Suppose that you have a machine that completes a specific process for manufactur

Question

Suppose that you have a machine that completes a specific process for manufacturing a product. This machine can complete the process of a sub-product within 3 minutes on average and the process completion time is exponentially distributed. Sub-products arrive randomly with a rate of 15 per hour at the station in front of the machine. The inter-arrival times of the sub-products is exponentially distributed. There should always be an operator next to the machine and an operator's cost is $15 per hour. The machine has a cost of $20 per each hour it is active, i.e., processing a sub-product. Furthermore, the subproducts have a penalty for the time they spend from the moment they arrive at the station until their processes have been completed. Specifically, due to just-in-time requirements, the penalties for subproducts are given by the following schedule: if the sub-product takes less than 10 minutes to be processed completely, the penalty is Si if the sub-product takes between 10 & 15 minutes to be processed completely, the penalty is $2 if the sub-product takes more than 15 minutes to be processed completely, the penalty is $3 Please answer the following questions about the above system. You can use the excel templates in your calculations. However, you need to show how you are using the information given by the excel template in your calculations 33 excel templates gives your only information for L, Lq, W, Wq, Pn, P{W>t), and P{Wq>t). Explain if the above queueing system satisfies the following criteria by showing your calculations for each criterion. On average, there should not be more than 2 sub-products waiting to start their processes at the station in front of the machine. On average, there should be less than or equal to 3 sub-products waiting to start their processes at the station in front of the machine for at least 75% of the time. On average, less than 50% of the sub-products should wait more than 5 minutes to start their processes at the station in front of the machine. Calculate the expected hourly cost of the queueing system. Expected hourly cost of the system includes the labor cost per hour plus the expected hourly cost of the machine plus the expected penalties charged per hour. Now suppose that the machine can be set to complete the process of a sub-product faster or slower. Assuming that the machine cost, labor cost, and the penalty costs will be the same for each setting of the machine, explain whether the following statements are true or false and explain your reasoning briefly. if the machine is set to work slower, the average machine cost per hour will increase if the machine is set to work faster, the average number of sub-products in the queueing system will decrease if the machine is set to work faster, the expected penalties per hour will increase

Explanation / Answer

Queuing System:

Waiting Time

Penalty

Less than 10 minutes

$1

10 to 15 minutes

$2

more than 15 minutes

$3

The service choices available:

First In First Out (FIFO) Queue

Last In First Out (LIFO) Stack

Sharing of the Processor between applications

Shortest Task First (STF)

Shortest Remaining Processing Time (SRPT)

Waiting Time

Penalty

Less than 10 minutes

$1

10 to 15 minutes

$2

more than 15 minutes

$3

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