Management Engineering - Operations Management

Full exam

QUEUE THEORY EXERCISE (9 Points) Italia Spa produces mechanical pieces used to produce industrial machiner y used for packaging . The c ompany delivers to the customer 200 good pieces/ day, and it produces only one product type. To achieve this output, the Italia Spa production process is composed of 3 stages: stage 1, stage 2 & stage 3. The pieces enter the production system first in Stage 1 , which is composed of one single machine. Stage 2 , the next step , is composed of 3 machines and is a bit problematic . Pieces enter ing the stage , join the single FIFO queue that serves all three resources. 10% of items processed by this stage are defective and should be reprocessed once. 50% of the reprocessed items turn out to be damaged and must be discarded. The rest of the pieces are considered good and move on to the next stage. The following step is Stage 3. It is composed of 2 machines and each machine has its own queue. After this last stage , the product is shipped to the customer . The company works 8 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 ) Stage 1 30 pieces/hour Stage 2 25 pieces/hour Stage 3 20 pieces/hour Question 1) (1 point ) You are given four queueing model system s, only one of them is the right one. Indicate 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) (4 points ) Calculate the expected throughput time for each path as well as the expected throughput time of the system , considering all the pieces sent to the customer.