Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful
catalog sales department in which a clerk takes orders by telephone. If the clerk is
occupied on one line, incoming phone calls to the catalog department are
answered automatically by a recording machine and asked to wait. As soon as the
clerk is free, the party who has waited the longest is transferred and serviced first.
Calls come in at a rate of about 12 per hour. The clerk can take an order in an
average of 4 minutes. Calls tend to follow a Poisson distribution, and service
times tend to be negative exponential. The cost of the clerk is RM10 per hour, but
because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per
hour of customer time spent waiting for the clerk to take an order.

 

a) Prepare the total cost for this waiting line system.

Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful
catalog sales department in which a clerk takes orders by telephone. If the clerk is
occupied on one line, incoming phone calls to the catalog department are
answered automatically by a recording machine and asked to wait. As soon as the
clerk is free, the party who has waited the longest is transferred and serviced first.
Calls come in at a rate of about 12 per hour. The clerk can take an order in an
average of 4 minutes. Calls tend to follow a Poisson distribution, and service
times tend to be negative exponential. The cost of the clerk is RM10 per hour, but
because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per
hour of customer time spent waiting for the clerk to take an order.
1. What is the suitable method to solve this problem?
2. Compute the average time that customers must wait before their calls are
transferred to the clerk.
3. Prepare the total cost for this waiting line system

Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the
clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential. The cost of the clerk is RM10 per hour, but because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per hour of customer time spent waiting for the clerk to take an order.

a) What is the suitable method to solve this problem?

Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful
catalog sales department in which a clerk takes orders by telephone. If the clerk is
occupied on one line, incoming phone calls to the catalog department are
answered automatically by a recording machine and asked to wait. As soon as the
clerk is free, the party who has waited the longest is transferred and serviced first.
Calls come in at a rate of about 12 per hour. The clerk can take an order in an
average of 4 minutes. Calls tend to follow a Poisson distribution, and service
times tend to be negative exponential. The cost of the clerk is RM10 per hour, but
because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per
hour of customer time spent waiting for the clerk to take an order

 

a.Prepare the total cost for this waiting line system.

Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful
catalog sales department in which a clerk takes orders by telephone. If the clerk is
occupied on one line, incoming phone calls to the catalog department are
answered automatically by a recording machine and asked to wait. As soon as the
clerk is free, the party who has waited the longest is transferred and serviced first.
Calls come in at a rate of about 12 per hour. The clerk can take an order in an
average of 4 minutes. Calls tend to follow a Poisson distribution, and service
times tend to be negative exponential. The cost of the clerk is RM10 per hour, but
because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per
hour of customer time spent waiting for the clerk to take an order.

 

a.What is the suitable method to solve this problem?

b.Compute the average time that customers must wait before their calls are
transferred to the clerk.