Coordinating Pricing and Inventory Replenishment with Nonparametric Demand Learning

Abstract

We consider a firm (e.g., retailer) selling a single nonperishable product over a finite-period planning horizon. Demand in each period is stochastic and price-dependent, and unsatisfied demands are backlogged. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity, but it knows neither the form of demand dependency on selling price nor the distribution of demand uncertainty a priori, hence it has to make pricing and ordering decisions based on historical demand data. We propose a nonparametric data-driven policy that learns about the demand on the fly and, concurrently, applies learned information to determine replenishment and pricing decisions. The policy integrates learning and action in a sense that the firm actively experiments on pricing and inventory levels to collect demand information with the least possible profit loss. Besides convergence of optimal policies, we show that the regret, defined as the average profit loss compared with that of the optimal solution when the firm has complete information about the underlying demand, vanishes at the fastest possible rate as the planning horizon increases.

A heuristic policy for dynamic pricing and demand learning with limited price changes and censored demand

“…If no stockout occurs, then we keep the order-up-to level the same as in the previous period. We note that a similar rule was also used by [12] in a stochastic inventory problem with no pricing decisions and by [9], [10] in a pricing problem with inventory decisions and unlimited price changes.…”

“…The studies that are most relevant for the work presented in this paper are [1], [9], [10], [11]. In [1] the authors study a dynamic pricing problem with limited price changes but there is no demand censoring and no inventory decisions.…”

“…In this paper we do not make such an assumption. In [9], [10] a problem similar to the one in this paper is considered, but in [9], [10] there are no restrictions on the number of price changes. We note that demand censoring has also been studied in the setting of (repeated) newsvendor and stochastic inventory problems (e.g.…”

“…In this section we give a formal description of the problem statement. The model considered here is based on the demand assumptions made in [1], but is extended to include a stochastic inventory control component similar to [12], [13], [9], [10].…”

An Extension to the Economic Production Quantity Problem with Deteriorating Products Considering Random Machine Breakdown and Stochastic Repair Time

“…Therefore, they decrease under the effect of the learning process. Finally, Chen et al, [38] considered a firm (e.g., retailer) selling a single nonperishable product over a finite-period planning horizon. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity with the objective of maximizing total profit, but it knows neither the average demand (as a function of price) nor the distribution of demand uncertainty a prior; hence, it has to make pricing and ordering decisions based on observed demand data.…”