Question

The Naples Newspaper completes production of its daily edition by 5 a.m. A truck picks up pallets loaded with newspapers and delivers them to four neighbor sites, where carriers sort and fold the papers for individual routes. The mileage between locations is shown in the table below. Currently, the truck picks up the number of pallets required by each customer at the factory, delivers them, and then returns to the factory to get the papers for the next customer (i.e., current route 0-1-0-2-0-3-0-4-0). The truck always returns to Scottsville and gets 10 miles per gallon using diesel fuel. A truck can carry up to 17 pallets. A gallon of diesel fuel is $2.50. The newspaper operates 365 days per year.

	Factory (0)	Scottsville (1)		Hudson (2)		Bonita (3)		Walker (4)		Pallets Demanded
Factory (0)	—	7		5		15		17
Scottsville (1)		—		16		8		11		11
Hudson (2)				—		9		6		6
Bonita (3)						—		4		8
Walker (4)								—		9

1. How many miles does the truck travel each day using the current route? What is the total number of miles traveled annually? Round your answers to the nearest whole number.

   miles per day
   miles per year

2. Use the Clarke-Wright Method to find a more efficient route. Round your answers to the nearest whole number.

   Routes	Travel Distance (miles)
   0-1-0, 0-1-2-0, 0-1-3-0, 0-1-4-0
   0-2-0, 0-2-3-0. 0-2-4-0
   0-2-3-0, 0-4-0, 0-3-4-0
   Total

3. How many miles, gallons, and dollars can be saved per year by adopting the current versus shorter route found by the Clarke–Wright Method? Do not round intermediate calculations. Round your answers to two decimal places.

   miles per year
   gallons per year
   $  per year

4. How many pounds of gas are emitted into the atmosphere and saved per year using the shortest truck route versus the current truck route? Assume that one gallon of gas generates 13 pounds of carbon dioxide and other global-warming gases from the truck's tailpipe. Do not round intermediate calculations. Round your answer to one decimal place.

   lbs of gas per year

Answer 1

ANSWER:

Existing route

Miles per day = 88

Miles per year = 88 x 365 = 32,120

Clarke-Wright Method

Find the time savings s(i, j) for all pairs of customers i and j. Sort them as per the descending order of s(i, j).

The largest saving is there for s(3,4) and the total demand is 8+9=17 which is not more than the capacity. So, combine them. However, no further extension to this route is possible as the capacity is reached.

Roue 1: 0 - 3 - 4 - 0 (distance travelled = 36 miles)

The next four routes cannot be used as already 3 and 4 are coming in the first route. The last route is also not possible as it has a negative saving. So, other routes are:

Route 2: 0 - 1 - 0 (distance travelled = 14 miles)
Route 3: 0 - 2 - 0 (distance travelled = 10 miles)

Total distance per day = 36+14+10 = 60 miles

So, miles per year = 60 x 365 = 21,900 miles

Saved miles per year = 32,120 - 21,900 = 10,220
Saved gallons per year = 10,220 / 10 = 1,022 gallons
Saved $ per year = 1022 x 2.5 = $2,555

Emission reduction = 1022 x 13 = 13,286 lbs

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