# Unconstrained Estimation of Multitype Car Rental Demand
## 1 Introduction  
The car rental industry plays a huge role globally. It can act as a lubricant for production and consumption to ease their mutual restraints. It can also expand the automotive consumer market and evaluate the popularity of new cars before they come into the market. At the same time, because the public transportation system is limited by operating time, departure frequency, accessible range, comfort, privacy, and other conditions, car rental, with its outstanding advantages such as high flexibility, ease of use, and privacy, has shown considerable growth over the years. The global car rental market was valued at $79.5 bn in 2018 and is expected to reach $125.4 bn by 2025, registering a CAGR of 5.1% from 2019 to 2025 [1]. In recent years, the demand for car rental services in the Asia-Pacific region has become the largest and fastest growing segment, especially in China and India, where there are high population density and rapidly growing demand. Mainstream car rental companies started to use revenue management (RM) as a crucial tool for reducing operating costs and improving competitiveness in the 1990s. RM is an important interface between enterprises' supply and market demand, and its objective is to maximize profits. The most widely known RM application occurs in the airline industry. It mainly includes four aspects, namely forecasting, overbooking, capacity control, and pricing [2]. Among them, forecasting is the foundation and provides vital input information for other work. A 12.5-25% reduction of forecast error could translate into 1-3% incremental revenue generated from the RM system [3, 4]. Therefore, to achieve the desired level of accuracy, it is important and necessary to innovate the forecast method constantly [5]. In reality, influenced by booking and/or capacity limits, the customer's present demandmay not be satisfied, which will lead to it being lost (spilled) or recaptured by a more expensive (buyup) or cheaper (buydown) available product. The sample booking curves with three grades of products (the fare order is A > B > C) are shown in Figure 1[6,7]. Therefore, in order to repair the constrained demand, it is necessary to carry out an unconstrained estimation of the customer's actual demand and forecast the future demand on this basis [8,9]. Research into unconstrained estimation (sometimes also called deturuncation, uncensoring) in the RM system started more than 40 years ago and mainly focused on the airline industry. Unconstrained estimation mainly uses observed \"censored demand\" to estimate and calculate the \"uncensored demand\". The original methods were based on statistics, such as the expectation maximization (EM), projection deturuncation (PD), booking curve (BC), and mean imputation. Since the beginning of this century, discrete customer choice models have grown in popularity to estimate unconstrained demand [8,10,11]. Forecasting usually yields the demands and no-show rate by booking class, the latter of which will not be discussed here. The common methods include time series, linear regression, exponential smoothing, double exponential smoothing, pickup, neural networks, principal component analysis, and adaptive models [6,12,13]. Since air transportation can meet the travel demand between two points, the prediction of OD demand is necessary [14,15,16]. [PERSON] surveyed the history of research on unconstraining methods by reviewing over 130 references [17]. [PERSON] provided two reviews of unconstrained estimation and forecast methods broadly used in different industries up to 2016 [18,19]. Recent discussions include forecast multipliers and hybrid forecasting [9], the effect of customers' reference price on demand [20], Gaussian processes for unconstraining demand [21], and demand forecast accuracy [22].