Waiting Lines simulation - Equilibrium & Absorbing States Problems

QUESTION 1

Management of a local retail store is concerned about a loss of customers. One solution that has been proposed is to add one or more cashier-stations to make it easier for customers to obtain quick service without waiting. The manager of the store thinks that the business should risk only the cost of installing one medium cashier-station. He is informed by his staff that the cost of building a cashier-station is R20 000 per year (amortized over a 10 years period). It also costs R5 300 per month in wages and benefits to staff.

A consultant believes that the following two factors encourage the immediate construction of two cashierstations however. According to a recent article in retailing research magazine, customers who wait in long lines for cashier service will cost the store an average of R15 per minute in loss of goodwill. Also, adding a second cashier will cost R8 500 in staffing per month, but amortizing construction costs can be cut to a total of R35 000 per year if a two cashier-stations are installed together instead of one at a time. To complete the analysis, the consultant data on arrival and service rates at a competing downtowns retail store. These date are shown in observation analysis 1 & 2 in the table below:

OBSERVATION ANALYSIS 1: INTERVAL TIMES
Time between arrivals (minutes)	Number of Occurrences
1	150
2	300
3	250
4	175
5	125

OBSERVATIONS ANALYSIS 2: CUSTOMER SERVICE
Service Time (Minutes)	Number of Occurrences
1	90
2	160
3	300
4	200
5	125
6	75
7	50

1. Simulate a 2-hours time period, from 9 AM to 11 AM for a single line of people waiting for service in a

single-cashier system.

2. Simulate a 2-hours time period, from 9 AM to 11 AM for a single line of people waiting for the next available cashier in a two-cashier system.
3. Conduct a cost analysis of the two options. Assume that the bank is open 9 hours a day and 250 days a year.