Finite-Horizon Bayesian Dynamic Pricing Model in Determining the Willingness to Pay for Non-Market Regional Natural Resources (Case Study: Chalidareh Tourism Complex in Mashhad)

Underestimation of this high-demand services in today's world has resulted in the non-optimal allocation of resources and incorrect management and planning. In this research, focusing on Chalidareh Tourism Complex in Mashhad, a finite-horizon bayesian dynamic pricing model has been used to determine the extent of willingness to pay for non-market regional natural resources. In so doing, based on Chen and Wu (2016), Gamma and Two-Point priors with exponential and normal WTP (Willingness to Pay) distribution have been used. The results showed that the average WTP for general exploitation of this complex is within the extent of 12230 IRR (as minimum) in Gamma prior and exponential distribution and 45270 IRR (as maximum) in the Two-Point prior and exponential distribution. Also, the average of WTP is 28750 IRR, while the WTP is 10623 IRR in non-Bayesian approach, which is lower than any of Bayesian estimations. Therefore, the application of Finite-Horizon Bayesian Dynamic Pricing (FHBD) algorithm in dynamic pricing can be an appropriate way to determine the threshold amount of WTP for the exploitation of natural resources.
An important insight from the literature on dynamic pricing is that the optimal selling price of such products depends on the remaining inventory and the length of the remaining selling season (see e.g., Gallego & Van Ryzin, 1994). The optimal decision is, thus, not to use a single price but a collection of prices: one for each combination of the remaining inventory and the length of the remaining selling season. To determine these optimal prices it is essential to know the relation between the demand and the selling price. In most literature from the 1990s on dynamic pricing, it is assumed that this relation is known to the seller, but in practice, the exact information on the consumer behavior is generally not available. It is, therefore, not surprising that the review on dynamic pricing by Bitran and Caldentey (2003) mentions dynamic pricing with demand learning as an important future research direction. The presence of digital sales data enables a data-driven approach of dynamic pricing, where the selling firm not only determines optimal prices, but also learns how changing prices affects the demand. Ideally, this learning will eventually lead to optimal pricing decisions.
Theoretical Framework: In this paper, we focus on the dynamic pricing problem of selling a limited amount of inventory over a short selling horizon. In this regard, dedicating a certain number of periods for exploratory experimenting may be costly due to the limited time and inventory. Instead, a simultaneous optimization of pricing and learning is desired, which can be achieved by formulating the problem as a Bayesian dynamic program. However, computing the optimal policy for the dynamic program can be difficult, if not intractable due to the high dimensionality. Moreover, the binary customer choice model described above gives a rise to a two-sided censoring effect, that is, the observation of the customer’s WTP is censored either from the left or from the right side by the posted price. Because no simple conjugate prior distribution exists under the two-sided censoring (Braden & Freimer, 1991), one cannot resort to the conjugate prior technique to reduce the problem dimensionality.
Consider a finite-horizon dynamic pricing problem for a single product. Inventory replenishment is not possible during the selling horizon, and the terminal value at the end of the horizon is zero. At the beginning of each period, given the available inventory quantity q, the seller determines the unit price p for the product. The goal is to maximize the expected total revenue over the finite horizon. Specifically, we divide the finite selling horizon into T periods to guarantee that there is one customer arrival in each period (e.g., Broder & Rusmevichientong, 2012; Talluri & Van Ryzin, 2004). Time periods are indexed in reverse order, with the first selling period being period T and the last period being period 1. The customer arriving in period t has WTP Xt, which is a random draw from an i.i.d. distribution with a continuous density f (x|θ), where x ≥ 0 is the actual WTP and θ ∈ Θ is an unknown parameter of the distribution. At the beginning of period t, the seller has a prior belief concerning the value of θ, denoted by πt (θ). For the ease of exposition, we assume that Θ is a continuous set and that πt (θ) is a density over this set. When Θ is a discrete set, all our analysis will carry through by treating πt (θ) as a probability mass function. We shall use πt (θ) and πt (θ) interchangeably and suppress the subscript t whenever appropriate within the context.
A Finite-Horizon Bayesian Dynamic Pricing Model base on Chen and Wu (2016), Gamma and Two-Point priors with exponential and normal WTP distribution have been used. Results showed that the average WTP for general exploitation of this complex is within the extent of 12230 IRR (as minimum) in Gamma prior and exponential distribution and 45270 IRR (as maximum) in Two-Point prior and exponential distribution. Also, the average is 28750, while the WTP is 10623 IRR in non-Bayesian approach, which is lower than all the Bayesian estimation results. Therefore, the application of FHBD algorithm in dynamic pricing can be an appropriate way to determine the threshold amount of WTP for the exploitation of natural resources.
Conclusions & Suggestions: In sum, we study the Bayesian dynamic pricing problem under two-sided censoring with a short time horizon and limited inventory. Upon comparing it with the exact-observation system, we found that having better information always improves the revenue performance, while the optimal price under the exact-observation system can be either higher and lower than that under the two-sided censoring system. When comparing the above two systems with the no-learning system, we discover a surprising result that learning can bring a negative value when the inventory is scarce due to the biased learning effect. A derivative approximation heuristic is then devised to numerically solve the two-sided censoring problem. We further develop a performance bound to compare our proposed heuristic with other benchmark heuristics. Numerical experiments demonstrate that our heuristic consistently outperforms others and is robust with respect to WTP distributions. The two-sided censoring effect in our problem is a result of the binary customer choice model. When a customer faces a choice among multiple products, a more general choice model that surveys in the substitution effect is needed.