Management Engineering - Operations Management

Full exam

O PERATIONS M ANAGEMENT E XAM Prof. Alberto Portioli Staudacher, Marco Taisch, Matteo Rossini QUEUE THEORY EXERCISE (9 Points) An Italian city has a small airport in which daily international flights are operated. The airport receives an average number of 250 passengers per hour, which are then distributed in several flights along the day. To achieve a correct and safe boarding of the passengers, th e airport is organized using diffentent stages, as follows: a check - in, the document check, the security control and the boarding pass control. Once arrived in the airport the passengers enter in the check in area, where luggages are weighted and the board ing pass are given. This phase is composed by one single line with three desks. Stage 2 , the document check , is composed of 2 desks managed by the border police and is a critical phase. In fact, here the people join the two different queues and their passports and VISA are checked. The 10 % of the passengers don ’t have the right documents a nd they can not take the flight , thus they exit the system . After this phase, for those remaining in the system, security control are performed using 2 metal detectors having each one its own queue. Historically, the 15% of the passengers which pass the document check have to re take the control s and after a second check they can mov e to the following stage. The 5% of the passengers after the second check are not allowed to proceed in the following phase, thus they exit the system. The last stage, is the control of the boarding pass performed before entering the aircraft. The airport has only a single person performing this activity. The airport works 16 hours per day. In the table below, the values of the service rate s of the different resources are indicated . For these resources, we can assume the arrival and the service rates follow a negative exponential distribution. Process Service rate (1 resource ) Check - In 100 p eople /hour Document Check 130 people /hour Security Control 150 people /hour Boarding Pass Control 300 people /hour Question 1) ( 1,5 point ) Draw the right queuing model system in the excel sheet given to you. Question 2) ( 4 points) Having chosen the model, please fill in the table with all the relevant parameters for each stage (Arrival rate, Service rate , Type of queue, Ws ( in minutes ), ρ ). Approximate values are acceptable, no need for interpolation Question 3 ) ( 3,5 points ) Calculate the expected throughput time for each path as well as the expected throughput time of the system , considering all the passengers.