Concept explainers
(a)
Interpretation: An electronics firm located near Phoenix, Arizona, is considering where to locate a new phone switch that will link five buildings. The buildings are located at (0,0), (2,6), (10,2), (3,9) and (0,4). The objective is to locate the switch to minimize the cabling required to those five buildings, for which the gravity solution needs to be determined.
Concept Introduction: In a gravity modeling, locations are determined that minimizes the cost of transportation of raw materials from the supplier as well as manufactured goods to the market.
(b)
Interpretation: An electronics firm located near Phoenix, Arizona, is considering where to locate a new phone switch that will link five buildings. The buildings are located at (0,0), (2,6), (3,9) and (0,4). The objective is to locate the switch to minimize the cabling required to those five buildings. Assuming a straight line distance measurement and if the problem is solved by hand, the appropriate equations needs to be iterated at least five times, and the optimal location needs to be determined.
Concept Introduction: The simple measurement of distance in a straight line between two facilities is called Euclidean Distance.
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Chapter 11 Solutions
EBK PRODUCTION AND OPERATIONS ANALYSIS
- A larger and more modern main post office is to be constructed at a new location in Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years ago, when the current facility was built. Annette Werk, the postmaster, asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post office, M, are shown in the following table. M will continue to act as a mail source point after relocation. Mail Source Point Round trips per day x, y, Coordinates (miles) 1 4 (4, 6) 7 (8, 4) (3, 14) (6, 10) (12, 11) (13, 5) (13, 6) (14, 10) 3 1 4 11 7 3 7 3 M 8 a. Calculate the center of gravity as a possible location for the new facility. (Enter your responses rounded to the nearest whole number.) The center of gravity "X" coordinate = The center of gravity "Y" coordinate =arrow_forwardA larger and more modern main post office is to be constructed at a new location in Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years ago, when the current facility was built. Annette Werk, the postmaster, asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post office, M, are shown in the following table. M will continue to act as a mail source point after relocation. Mail Source Point Round trips per day x, y, Coordinates (miles) 1 8 2 2 1 6 3 4 6 7 M 2 4 8 The center of gravity "X" coordinate = 10 The center of gravity "Y" coordinate = 6 (11,5) (15,5) (1, 13) (2, 1) (4, 14) (16, 12) (15,5) (14,2) a. Calculate the center of gravity as a possible location for the new facility. (Enter your responses rounded to the nearest whole number.) b. Compare the load-distance scores for the…arrow_forwardRauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers (located in cities A, B, and C). As shown in the table below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following information: Location Coordinates (miles) Deliveries per day (200,100) (300,100) (300,300) A 9 B 5 7 a. Which of these three locations yields the smallest load-distance score, based on Euclidean distances? Location V yields the smallest load-distance score of : (Enter your response rounded to one decimal place.)arrow_forward
- Answer the given question with a proper explanation and step-by-step solution. Medco plans to open a new medical center and is looking for a suitable location. They have narrowed their choice down to three locations, on Oak, Elm, and Ash Streets. They have defined four factors and have assigned weights to these factors as follows: proximity to hospitals (40), customer parking (30), appearance (20), and ease of expansion (10). They then rated the three locations for the four factors, using a scale of one to five. Their ratings are as follows: Location Factor Weight Oak Elm Ash Proximity to hospitals 40 2 5 3 Customer parking 30…arrow_forwardTask 1: An oil refining company ships the following gasoline volumes from its refining plant in Long beach to its major distributors: Coordinates (x, y) 400, 150 450, 350 350, 400 25, 450 Distributor Gallons (in millions) Anaheim 150 LaHabra 350 Glendale 250 Thousand Oaks 450 The location coordinates of the refining plant in Long Beach are: (325, 75). Under a new proposed distribution setting, the company wants to setup an