Answer to Question #176835 in Management for Nana kofi

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.

Answer 1

A. Existing Scenario:

Excel Formulation

A C D E 1 B Existing Scenario Average time for customer arrival average service time 2 2 B 4 =12/2 =15/3 3 4 2 5 6 Customer A

Eating Scenario

Average time for customer arrival = 6

average service time =5

Customer Arrival Rate( λ ) = 0.17

Service rate(μ) = 0.2

Server Utilization P = 8.83

Number in the Queue Lq = 4.17

Number in the System Lr = 5.00

Waiting time In Queue Wq = 25

Waitin time in System Ws = 30

Part i:

Before the service starts, the average wait time in the system is 30 minutes.

Part ii:

The 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 the system is 25/30 min i.e. 5/6

Answer B:

Case 1: Employing assistant:

Excel Formulation

I =12/2 =15/4 =1/12 =1/13 =15/16 G Н. 1 Case 1: Employ an assistant for the cashier 2 Average time for customer arrival 3 ave

F Н 1 G Case 1: Employ an assistant for the cashier Average time for customer arrival average service time 2 3 4. 5 2 3 4 6 3

Case 2: Employing additional Cashier and Cash machine

Excel Formulation

M N =12/1 =15/4 2 =1/N2 =1/N3 L 1 Case 2: Open a second cash machine 2 Average time for customer arrival 3 average service ti

M N 12 3.75 2 u 0.08 0.27 P 0.31 L 1 Case 2: Open a second cash machine 2 Average time for customer arrival 3 average service

Considering initial capital outlay as a sunk cost,

N 12 3.75 0.08 0.27 0.31 L M 1 Case 2: Open a second cash machine 2 Average time for customer arrival 3 average service time

Part I:

The financial gain in employing option 1 = 1440 units per month. Management may go for this option as the overall gain is on the much higher side than the investment needed.

Part ii:

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

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