Management Engineering - Operations Management

Full exam

OPERATIONS MANAGEMENT EXAM Prof. Alberto Portioli Staudacher, Prof. Marco Taisch, Prof. Matteo Rossini January 29th, 202 5 Queue Exercise ( 6 Points) MVE is a famous pastry shop that receives plenty of customers every day . On average, the shop receives 120 customers per hour and is composed of three stages: ordering counter , cash register , and picking counter . Since the shop is always very busy, 10% of the customers that arrive at the shop are demotivated by the long queues and decide to leave the shop without passing through any stage. On the other hand, customers that d ecide not to leave, move to the ordering counter where they make their order and receive an order slip . In this ordering stage customers join a single queue that is served by three shop assistants. It always happens that 5% of customers that decide to place an order, just after they get their order slip and leave the stage , they realize they forgot to order some items and must rejoin the queue of the ordering stage again to make another order and get another order slip . After the second time , they never rejoin the ordering queue again. After that , 98% of the customers who have not exited the system before the ordering stage head to the cash register to pay and get a receipt , while the remaining 2% of customers are discourage d by the long queue and decide to leave the shop before joining the cash register queue . The cash register stage is formed by a single queue served by one cashier. Customers that have paid at the cash register head afterwards to the picking counter to present the receipt and pick up their order . The picking stage is formed of two queues, each served by one shop assistan t. After pick ing up their order, customers are ready to leave the shop with their order. In the table below, the service rates for all stages are indicated. It is assumed that arrival rates and service rates follow a negative exponential distribution. Stage Service rate per resource Ordering Counter 42 passengers/hour Cash Register 120 customer s/hour Picking Counter 55 customer s/hour Question 1: Choose the right queuing model system in the excel template given to you. (1 Point) Question 2: Fill in the table with all the relevant parameters for each stage: arrival rate, service rate, type of queue, average waiting time in system (in minutes), and utilization rate ( ρ). Approximate values are acceptable, no need for interpolation. (2.5 Points) Question 3: Compute the average waiting time in system (Ws) considering only the customers that have passed through all stages. (2.5 Points) Yield Exercise ( 3 Points) SAB airlines is an airline company that applies yield management to maximize their profit. The company sells full price ticket s at € 900 and discounted price ticket s at € 600. The demand for full -price tickets per flight is normally distributed with a mean of 90 passengers and a standard deviation of 20 passengers . The company purchase s in advance a meal for every passenger which costs €15 per discounted price passenger and €20 per full price passenger . Passengers who have purchased a full -price ticke t get a free snack after their meal , while for a discounted price passenger , he/she must pay € 3 if they w ant to get the snack . Historical data shows that 40% of discounted price passengers will buy the snack . The cost of each snack is €2, which is paid in advance by an external company that sponsors SAB airlines. The revenues from the snacks go to SAB airlines. Discounted price customers have a no -show rate of 10% and tickets are non -refundable. It is assumed that the demand for discounted price tickets exceeds the flight’s capacity (500 seats) and that empty seats can all be sold at the last minute at a price of €450 . Passengers who purchase the last -minute ticket have the same behavior as discounted price ticket passengers and receive the same services offered to discounted price ticket passengers. Question: Compute the cost s of underestimation and overestimation and the protection level for full price passengers . (3 Points)