Using the centre of gravity location technique, determine the location coordinates that will minimize the transportation costs for their family of products.
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A food manufacturer wants to locate a warehouse to serve its major customers. The customers, annual volume and the X and Y coordinates are shown in the table below.
|
Customer |
Annual Volume |
X Coordinate |
Y Coordinate |
|
Judy Inc |
25 |
3 |
7 |
|
Zac Supermarket |
13 |
5 |
2 |
|
Harry Inc |
6 |
8 |
4 |
|
Sky Productions |
4 |
1 |
5 |
- Using the centre of gravity location technique, determine the location coordinates that will minimize the transportation costs for their family of products.
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- 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 275,000 5 5 Scottsdale 415,000 5 10 Chandler 310,000 5 0 Mesa 660,000 10 1 Glendale 335,000 1 10 a. Where should Oscar build? Oscar should build at an x coordinate of nothing and a y coordinate of nothing. b. If Oscar wanted to relocate to the closest city near his new facility, where would he live? (Enter your responses rounded to one decimal place.)A farmers' cooperative association plans to build a new sugar mill in Georgetown. Theprimary objective of the mill is to provide the farmers with a place to take their crop forprocessing that will reduce their transportation costs. The members of the co-op believe thatthe center-of-gravity method is appropriate for this objective. While there are over 200 sugarcane farms in the region, they are tightly clustered around six villages. Using the data below,use the center-of-gravity method to calculate the coordinates of the best location for this mill.All mileage references use Browns Town as (0,0).VillageMiles East ofBrowns TownMiles North ofBrowns TownSugar CanetonnageBarney Valley 90 10 240,000Blue Pasture 140 60 320,000Congo Valley 20 70 450,000Bower 50 20 120,000Rabacca 100 80 60,000Salem 10 120 140,000Three 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.
- East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. Calculate the volume-weighted center of gravity. X-coordinate Y-coordinate Volume Athens, Texas 30 40 100 Beaumont, Texas 20 15 400 Carthage, Texas 55 60 150 Denton, Texas 20 70 250ElectroMart wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop and solve a model to find the best location, assuming that straight-line distances can be used between the locations The best location for the warehouse is at X....... and Y......... (Round to two decimal places as needed.)Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. Region DC A B C D 1 1 3 3 2 2 2 4 1 3 3 3 2 2 3 The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Write the constraints for the three distribution centers.
- For the the Clayton County Rescue Squad and Ambulance Service (Facility Location Nonlinear Model) example from Lecture 6, the number of estimated trips to Dunning has changed to 15. Which one of the options below, best represents the new optimal point (x,y) - best location to place the facility? Group of answer choices (19.24,16.30) (12.24,8.30) (20.24,21.30) (18.24,15.30) None of the aboveA small manufacturing facility is being planned that will feed parts to three heavy manufacturing facilities. The locations of the current plants with their coordinates and volume requirements are given in the following table: Use the centroid method to determine a location for this new facility.A logistics company plans to provide coal logistics transportation services to HY coal sales enterprise. HY coal sales enterprise has coal storage and sales points in B and D, with available coal quantities of 1600t and 8000t, respectively; A and C represents the locations of two coal users, with a demand of 8000t and 1600t respectively. The distribution of relevant locations and travel distances are shown in Figure 1. Based on the above conditions, try to calculate and explain from the perspective of transportation capacity consumption: How should logistics company HY plan transportation routes in order to make them more reasonable? (a transportation route planning scheme needs to be illustrated) . Note:The solution should not be hand written.
- 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?A single facility is needed to meet the demands of four markets. The locations and demands ofthese four markets are shown below. Market Coordinates Demand A (8,6) 10 B (4,12) 15 C (3,2) 10 D (9,6) 6 1.Using the data in the table above, identify an optimal location for the new facility. 2. A manufacturing firm is considering three potential locations for a new parts manufacturing facility. Aconsulting firm has assessed three sites based on the four factors supplied by management as critical tothe location's success. Management-supplied the factor weights and the consultant team scores as seen as in the table below. Scores are based on 50 = best. Location Factor Weight A B C Labour climate 10 35 45 20 taxes 30 30 40 40 utilities 20 25 20 45 wages 40 10 25 25 Which location should be selected and why?Dennison Manufacturing makes large helical springs used in aircraft landing gear. The company has narrowed its potential choices for its new manufacturing facility to four cities. The following information is known about the manufacturing and shipping costs of locating in each of these four cities: Fixed Costsper Year Variable ManufacturingCosts per Unit Variable ShippingCosts per Unit Phoenix Buffalo Seattle Atlanta $300,000 $600,000 $1,500,000 $1,750,000 $70.00 $56.00 $36.00 $42.00 $5.00 $4.00 $2.00 $5.00 a. Use break-even point analysis to determine where Dennison should locate.b. Based solely on break-even quantity, if Dennison’s manufacturing forecast for the foreseeable future is 40,000 units annually, where should he locate?