Managerial Analytics @ working place

1. Managerial Analytics @ working place Presented by: Rajeev Krishna Baddepudi Philip Cesar Balicat Docena Tan Xiaoling Zeng Ming

2. Scenario: To renew the ISB A1 route contract, NUS is requiring that Comfort Bus should provide enough buses to limit each passenger’s waiting time within 5 minutes, on average. How can Comfort meet NUS’s requirement while minimizing the number of buses needed? Introduction

3. NUS Shuttle Bus A1 Route Map Science YIH NUH Sheares Central Lib Biz/Law PGP

4. Objective • Utilize Linear Programming (LP) to find the minimum number of buses Comfort should provide while meeting the requirements of NUS.

5. Assumptions • We only consider the peak time from 7:30 am to 9:00 am in the bus route of A1. • Time to get on and off is factored into the transit time. • Each ISB has a capacity of 70 passengers. • All staff come during peak time and use the ISB.

6. Data and Data Gathering • 40% of students attend the morning class. • 40% of undergraduate & postgraduate students and staff use ISB. • Only several main stops are considered: • Source: PGP, NUH, Sheares Hall, Central Library (CL) • Destination: Science/Med/SOC, YIH, CL, Biz/Law,

7. NUS Shuttle Bus A1 Map SBS 97 SBS 97 SBS 95 Science NUH Sheares Internal Shuttle Bus A1 PGP ISB B YIH Biz/Law Central Lib Legend: SBS 95 SBS 96, 151 -- Source SBS 96, 151 -- Destination

8. Routes Included in Model (not included) PGP ------ NUH ------------- Science ------------------------ Sheares Hall ----------------------------------------- YIH ----------------------------------------------- CL ----------------------------------------------------- Biz/Law NUH ------------- Science ------------------------ Sheares Hall ----------------------------------------- YIH ----------------------------------------------- CL ----------------------------------------------------- Biz/Law SH ----------------------------------------- YIH ----------------------------------------------- CL ----------------------------------------------------- Biz/Law CL ------------------------------------------------------ Biz/Law (not included) (not included) (not included) (not included)

9. Goal: Minimize number of buses Requirements: Maximum wait time should be equal to less than five (5) minutes. Min (# of buses) Min (total time around NUS / time between buses) Subject to the constraints: Maximum (wait time in queue + service time) <= 5 Or Lq / λ + 1 / μ <= 5 μ > λ Lq, λ, μ, wait time, service time >= 0 Notes: Wait time in queue + service time Wq + 1 / μ Lq / λ + 1 / μ <= 5 Where: Lq – mean average students in queue λ – mean arrival rate μ – mean service rate = available bus capacity / time bet. Buses Every stop has its own waiting line model because μ may vary LP Model Creation

10. Excel LP Model

11. Conclusion and Further Applications Conclusion: • We conclude that to provide a service with an average waiting time of less than 5 minutes on any bus stop, Comfort should have 9 buses on the A1 route, spaced at roughly one bus every 3 minutes. Further Application: • Our model can be modified and extended to other NUS ISB routes • It can also form the basis for analyzing all ISB routes simultaneously

12. Thank You! Thank you Q & A