intermediate holding facility, such that gasoline will first get transported to this holding facility, and then, from there, to the distributors. What will be the ideal location (coordinates) for the intermediate holding facility? (Round to 2 decimal places.)arrow_forwardA company has a manufacturing plant that supply three markets in city A, B, and C. Management is looking for a place to locate a single distribution that will minimize total transportation costs. The plant is estimated to move (send) a total of shipment of 12,700 ton per month to the new distribution center. The transportation rate of moving shipment from the plant to the distribution center is $ 0.08 per ton per mile. Market A will receive a total shipment of 6,200 ton per month, market B will receive a total shipment of 2,000 ton per month, and market C will receive a total shipment of 4,500 ton per month. The transportation rate between the distribution center and the markets are as follows: $0.19 per ton per mile to market A, $0.37 per ton per mile to market B, and $0.25 per ton per mile to market C. The horizontal and vertical coordinates of the plants and markets are follows: Plant, 25, 75 Market A, 30, 5 Market B, 36, 24 Market C, 15, 40 Use the Center-of-Gravity method to find…arrow_forward
- Microserve provides computer repair service on a contract basis to customers in five sections of the city. The five sections, the number of service contracts in each section, and the x and y coordinates of each section are as follows: Section Parkview Mt. Airy Valley Norwood Southgate No. of Contracts 90 220 60 3.4 14.2 290 17.7 160 14.0 Use the center-of-gravity method to determine an ideal location for a service center. Round your answers to two decimal places. Cx: Cy: Choose the correct graph representing the center of gravity. The correct graph is -Select- v A. C. Center of Gravity 20 Y- Coordinate y- 16- 12- 8 4+ 20- 16- 12 ● ● • 12 x- Coordinate Center of Gravity y- Coordinate: 16 ● B. D. -20+ -16- 12 8+ 20 16- 12 Center of Gravity y- Coordinate 8 12 x- Coordinate Center of Gravity y- Coordinate ● 16 Coordinates X Y 6.2 11.9 4.2 5.3 4.4 10.9arrow_forwardA company that handles hazardous waste wants to minimize the shipping cost for shipments to a disposal center from five receiving stations it operates. Given the locations of the receiving stations and the volumes to be shipped daily, determine the location of the disposal center.arrow_forwardThe new Health-Watch facility is targeted to serve seven census tracts in Erie, Pennsylvania, whose lati-tudes and longitudes are shown in Table 13.1, along with the population in each census tract (in thou-sands). Customers will travel from the seven census-tract centers to the new facility when they needhealth care. What is the target area’s center of gravity for the Health-Watch medical facility?arrow_forward
- Locating Warehouses. Southeastern Foods has hired you to analyze their distribution-system design. The company has 11 distribution centers, with monthly volumes as listed below. Seven of these sites can support warehouses, in terms of the infrastructure available, and are designated by (W). The monthly fixed cost for operating one of these warehouses is estimated at $3,600, although there is no capacity limit in their design. Southeastern could build warehouses at any of the designated locations, but its criterion is to minimize the total of fixed operating costs and variable shipment costs. The table below shows the cost per carton of shipping from any potential warehouse location to any distribution center. Using the evolutionary solver, find the minimum monthly cost for Southeastern Foods.arrow_forwardI have two locations where I will be delivering goods. Vaalbara is located at coordinates (10,0) and I have 10 truckloads going to it. Kenorland is located at coordinates (20,20) and I have 40 truckloads going to it. What is the center of gravity's X coordinate? Round to the nearest whole number (e.g. 33.2 -> 33). I have two locations where I will be delivering goods. Vaalbara is located at coordinates (10,0) and I have 10 truckloads going to it. Kenorland is located at coordinates (20,20) and I have 40 truckloads going to it. What is the center of gravity's Y coordinate? Round to the nearest whole number (e.g. 33.2 -> 33). 0*10 + 20*40 = 800. Sum of loads = 50. Y coordinate = 16arrow_forwardEve 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.arrow_forward
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