Question 10.73: Determining the capacity of a parking garage

An entrepreneur is building a parking garage in a downtown area of a congested city. It will operate 24 hours per day and 7 days a week. If the parking deck is full when potential customers arrive, they will go elsewhere to park. Customers arrive randomly, following a Poisson process. The length of time a customer parks in the garage is a random variable.

Construction cost for the parking garage is \$ 100,000 per space, including the cost of land. Computing the discounted cash flow daily cost of ownership of the garage, including taxes and daily operating costs, it is estimated that C_{5}=\$ 2 / hour for each parking space. Parking in the downtown area costs \$ 12 /hour, which is what the entrepreneur plans to charge (R) . The entrepreneur assigns a value of \$ 50 / hour to C_{6} . It is anticipated that \lambda= 150 cars per hour and \mu=2 cars per hour. Recall,

As shown in Table 10.39, the optimum number of parking spaces is 100 .

Interestingly, for C_{6}=\$ 12 / hour, c^{*}=96 ; for C_{6}=\$ 25 / hour, c^{*}=98 ; and for C_{6}= \$ 37.50 / hour, c^{*}=100 . Hence, the optimum size of the parking garage is not sensitive to the value of C_{6}. However, what if demand is not as strong as anticipated? With C_{6}=\$ 25 per hour and \lambda=120 cars per hour, c^{*}=81 ; and with \lambda=100 cars per hour, c^{*}=69 . The entrepreneur needs to be far more confident about the demand for parking than about the values of the cost parameters.