Concept explainers
a)
1)
To determine: The system utilization rate.
Introduction: System utilization refers to percentage amount of capacity which is utilized or we can say that actual output is divided by potential output. It is operational metric for business which indicates aggregate productive capacity.
It reflects the ratio of demand to capacity or supply, it is also commonly known as Capacity utilization rate.
a)
1)
Answer to Problem 1P
Explanation of Solution
Given information:
Formula,
Where,
System utilization rate denoted by
Demand rate (measured as arrival) denoted by
Supply rate (measured as service) denoted by
Calculation of the system utilization:
Therefore, system utilization rate is 0.6000.
1)
To determine: The system utilization rate.
Introduction: System utilization refers to percentage amount of capacity which is utilized or we can say that actual output is divided by potential output. It is operational metric for business which indicates aggregate productive capacity.
It reflects the ratio of demand to capacity or supply, it is also commonly known as Capacity utilization rate.
1)
Answer to Problem 1P
Explanation of Solution
Given information:
Formula,
Where,
System utilization rate denoted by
Demand rate (measured as arrival) denoted by
Supply rate (measured as service) denoted by
Calculation of the system utilization:
Therefore, system utilization rate is 0.6000.
2)
To determine: The average number customers waiting for service in line.
2)
Answer to Problem 1P
Explanation of Solution
Explanation
Given information:
Formula as per single server model of average number customers waiting for service in line
Where,
Demand rate (measured as arrival) denoted by
Supply rate per server denoted by
Calculation of Average number of customers waiting in line (Lq):
Therefore, average number of customers waiting in line (Lq) is 0.9000.
3)
To determine: Average number of customers waiting time.
3)
Answer to Problem 1P
Explanation of Solution
Given information:
Formula as per single server model of average number customers waiting for service in line:
Where,
Demand rate (measured as arrival) denoted by
Calculation of Average number of customers waiting in line (
Therefore, average number customers waiting time (
b)
1)
To determine: The average number of customer waiting for repairs.
b)
1)
Answer to Problem 1P
Explanation of Solution
Given information:
Mean service time: 2 hours
M =1
Calculation of
Formula as per single server model of average number customers waiting for service in line:
Where,
Demand rate (measured as arrival) denoted by
Supply rate per server denoted by
Calculation of Average number of customers waiting in line (Lq):
Therefore, Average number of customers waiting in line (Lq) is 2.250.
1)
To determine: The average number of customer waiting for repairs.
1)
Answer to Problem 1P
Explanation of Solution
Given information:
Mean service time: 2 hours
M =1
Calculation of
Formula as per single server model of average number customers waiting for service in line:
Where,
Demand rate (measured as arrival) denoted by
Supply rate per server denoted by
Calculation of Average number of customers waiting in line (Lq):
Therefore, Average number of customers waiting in line (Lq) is 2.250.
2)
To determine: The system utilization rate.
Introduction: It reflects the ratio of demand to capacity or supply, it is also commonly known as Capacity utilization rate.
2)
Answer to Problem 1P
Explanation of Solution
Given information:
Formula,
Where,
System utilization rate denoted by
Demand rate (measured as arrival) denoted by
Supply rate (measured as service) denoted by
Calculation of the system utilization:
Therefore, system utilization rate is 0.750.
3)
To determine: The idle time.
3)
Answer to Problem 1P
Explanation of Solution
Calculation of the idle time:
Therefore, idle time per day per hours is 2hours per day.
4)
To determine: Probability of two or more customers in the system.
4)
Answer to Problem 1P
Explanation of Solution
Step 1: Calculate the probability of less than two:
Therefore, probability of less than two is 0.4375.
Step 2: Calculation probability of two or more than customer in the system:
Therefore, probability of less than two is 0.5625.
c)
1)
To determine: The system utilization rate.
c)
1)
Answer to Problem 1P
Explanation of Solution
Given information
Formula:
Where,
System utilization rate denoted by
Demand rate (measured as arrival) denoted by
Supply rate (measured as service) denoted by
Calculation of the system utilization:
Therefore, system utilization rate is 0.7500.
1)
To determine: The system utilization rate.
1)
Answer to Problem 1P
Explanation of Solution
Given information
Formula:
Where,
System utilization rate denoted by
Demand rate (measured as arrival) denoted by
Supply rate (measured as service) denoted by
Calculation of the system utilization:
Therefore, system utilization rate is 0.7500.
2)
To determine: Average number of customers in the system (Ls).
2)
Answer to Problem 1P
Explanation of Solution
Step 1: Calculation of the average number of customer served
Therefore average number of customer served is 1.5.
Step 2: find the value of
Given information:
Then, from Infinite-source values table we find that value for
For reference:
Step 3: Calculation of the average number of customers in the system (Ls)
Therefore, the average number of customers in the system (Ls) is 3.429.
3)
To determine: Average time customers wait in line for service (Wq).
3)
Answer to Problem 1P
Explanation of Solution
Therefore, the average time customers wait in line for service (Wq).is 0.107.
4)
To determine: The average waiting time for an arrival not immediately served (hours) (Wa).
4)
Answer to Problem 1P
Explanation of Solution
Calculation of average waiting time for an arrival not immediately served (hours) (Wa):
Therefore, average waiting time for an arrival not immediately served (hours) (Wa) is 0.167 hours.
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Chapter 18 Solutions
Operations Management
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- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,