Solved assignments on Marketing Management and Queuing Theory

MARKETING MANAGEMENT
Assignment
Student Name
[Pick the date]

Question 7
Service rate μ= 60
10 =6customers each hour
Arrival rate ƛ=2.5 customers each hour
(a) Average number of customers in waiting line
Lq= ƛ2
μ ( μ− ƛ ) = (2.5)2
6 ( 6−2.5 ) =0.29
 Average number of customers in system
L= ƛ
( μ− ƛ ) = 2.5
6−2.5 =0.71
 Average time in queue
W q= ƛ
μ ( μ−ƛ ) = 2.5
6 ( 6−2.5 ) =0.11∨7.14 min
 Average time in system
W = 1
( μ−ƛ ) = 1
6−2.5 =0.28 hour
b) It is apparent that the waiting time is 7.14 minutes. Average waiting time is greater than
service goal. It means that the service goal that customer arriving must not wait for the services
more than 5 minutes on an average. Hence, the goal does not meet. Therefore, consultation
duration needs to be reduced or else one consultant should be added in order to achieve the
service goal.
(c) Service rate ¿ 8 minutes per customer
Number of customers served = 7.5 customers
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Arrival rate ƛ=2.5 customers each hour
The service rate μ= 60
8 =7.5 customers each hour
 Average number of customers
Lq= ƛ2
μ ( μ− ƛ ) = (2.5)2
7.5 ( 7.5−2.5 ) =0.1667
 Average number of customers in system
L= ƛ
( μ− ƛ ) = 2.5
7.5−2.5 =0.5
 Average time in queue
W q= ƛ
μ ( μ−ƛ ) = 2.5
7.5 ( 7.5−2.5 ) =0.06 hour
 Average time in system
W = 1
( μ−ƛ ) = 1
7.5−2.5 =0.20 hour
Therefore, the consultant can reduce the average time spent per customer to 8 minutes and the
mean service rate is 4 minutes. Hence, the service goal would be met.
Question 10
Car arrives at a mean rate ƛ = 10 per hour
Mean service rate μ= 12 cars per hour
(a) Probability that the service facility will be idle
P0=1−( ƛ
μ )=1− (10
12 )=0.1667 0.17
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