From Low-Cost Airline Baggage to By-Minute Car Rental, the Impact of Penalty Cost on Customers' Booking Decisions

Abstract

This paper studies two problems that are both related to the impact of shortage penalty cost on customers' booking decisions. The first problem looks at low-cost airline passengers' baggage allowance purchasing decisions. The second problem looks at by-minute car rental customers' rental booking decisions. Both of the problems are newsvendor type of problems. However, from practical observations, customers' baggage booking allowance (rental booking time duration) does not monotonically increase with the baggage overweight (return delay) penalty cost (i.e., the shortage cost), which is unexpected for newsvendor systems. In this paper, we explain this interesting phenomenon by looking into the influence of shortage penalty cost on customers' baggage (trip) planning and weight (time) estimation, which in turn, affects the actual baggage weight (usage time) distribution. We then incorporate this into stochastic decision models and analytically characterize how important quantities (e.g., customers' booking allowance, customers' total cost, and firm's profit) change with the penalty cost. We prove that both the customers' booking allowance and the firm's profit are quasiconcave in the penalty cost. For the by-minute car rental problem, we also study the optimal delay penalty cost for the rental firm to maximize its profit. We show that, when a rental car is shared by more customers, a higher delay penalty cost is preferred.