Dynamic Pricing with Variable Order Sizes for a Model with Constant Demand Elasticity

TL;DR

This paper develops a dynamic pricing model for scenarios where customers can order multiple items, deriving optimal strategies and analyzing how average order size influences pricing behavior and revenue.

Contribution

It introduces a generalized model allowing variable order sizes, providing closed-form solutions for optimal revenue and analyzing asymptotic pricing behavior.

Findings

Optimal expected revenue formula derived

Comparable models share the same asymptotic pricing behavior

Order size distribution governs differences between models

Abstract

In this paper we investigate a dynamic pricing model for constant demand elasticity where customers have a probability distribution on the number of items they order. This is a generalization from standard models which restrict customers to buy only one item at a time. For the generalized model, we first obtain a closed form expression for the optimal expected revenue and optimal pricing strategy. This expression involves a recursively defined term for which we investigate the behavior. We call comparable models those which have the same demand, which is the customer arrival rate times the average order size. In fact, the average order size plays an important role for results for the generalized model. An important result we show is that comparable models have the same asymptotic pricing behavior. Numerical results also show that comparable models are relatively close even for low inventory levels. Lastly, we prove that the relative difference between comparable models is governed not by the customer arrival rate, but solely by their order size distributions.