# Logistics (economics), profit maximization, cost minimization

A driver needs to decide how much to pay for parking at a parking meter. Let τ denote the period
of parking time that the vehicle needs, which is a random variable following a cumulative
distribution function F(τ). The amount of time the driver decides to pay upfront for is p. The
parking enforcement agency has a patrol frequency of H (number of patrol visits per unit time),
such that an illegally parked vehicle may receive a ticket each time a patrol officer visits. The
drivers have good knowledge of H, but the exact visit schedule remains confidential. The fine per
ticket, γ, is far larger than the parking price per unit time, β.
(a) Show that the driver’s problem resembles a Newsvendor Problem by providing a similar
formulation that minimizes the driver’s expected cost.
(b) What is the optimal time p* that the driver should pay?
(c) Discuss impacts of the ticket fine and patrol frequency (γ, H) on overtime parking
occurrences.

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