shipping requests from 12 customers. The follow-ing table shows the mileage for a truck to travel to a customer location, pick up the load, and deliver it. Determine the optimal assignment of trucks to customersthat will minimize the total mileage. Customers Truck A B C D E F G H I J K L1 500 730 620 410 550 600 390 480 670 710 440 5902 900 570 820 770 910 660 650 780 840 950 590 6703 630 660 750 540 680 750 810 560 710 1200 490 6504 870 1200 810 670 710 820 1200 630 700 900 540 6205 950 910 740 810 630 590 930 650 840 930 460 5606 1100 860 800 590 570 550 780 610 1300 840 550 7907 610 710 910 550 810 730 910 720 850 760 580 6308 560 690 660 640 720 670 830 690 880 1000 710 680