Maximum Flow
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- Val’s Pizza is looking for a single central location to make pizza for delivery only. This college town is arranged on a grid with arterial streets, as shown in Figure. The main campus (A), located at 14th and R, is the source of 4,000 pizza orders per week. Three smaller campuses (B, C, and D) are located at 52nd and V, at 67th and Z, and at 70th and South. Orders from the smaller campuses average 1,000 pizzas per week. In addition, the State Patrol headquarters (E) at 10th and A orders 500 pizzas per week.a. At about what intersection should Val start looking for a suitable site? (Estimate coordinates for the major demands accurate to the nearest one-quarter mile, and then find the center of gravity.)b. What is the rectilinear weekly load–distance score for this location?c. If the delivery person can travel 1 mile in 2 minutes on arterial streets and ¼ mile per minute on residential streets, going from the center of gravity location to the farthest demand location will take how long?If the amount of fabric shipped to each plant is equal, what is the optimal location for the fabric plant? Show your computationThe new Health-Watch facility is targeted to serve seven census tracts in Erie, Pennsylvania, whose latitudes and longitudes are shown in Table, along with the population in each census tract (in thousands). Customers will travel from the seven census-tract centers to the new facility when they need health care. What is the target area’s center of gravity for the Health-Watch medical facility?
- For each alternative new plant location, determine the shipping pattern that will minimize total transportation costs. Where should the new plant be located? Plant Capacity (Cases per Week) Warehouse Demand (Cases per Week) Chicago 10,000 Miami 7,000 Houston 7,500 Denver 9,000 New plant 8,000 Lincoln 4,500 Total 25,500 Jackson 5,000 Total 25,500 Shipping Cost to Warehouse (per Case) Plant Miami Denver Lincoln Jackson Chicago $7.00 $2.00 $4.00 $5.00 Houston $3.00 $1.00 $5.00 $2.00 Buffalo (alternative 1) $6.00 $9.00 $7.00 $4.00 Atlanta (alternative 2) $2.00 $10.00 $8.00 $3.00Suppose that you are an engineer tasked with finding a new location for your distribution center (let's say you work as an industrial engineer at a cosmetics company). You have a good idea of who your customers are and how many tons of cosmetics you must ship per week. Using your company headquarters as the origin, you plot out the following table: Customer x-location (miles) y-location (miles) Quantity (tons/week) JC Penney 10 280 3 BB&B 70 180 7 Target 80 160 4 Bath&Body Works 170 20 5 Walmart…. A company has a central supply facility and a distribution center located 400miles away. The central supply product cost is $75, TL transportation rates fromcentral supply to the DC are $60 per unit, and handling costs at the DC are $4 perunit. Calculate the market boundary location and the landed cost at the marketboundary. LTL rates are $2 per unit per mile.
- Jk.335. Propiem 14-8 Rent'R Cars is a multisite car rental company in the city. It is trying out a new "return the car to the location most convenient for you" policy to improve customer service. But this means that the company has to constantly move cars around the city to maintain required levels of vehicle availability. The supply and demand for economy cars, and the total cost of moving these vehicles between sites, are shown below. From To A B C Demand D $9 9 5 50 From/To $8 Candidate solution A B C Total shipped Cost A - B C Total costs 8 3 60 $6 8 3 25 $5 D 0 10 a. Find the solution that minimizes moving costs using Microsoft Excel. (Leave no cells blank - be certain to enter "0" wherever required.) Supply 50 40 75 30 165 165 E F G Supply $A manufacturing company is considering two alternative locations for a new facility. The fixed and variable costs for the two locations are found in the table below. For which volume of business would the two locations be equally attractive (Hint: the crossover point)? Please show your work. New Jersey Delaware Variable Costs ($ per unit) _____ (Please pick a number from 11-20 and fill in the blank above. Use the number for your calculation.) _____ (Please pick a number from 21-30 and fill in the blank above. Use the number for your calculation.) Fixed Costs $___________ (Please pick a number from 1,000,000-1,200,000 and fill in the blank above. Use the number for your calculation.) $___________ (Please pick a number from 800,000-1,000,000 and fill in the blank above. Use the number for your calculation.)ART Contractors must locate an equipment staging area to serve three construction sites, located at coordinates (0,2), (0,4), and (5,5). Traffic between the staging area and each of the three sites will be equal. What is the best set of coordinates for the equipment staging area? Please show the math.
- A small rural county has experienced unprecedented growth over the past 6 years, and as a result, the local school dis-trict built the new 500-student North Park Elementary School. The district has three older and smaller elementary schools:Washington, Jefferson, and Lincoln. Now the growth pressure isbeing felt at the secondary level. The school district would like tobuild a centrally located middle school to accommodate studentsand reduce busing costs. The older middle school is adjacent tothe high school and will become part of the high school campus.a) What are the coordinates of the central location?b) What other factors should be considered before building aschool?The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub. Using the Center of Gravity method, near which map coordinates should the hub be located? STORE LOCATION CONTAINERS SHIPPED PER MONTH X Y Chicago 2,000 50 120 Pittsburgh 1,000 110 100 New York 3,000 160 130 Atlanta 2,000 120 40A bank has its head office in the financial district in the middle ofa city. A bank has six branches, three in the north of the city and threein the south all 5 km from the centre and spaced 3 km apart. The bankwishes to link all its branches via private leased lines but mustdecide between providing an individual line to each branch via anumber of inter-branch links and a smaller number of multiplexed linesto the centre. If a modem costs £100, a multiplexer/demultiplexercosts £200 and leased lines cost £100 per km per year to rent, suggesta design that will yield the most cost effective solution if theinstallation is to remain in operation for four years. 1st option is - link all branches by providing individual line to each branch via a number of inter branch links to the centre. 2nd option is - link all branches by providing smaller number of multiplexed lines to the centre Please calculate both options and choose the most cost effective solution for four years?