The following matrix represents the driving times (in hours) between the custome
ID: 3184866 • Letter: T
Question
The following matrix represents the driving times (in hours) between the customers of a company that delivers product to them on a daily basis. The number of units to meet the daily requirement for each customer is also given X = 36 To Customer Units WABC DERequired X20 40 32 35 2245 21 42 2X 18X FromB 20 22 Customer C40 45 2X 10 21X+10 15 X-5 2x D32 21 18 10 E 35 42X21 15 X+15 The company uses a single vehicle that has 100+X units of capacity to make deliveries a. Using the time-saved heuristic, develop the route(s) that a vehicle should use (i.e., the order in which the customers should be visited) b. How long will it take the vehicle to make the deliveries? How many trips will the vehicle make? c. Show in detail the steps in the procedure used to solve this problenmExplanation / Answer
a) Vehicle capacity = 100+X = 100+36 = 136
Using time-saved heuristic, we take the route from a location with the minimum time. From W, minimum time is 20 hrs, for location B. 72 units out of 136 are delivered to B.
From B, minimum time is 18 hrs, for location D. 31 units are delivered to D. Now remaining capacity = 136-72-31 = 33
Locations remaining are A, C and E, which require 36, 46 and 51 units repectively. Therefore, none of the locaitons can be served in full.
So vehicle will return from D to W and get reloaded with 136 units.
This time vehicle should take route W-E-C-A-W
b) Distance travelled to complete the deliveries on first trip (W-B-D-W) = 20+18+32 = 70
Distance travelled to complete the deliveries on second trip (W-E-C-A-W) = 35+21+45+36 = 137
Total distance travelled = 70+137 = 207
c) The steps are explained in the above solution.
To Customer Units W A B C D E Required From Customer W - 36 20 40 32 35 - A 36 - 22 45 21 42 36 B 20 22 - 72 18 36 72 C 40 45 72 - 10 21 46 D 32 21 18 10 - 15 31 E 35 42 36 21 15 - 51Related Questions
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