# Bus Optimization

PROBLEM: A local bus company named “BAHON PORIBAHAN LIMITED” provides service from khilgaon to Mirpur-14.It starts service at 6 A.M and continues till 10 P.M. At present it has 50 drivers and many of them remain idle most of the time. The owner of the company feels that they have extra drivers and decided to maximize their profit by re-scheduling drivers. A driver can work for 8 hours and can remain idle for next 4 hours. Drivers start their job at 6 AM,10 AM,2 PM, 6 PM or 10 PM. Drivers will be paid depending on the number of trips completed. The number of buses varies from hour to hour ,so does the number of passengers. An OR team has been formed to optimize their number of drivers. From a recent survey, OR team has found the following data: Time Zone 6 AM---------------------10 AM 10 AM------------------- 2 PM 2 PM --------------------6 PM 6 PM---------------------10 PM Number of buses needed 14 09 12 07

We assume that requirement of buses is the same every day. The problem is to determine how many drivers to schedule at each starting time to cover the requirement for buses.

OPTIMIZATION: Variable Definition: x(t)=Number of drivers scheduled at time t; t= 6 ,10,14,18,22 This problem is for infinite number of days and x(t) is the number used every day at time t. Objective: So the main objective is…. Min z=x(6)+x(10)+x(14)+x(18) Constraint: Now we need constraints. For the rime interval 2 PM to 6 PM,drivers starting at time 10 AM and 2 PM cover the need from time 2 PM to 6 PM.

x (6) ≥ 14 x(6)+x(10) ≥ 9 x (10) + x (14) ≥ 12 x (14)+ x (18) ≥7 x (6) x (10) x (14) x (18) ≥ 0

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