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• Level: GCSE
• Subject: ICT
• Word count: 1501

# Shortest Routes Problem Solving - School Driver

Extracts from this document...

Introduction

Shortest Routes Problem Solving - School Driver My aunt, a school driver, she has a problem of picking the student up to school. She lives in Belvedere Garden, and picks student to the school in Shek Lei Estate (the map is on the last page). In order to save the cost by shorten the distance to the school, she asked me to solve the problem for her. By the virtue of keen competition, she couldn't charge for the high fees from the students. Besides, the fuel is very costly and variable. Thus, her income becomes unstable. She tries to solve it by picks up more students from different places, but the routes will be more complex and the time does not allow her to do so. She has to pick 50 students up from 12 places, there are 10 seats left and therefore she can only save the cost by pick more students up from these 12 places but not the other places. I also found her driving routes have a great problem, she didn't choose the fastest way. So I will choose the fastest routes for her. She has to drive 4 times per school day 1. From BG to SLE (through all places in shortest routes) ...read more.

Middle

total distance of one month is 35.69 x 22 = 785km In HK, the cost of the fees are 15p per km average, thus her original cost per month is 785 x 15p = �118 and her income is �810. So her actual income decreases to �810 - �118 = �692 Now I am going to find out the shortest routes of four drives. For the first drive and the last drive, I solve the problem by showing all possible ways as she has to go through all 12 places. The second and the third drive, I do only find the shortest routes and therefore I will use the Dijkstra's algorithm. There are 52 way in the first drive and 66 ways in the fourth drive. Possible ways for first drive: BG�TKG�PTPT�DP�CGE�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 14.57km BG�TKG�PTPT�DP�CGE�WSP�LYSC�KYC�LMSE�SYE�SYEE�SLE 13.8km BG�TKG�PTPT�DP�WSP�CGE�LYSC�KYC�LMSE�SYE�SYEE�SLE 15.3km BG�TKG�PTPT�DP�LYSE�CGE�WSP�KYC�LMSE�SYE�SYEE�SLE 15.41km BG�TKG�PTPT�DP�LYSE�WSP�CGE�KYC�LMSE�SYE�SYEE�SLE 15.66km BG�TKG�PTPT�LYSC�DP�CGE�WSP�KYC�LMSE�SYE�SYEE�SLE 13.86km BG�TKG�PTPT�LYSC�DP�WSP�CGE�KYC�LMSE�SYE�SYEE�SLE 15.59km BG�TKG�PTPT�LYSC�WSP�DP�CGE�KYC�LMSE�SYE�SYEE�SLE 14.73km BG�TKG�PTPT�LYSC�WSP�CGE�DP�KYC�LMSE�SYE�SYEE�SLE 14.2km BG�TKG�DP�PTPT�LYSE�CGE�WSP�KYC�LMSE�SYE�SYEE�SLE 13.65km BG�TKG�DP�PTPT�LYSE�WSP�CGE�KYC�LMSE�SYE�SYEE�SLE 13.9km BG�TKG�DP�CGE�WSP�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 12.12km BG�TKG�DP�CGE�WSP�LYSC�PTPT�LMSE�KYC�SYE�SYEE�SLE 14.32km BG�TKG�DP�CGE�KYC�WSP�LYSC�PTPT�LMSE�SYE�SYEE�SLE 13.06km BG�TKG�DP�WSP�CGE�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 13.85km BG�TKG�DP�WSP�KYC�CGE�LYSC�PTPT�LMSE�SYE�SYEE�SLE 14.56km BG�TKG�CGE�DP�PTPT�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 13.01km