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C) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (lambda) Performance measures Percentage of carpentry utilization (%) Average number of orders in the system Average number of orders in queue Average waiting time in the system Average waiting time in line Total cost per day Explain if it is advisable to extend the carpentry? Current carpentry Expanded carpentry

C) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (lambda) Performance measures Percentage of carpentry utilization (%) Average number of orders in the system Average number of orders in queue Average waiting time in the system Average waiting time in line Total cost per day Explain if it is advisable to extend the carpentry? Current carpentry Expanded carpentry

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 30P
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C) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) Performance measures Percentage of carpentry utilization (%) Average number of orders in the system Average number of orders in queue Average waiting time in the system Average waiting time in line Total cost per day Explain if it is advisable to extend the carpentry? Current carpentry Expanded carpentry
Transcribed Image Text:C) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) Performance measures Percentage of carpentry utilization (%) Average number of orders in the system Average number of orders in queue Average waiting time in the system Average waiting time in line Total cost per day Explain if it is advisable to extend the carpentry? Current carpentry Expanded carpentry
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