a. Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. b. Solve the problem in part (a).
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Linear programming is a method of operation optimization with specific restrictions. The main objective of linear programming is to increase or reduce a numerical value. A common method for assessing the best use of resources is linear programming. An example of a linear programming problem is one that aids in identifying the feasible area and optimizing the solution to obtain the highest or lowest function value.
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- b. 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 thetable below. Customer Annual Volume X-Coordinate Y-Coordinate Judy inc. 25 3 7Zac Supermarket 13 5 2Harry Inc. 6 8 4Sky Productions 4 1 5 i. Using the centre of gravity location technique, determine the locationcoordinates that will minimize the transportation costs for their family ofproductsProblem 15-10 (Algo) A 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: PLANT LOCATION Peoria Decatur Joliet COORDINATES (x, y) 306, 307 373, 468 468, 175 Cx Cy VOLUME (PARTS PER YEAR) 4,200 6,150 2,900 Use the centroid method to determine the best location for this new facility. (Round your answers to 1 decimal place.)J 2 An electronics store 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 a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)
- 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: No. of Coordinates Section Contracts x y Parkview 70 5.2 8.3 Mt. Airy 200 3.6 3.0 Valley 70 13.6 7.2 Norwood 300 15.1 4.0 Southgate 170 13.8 8.7 Use the center-of-gravity method to determine an ideal location for a service center. Round your answers to two decimal places. Cx: ____________Cy: ____________ A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Location Criteria Weight 1 2 3 4 Raw material availability 0.06 P VG OK VG Infrastructute 0.07 P G VG OK Transportation costs 0.33 G P OK P Labor relations 0.25 VG G…Problem 14-10 A 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: VOLUME COORDINATES (x, y) 299, 298 380, 462 478, 190 PLANT LOCATION (PARTS PER YEAR) 4,000 6,000 3,000 Peoria Decatur Joliet Use the centroid method to determine the best location for this new facility. (Round your answers to 1 decimal place.) Сх CyA company that handles hazardous waste wants to minimize the shipping cost for shipments to a disposal center from five receiving stations it operates. The locations of the receiving stations and the volumes to be shipped daily are given in the below table: Location ( x, y ) Daily Volume ( in truck loads ) A (5.70,5.00) 15 B (4.00,7.70 ) 9 C (1.90,2.80 ) 18 D (2.10,5.20 ) 16 E (7.50, 6.30) 17 1. Which one of the following coordinate is closest to the optimal location using median method? a) (4.00,5.20) b) (4.00,3.64) c) (2.60,5.20) d) (5.80,3.12) 2. Which one of the following coordinate is closest to the optimal location using gravity method? a) (4.22,4.62) b) (5.91,6.16) c) (4.22,5.13) d) (5.28,5.13) 3. Which one of the following is closest to the total distance traveled (optimal objective function value) using Rectilinear distance measure for the optimal median solution? a) 241 b)352 c)157 d)133
- a. A farmers' cooperative association plans to build a new sugar mill in Georgetown. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the co-op believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane 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). Village Barney Valley Blue Pasture Congo Valley Bower Rabacca Salem Miles East of Miles North of Sugar Cane Browns Town Browns Town 90 140 20 50 100 10 10 60 70 20 80 120 tonnage 240,000 320,000 450,000 120,000 60,000 140,000Consider you are an owner of one IT organization with 200 employees and youwant to keep track of the location information of each employee. You know thatnone of the employees will go out from the city and the radius of the city is 50 km.What kind of location measure technique will be appropriate for you to keep trackcontinuous location information?Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: PotentialLocations forSubstations AreasCovered A 1, 2, 5, 7 B 1, 3, 5 C 2, 4, 5 D 3, 4, 6 E 4, 5, 6 F 1, 5, 6, 7 G 1, 5, 7 xA + xB + xC + xD + xE + xF + xG (area 1 covered) xA + xB + xC + xD + xE + xF + xG ≥, =, or less than or equal to (area 2 covered) xA + xB + xC + xD + xE + xF + xG (area 3 covered) xA + xB + xC + xD + xE + xF + xG (area 4 covered) xA + xB + xC + xD + xE + xF + xG (area 5 covered) xA + xB + xC + xD + xE + xF + xG (area 6 covered) xA + xB + xC + xD + xE + xF + xG (area 7 covered) (a) Formulate an integer programming model that could be used to find the minimum number of…
- As part of a locational break-even analysis, an operations analyst at MGX Ltd produced the graph below. Locational break-even analysis 140000000 120000000 100000000 80000000 360000000 40000000 20000000 2000 OA. Johannesburg O 8. Cape Town OC Durban COD. None WT. 4000 0000 6000 Quantity produced Unis 10000 12000 14000 **** Johannesburg Cape Town Durban Suppose that the management of MGX Ltd has decided on a daily capacity of 8 000 units of the product to be manufactured at the selected location, which of the locations should be selected? O 16000 Time left 1:56 P Flag question1. Using the center-of-gravity method, compute the centralized coordinates among the following locations, which are indicated via black cells with white text in LOCATION.xlsx: 7,1 10,1 4,2 2,5 6,6 9,6 2,8 6,10 2. Using the weighted average center-of-gravity, which accounts for quantities to be shipped from locations, compute the centralized coordinates among the following locations: 7,1 10,1 4,2 2,5 6,6 9,6 2,8 6,10 *Quantities to be shipped are listed within the existing locations (i.e. Location 7,1 ships 17 units) in LOCATION.xlsxI have two marlets , Hilltor & Biztop, where I will be delivertrg 1 900ds 9oods. Hilltop is located at coordinates L2,0) ano I have 14 twckloads gorp to it. Biztop is lo cated at Coordinetes (16,14) and I have 7 truckloads goirg to it. Use an optimol method to find the location for building a ware house to the two marketi. Record the X Supply Coordinate of the optimal aarehouse location . Round to 2Decimali