BG�TKG�CGE�DP�WSP�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 12.96km BG�TKG�CGE�DP�KYC�WSP�LYSC�PTPT�LMSE�SYE�SYEE�SLE 13.37km BG�TKG�CGE�LYSC�WSP�KYC�DP�PTPT�LMSE�SYE�SYEE�SLE 13.94km BG�TKG�CGE�WSP�DP�PTPT�LYSC�KYC�LMSE�SYE�SYEE�SLE 13.74km BG�TKG�CGE�WSP�DP�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 14.16km BG�TKG�CGE�WSP�LYSC�KYC�DP�PTPT�LMSE�SYE�SYEE�SLE 14.17km BG�TKG�CGE�WSP�KYC�LYSE�DP�PTPT�LMSE�SYE�SYEE�SLE 13.89km BG�CGE�TKG�PTPT�DP�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 14.37km BG�CGE�TKG�PTPT�DP�WSP�LYSC�KYC�LMSE�SYE�SYEE�SLE 14.24km BG�CGE�TKG�PTPT�LYSC�DP�WSP�KYC�LMSE�SYE�SYEE�SLE 14.3km BG�CGE�TKG�PTPT�LYSC�WSP�DP�KYC�LMSE�SYE�SYEE�SLE 14.64km BG�CGE�TKG�DP�WSP�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 12.56km BG�CGE�TKG�DP�KYC�WSP�LYSC�PTPT�LMSE�SYE�SYEE�SLE 12.97km BG�CGE�LYSC�KYC�WSP�DP�TKG�PTPT�LMSE�SYE�SYEE�SLE 14km BG�CGE�LYSC�PTPT�TKG�DP�WSP�KYC�LMSE�SYE�SYEE�SLE 14.1km BG�CGE�KYC�LYSC�WSP�DP�TKG�PTPT�LMSE�SYE�SYEE�SLE 14.35km BG�CGE�KYC�WSP�LYSC�DP�TKG�PTPT�LMSE�SYE�SYEE�SLE 14.42km BG�CGE�WSP�DP�TKG�PTPT�LYSC�KYC�LMSE�SYE�SYEE�SLE 13.33km BG�CGE�WSP�LYSC�KYC�DP�TKG�PTPT�LMSE�SYE�SYEE�SLE 13.76km BG�CGE�TKG�DP�PTPT�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 12.61km BG�CGE�DP�TKG�PTPT�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 12.6km BG�CGE�WSP�KYC�LSYC�DP�TKG�PTPT�LMSE�SYE�SYEE�SLE 13.48km BG�DP�TKG�PTPT�LYSC�WSP�CGE�KYC�LMSE�SYE�SYEE�SLE 14.39km BG�DP�TKG�PTPT�LYSC�CGE�WSP�KYC�LMSE�SYE�SYEE�SLE 14.14km BG�DP�TKG�CGE�WSP�KYC�LYSC�PTPT�LMSE�SYE�SYEE�SLE 12.62km BG�DP�TKG�CGE�KYC�WSP�LYSC�PTPT�LMSE�SYE�SYEE�SLE 13.56km BG�DP�CGE�TKG�PTPT�LYSC�WSP�KYC�LMSE�SYE�SYEE�SLE 13.5km BG�DP�WSP�CGE�TKG�PTPT�LYSC�KYC�LMSE�SYE�SYEE�SLE 14.23km ...read more.

Conclusion

It saves almost �33 more (4.93 x 2 x 22 x 15p ). It would spend her leisure at home during the resting time but save her more money. She could also earn more by picking more students from those 12 places. The cost cannot save so much because the routes in Hong Kong are not very long but complex, Hong Kong is just a point in the map only. In addition, she picks students up from 2 districts only and therefore the roads are shorter. The time is a problem as well, she is not allowed to pick more students. Otherwise, all of the students will be late for school and their parents will complain her. In the first drive and fourth drive, I have found out the shortest routes by showing all possible. Actually, it's very difficult to find out and it's take me a long time. When I was doing it, I needed to check many times whether I had showed all the possible or not. Besides, it's easy to make mistakes when I was calculating the distance of the possible routes. In the second and the third drive, I used Djkstra's algorithm to find out the shortest easily. It is very convenience and hard to make a mistake. This is the best method for me which I have learned. I impacted my aunt as well and she found it is useful. 1 ...read more.

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