23 07 20

Page 1

QUEUE THEORY EXERCISE (9 Points) CC Bottle Spa is a family company that produces mechanical piec es used for the production of industrial machineries used for the bottling. Company’s output is 200 pieces/day and it produces only one product type. To achieve this output, CC Bottle production process is composed by 3 stages: stage 1, stage 2 & stage 3. The pieces enter the production system first in Stage 1, which is composed by one single machine. Stage 2, the next step, is composed by 3 machines and is a bit problematic. Pieces entering the stage, join the single FIFO queue that serves all three resources. At this stag e, there are three possibilities, for the pieces entering the production process, 10 % are considered highly damaged and must be discarded, 20% are defective and should be reprocessed by st age 2, and the remaining pieces are considered good and continue to the following stage. The following step is Stage 3. It is composed by 4 machines and each machine has its own queue. After this last stage there are two options for a piece: either it is good and it is shipped to the customer, or it has to be discarded. Those discarded are 5% of pieces reworked by Stage 2. The company works 10 hours per day. In the table below, the values of the service rates of the diff erent 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 10 pieces/hour Question 1) (2 points) You are given four queueing model system, only one of them is the right one. Indicate the right queuing model system in the excel sheet given to you. Question 2) (3 points) Having chosen the model, please fill in the table with all the…