Question

Question 3
A. Marina Mall is a busy centre for residents in airport and its
sourrounding community. Assume that 2 customers arrive
every 12 minutes and 3 customers are served every 15
minutes and that currently, there is only one cashier.
(i).Determine the average waiting time in minutes before
service begins.
(ii). Advice the management the proportion of the time that a
customer has to wait.
(B). Management perceives that the waiting time computed in
(ii) above is not acceptable and is faced with two options.
Management can either employ an assistant for the cashier or
open a second cash machine.
The former, if implemented, will enable 4 requests to be
served every 15 minutes and the assistant will receive a
monthly salary of GH₵160. The latter, if implemented will
improve the arrival rate to 1 customer every 12 minutes.
However, it requires an initial capital outlay of GH₵3000 and
the cashier who will operate the cash machine will receive a
monthly salary of GH₵250. The shop avoids a loss in sales of
GH₵80 per month for each minutes that average customer
waiting time is reduced.
(i). Calculate the financial gain to the mall under option 1 and
advice management on the option.
(ii). Calculate the financial gain to the mall under option 2,
assuming the initial capital outlay is sunk cost and advice management on this option.

Answer 1

Excel calculation

After solving the above part we will get

Answer i)

Average waiting time in system is 30 min before service begins

Answer ii). Average waiting time in a queue is 25 min, therefore customer has to wait 25 min before its turn come for service. The proportion with total waiting time in system is 25/30 min i.e. 5/6

Excel calculation for part B

Case 1: Employing an assistant:

              

Case 2: Employing additional Cashier and Cash machine

Excel Formulation

Considering initial capital outlay as sunk cost,

Answers:

i. Financial gain by utilizing option 1 = 1440 units per month. Management may go for this option as the overall gain is on much higher side than investment needed.

ii. Financial loss in utilizing option 1 = 1286.36 units per month. If we assume initial capital outlay as sunk cost, then financial gain comes at 1713.64 units per month. It is better option than option 1 gain and management can employ this case for implementation.

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