Ms. Esther Rumble recently graduated with a degree in Supply Chain Management fr
ID: 355999 • 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 cricial that driver capacity and fuel be used efficiently. Thus, Ms. Lee has tasked Ms, Rumble to ensure tha the collection vehicles are routed in the most efficient manner. The distances in miles between any pair of stores, including 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 weeks in the year. Oue 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 S2.45 per gallon and the estimated cost for vehicle maintenance and depreciation is $0.17 per mile. Put yourself in Esther Rumble's position and answer the ollowng questions. From To Store A Store B Store C Store D Store F 24 34 10 35 Store A Store B Store C Store D 46 48 34 46 35 18 20 15 35 12 26 12 (a) The route currently being used for operation is: DepotStore A Store B Store D Store E Depot. How much does it cost the Food Bank annually to nun this operation from the viewpoint of fuel and maintenance costs? [10 points] (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 pointsl (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 13 points] (ii) there is a requirement that the tuck 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 (13 points]. Clearly show full calculations and provide appropriate discussions of the results you have obtainedExplanation / Answer
(a) The distance covered in this route -
10+34+20+12+ 26 = 102 miles
Fuel cost per mile = 2.45/15 = 0.16
Maintenance cost per mile =0.17 per mile
Total cost per mile = 0.16+0.17 = 0.33
Total coat per trip = 0.33x102 = 33.66
No. of weeks of operation = 52-2 = 50
No. of days of operation = 50x6 =300
Annual cost = 300x33.66 = 10098
(b) According NN heuristic, the truck will move in following manner
Depot -->A -->B--->E--->D-->C--->depot
Kms run = 10+34+15+12+60 = 131
As we see that the distance has actually increased, hence the new cost per trip
131x0.33 =43.23
New annual cost = 300x43.23 =12969
The new cost is increased by nearly 30% so the older method is better than this.
(c) Distance in case I with route
B-->E-->D-->C-->A--Depot
15+12+15+46+10 = 98
New cost = 98x0.33 = 32.34
Annual cost = 9702
It will help to reduce the cost marginally, but everyday the truck will have to travel t the B from depot in any case, making the exercise futile.
Case II - New route
Depot ----> B --> E-->D-->C-->A--.B--Depot
Distance = 24+15+12+15+46+34+24 = 170
The nbew cost = 0.33x170 = 56.1
Annual cost = 56.1x300 =16830.
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