Ms. Esther Rumble recently graduated with a degree in Supply Chain Management fr
ID: 353552 • Letter: M
Question
Ms. Esther Rumble recently graduated with a degree in Supply Chain Management from the University of Miami. Ms Kimberly Lee, her supervisor, is the General Manager of the Greater Miami Food Bank. This company collects food donations from local grocery stores and transports them back to a distribution center where they are sorted and transferred to local food kitchens that feed the needy. Due to tight budgets and growing environmental concerns, it is crucial that driver capacity and fuel be used efficiently. Thus, Ms. Lee has tasked Ms Rumble to ensure that the collection vehicles are routed in the most efficient manner. The distances in miles between any pair of stores, inc luding the depot is shown in the table below. This company's van follows a chosen route from Monday through Saturday, each week of the year, except for a break of 2 wecks in the year. One is in June and the other one is in December. The vans run on 15 miles per gallon of gasoline. The estimated price of gasoline is $2.45 per gallon and the estimated cost for vehicle maintenance and depreciation is S0.17 per mile. Put yourself in Esther Rumble's position and answer the following questions. From/Te De Store A Store B Store C Store D Store E Store A Stere B Store C Store D Store E 35 20 15 15 35 12 34 60 48 35 15 (a) The route curently being used for operation is: Depot Store AStore BStore DStore EDepot. How much does it cost the Food Bank annually to run this operation from the viewpoint of fuel and maintenance costs? [10 peints (b) Using the Nearest Neighbor (NN) heuristic, determine another route for the operation and find out the percentage reduction in total annual fuel and maintenance costs and comment on your result. [14 points 21 (c) If Mr. Tom Brady, the manager for Store B, suggests that the truck should start the pickup from his store every day before going to other stores, what are the cost implications of following his suggestion (based on the NN heuristic) if (i) the truck need not start at the Depot and end at the Depot each day 113 points] (ii) there is a requirement that the truck needs to leave from the Depot initially every day before going to and leaving from store B and eventually returning back to the Depot after arriving at store B 113 points. Clearly show full calculations and provide appropriate discussions of the results you have obtained.Explanation / Answer
Cost of One Gallon Gasoline = 2.45
Distance Traveled in One Gallon = 15 Miles
Cost of Gasoline used to travel 1 Mile = 2.45/15 = 0.1633
Maintenance & Depreciation Cost per Mile = 0.17
Cost incurred for travel of 1 Mile = Gasoline Cost + M&D cost = 0.1633+0.17 = 0.3333
A) For Route Depot-A-B-D-E-Depot
Distance Traveled in a day = 10+34+20+12+26 = 102
No. of Days (Assuming Only 52 Sundays in a year) = 365- 52 Sunday - 2 Holidays = 311
Total Cost Incurred annually = Distance Traveled/day * Cost/Mile * No. of Days = 102 * 0.3333 * 311 = 10572.94
Note- Shop C is missing in question, adding Shop C after B and before D, we get
Distance Traveled in a day = 10+34+48+15+12+26 = 145
No. of Days (Assuming Only 52 Sundays in a year) = 365- 52 Sunday - 2 Holidays = 311
Total Cost Incurred annually = Distance Traveled/day * Cost/Mile * No. of Days = 145 * 0.3333 * 311 = 15030.16
B) Using the Nearest Neighbor Algorithm, the route obtained is Depot-A-B-E-D-C-Depot
Distance Traveled in a day = 10+34+15+12+15+60 = 146
No. of Days (Assuming Only 52 Sundays in a year) = 365- 52 Sunday - 2 Holidays = 311
Total Cost Incurred annually = Distance Traveled/day * Cost/Mile * No. of Days = 102 * 0.3333 * 311 = 10572.94
Improvement in Cost over the previous route = 15030.16 - 10572.94 = 4457.22
% Reduction = 4457.22*100/15030.16 = 29.65%
C)1) With Route having Shop B as first pickup followed by other, we get the route as Depot-B-E-D-C-A-Depot,
Distance Traveled in a day = 24+15+12+15+46+10 = 122
No. of Days (Assuming Only 52 Sundays in a year) = 365- 52 Sunday - 2 Holidays = 311
Total Cost Incurred annually = Distance Traveled/day * Cost/Mile * No. of Days = 122 * 0.3333 * 311 = 12646.06
Extra Costing over Original Nearest Neighbor Route = 12646.06 - 10572.94 = 2073.12
% Increase in cost = 2073.12*100/10572.94 = 19.6%
C)2) With Route having Shop B as first pickup then return to depot followed by other, we get the route as
Depot-B-Depot-A-D-E-C-Depot,
Distance Traveled in a day = 24+24+10+35+12+35+60 = 200
No. of Days (Assuming Only 52 Sundays in a year) = 365- 52 Sunday - 2 Holidays = 311
Total Cost Incurred annually = Distance Traveled/day * Cost/Mile * No. of Days = 200 * 0.3333 * 311 = 20731.26
Extra Costing over Original Nearest Neighbor Route = 20731.26 - 10572.94 = 10158.32
% Increase in cost = 10158.32*100/10572.94 = 96.07%
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