The time interval between arrivals of a series of trucks transporting ceramic tiles to a building construction site is indicated in the following table based on a historical record taken by a Project Coordinator within 50 consecutive days. All trucks enter the site one-by-one and are served for unloading in the order of arrival. Assume that it will take 8 minutes to unload all ceramic tiles from each truck, and no truck is being unloaded or waiting to be unloaded when the first truck arrives.
Time interval between arrivals of trucks | Frequency
6 minutes | 10 days
8 minutes | 15 days
10 minutes | 15 days
12 minutes | 10 days
Total | 50 days
(a) Suggest an exercise for the Project Coordinator to consider how the operating characteristics of the resources management of trucks can be studied in the above scenario. (15 marks)
(b) Assume that the arrival time of the first truck to be at minute "zero" and the random numbers are to start from 01, 02, 03, 04, ...... , 97, 98, 99, 00. Based on the following random numbers (R.N.) consecutively from left to right and then from the 1st row to the 2nd row for consistent calculations,
1st | | | | | | | | | | | | | | 15th
R.N. | 45 | 14 | 46 | 32 | 13 | 49 | 66 | 62 | 74 | 41 | 86 | 98 | 92 | 98 | 84
| 54 | 33 | 40 | 81 | 02 | 01 | 78 | 82 | 74 | 97 | 37 | 45 | 31 | 94 | 99
16th | | | | | | | | | | | | | | 30th
conduct the suggested exercise in (a) for the arrival of 25 trucks by tabulating the results showing the necessary information given by the scenario so as to comment on the operating characteristics in the use of trucks. (18 marks)