Discounting, pricing and ordering strategies for the United States automobile dealerships
Ghosh Dastidar, Satyaki
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Over the past 10-15 years, the U.S. domestic automobile industry has seen an increasing competition and at the same time has faced a shrinking base of customers. The U.S. automobile dealerships face these same disadvantages in addition to negotiating terms with the automakers. The automakers would force the dealers to stock more of their cars than the dealerships can sell. As a result, the dealerships incur further losses. To complicate matters further, newer model year vehicles are introduced every year and the mean length of the vehicles on the market is 16.7 months. This results in the cannibalization effect between the old and new model year vintages as overlapping sales period can last almost 4-6 months within a particular year. Most automobile models depreciate almost 12.5% in prices at the end of the product cycle with an average price premium of 7.9%. Therefore, the dealerships need intelligent pricing and ordering framework to maximize their revenue and attract customers. Traditionally, even the largest of the dealerships rely on quasi-sophisticated forecasting models and the experience of their sales force to sell their inventory. There has been little or no significant work done in the context of pricing and revenue management for the automobile industry, and particularly the dealerships. This research presents an analytical framework for discounting, pricing and ordering strategies for the U.S. automobile dealerships. For the first time, we introduce the concept of early commitments for the U.S. automobile dealerships. Early commitments help the sellers to get a better forecast and therefore better align their products. We present two revenue models based on (i) early commitment probability, and (ii) the market size. A Bayesian framework is used to update the conditional posterior demand distribution from a prior demand distribution where some customers would choose to commit early to avail of the special discounts. The research provides the model to calculate the optimal discount rates for both the cases. Further, we explored an exponential function based probability function and presented the conditions under which closed form expression for optimal discount rate can be derived. We also present the properties of the revenue function for the general class of monotonous probability functions that are increasing and concave. We also presented a bisection based algorithm has to calculate the optimal discount rate for concave revenue functions for which the closed form expressions of the optimal discount rates either do not exist or are computationally expensive to calculate. For such concave revenue functions, we present another bisection based algorithm to do sensitivity analysis. The algorithms can determine the range of discount rates such that the revenue function is within a certain gap of the optimal revenue function value. The results presented here show the benefit of discount based revenue models over the standard newsboy model. The early commitment based revenue model shows an average improvement of 64.41% in the value function of expected dealer profit. The same for the market size based revenue model shows an improvement of 63.31%. The research addresses the joint problem of pricing and ordering of model/year vehicles during the period of overlapping sales. We developed a multinomial logit (MNL) based regression model to model the discrete customer choice to buy either the previous (old) or current (new) model/year vintage. We also extended the MNL model to derive the utility functions that can be used for the early commitment based revenue model. The research presents the closed form expressions to determine the optimal price and ordering quantities for different scenarios. We used data to determine the optimal discounts for the revenue models used in the early commitment period. For the data obtained, the early commitment probability based revenue model suggests an average optimal discount rate of 2.18% to be offered in the prior period for the future model/year vehicles. The same for the market size based revenue model is 3.88%. 11 different vehicle characteristics were chosen for the regression model for the overlapping sales period. The optimal price and the ordering quantities are presented. Several factors like (i) household income, (ii) price, and (iii) new features were analyzed for their effects on the customer purchase probability of a particular model/year vintage. Even though an older model/year vehicle has a lesser selling price than the newer counterpart, when the combined effect of all the factors are considered, the probability of purchase of a newer model/year vehicle is about 4% higher than that of the corresponding older one.