1. A new strip mall is being considered and the developers want to determine how
ID: 2525723 • Letter: 1
Question
1. A new strip mall is being considered and the developers want to determine how many parking spaces there should be. It is assumed that if the lot is full, an arriving car will leave. Cars arrive at a rate of 15/hour. The average time a customer spends shopping is 30 minutes. Assume the interarrival times and the shopping times are exponentially distributed. Assume the average shopper purchases $150 worth of merchandise and also assume the mall is open 12 hours/day, 350 days/year. a) If there are 10 spaces, determine the throughput rate of cars departing after completing shopping, the expected number of cars in the parking lot and the rate of lost revenue due to cars leaving because they could not find a space to park. b) Assume the cost to create a parking spot is $2500. Assuming a 5 year horizon and an internal interest rate of 15%, how many spots should be built to minimize the combined construction and lost revenue costs?
Explanation / Answer
Arrival time of the car = 15/hour
Each car arrive ina an interval of = 60/15 = 4min
Time in the process =0.5 hrs
No of cars moving our in an hour =2 / hour
Since 15/2 is greater thna 1 . The system will not run and hence there will be loss in the revenue .
After 44 minutes all the space in the parking will be full with only 1 person been serviced and the next emoty slot will be done 64 minutes
Throughput rate for the system is 8.5 / hour[ a person entering at 0 will exit at 30. Next person entering at 4 will exit at 34..similaly 8.5 customers will be served till an hour's time]
b) With 12 hours time frame number of customers which will be = 8.5*12 = 102 customers
Total cost will be 12*150 = $1800
To serve the cost of 2500 the total number of customers to be served =2500/150 = 18 customers
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