Question

Shoprite is a busy centre for residents in East Legon 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 Shoprite under option 1 and advice management on the option.

(ii). Calculate the financial gain to Shoprite under option 2, assuming the initial capital outlay is sunk cost and advice management on this option.

Answer 1

The solution has follow from discussing existing scenario and case 1 & 2 subsequently.

A. Existing Scenario:

Excel Formulation

Answers

i. Average waiting time in system is 30 min before service begins

ii. Average waiting time in queue is 25 min, 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

Case 1: Employing assistant:

Excel Formulation

              

Case 2: Employing additional Cashier and Cash machine

Excel Formulation

Considering initial capital outlay as sunk cost,

Answers:

i. Financial gain in employing 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 employing 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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