Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

9-2006

Publication Source

Operations Research

Volume

54

Issue

5

Start Page

893

Last Page

913

DOI

10.1287/opre.1060.0296

Abstract

We consider the problem of dynamically cross-selling products (e.g., books) or services (e.g., travel reservations) in the e-commerce setting. In particular, we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product, what we call a “packaging complement.” Given consumer preferences and product inventories, we analyze two issues: (1) how to select packaging complements, and (2) how to price product packages to maximize profits.

We formulate the cross-selling problem as a stochastic dynamic program blended with combinatorial optimization. We demonstrate the state-dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem. In particular, we focus on two practical business settings: with (the Emergency Replenishment Model) and without (the Lost-Sales Model) the possibility of inventory replenishment in the case of a product stockout. For the Emergency Replenishment Model, we establish that the problem is separable in the initial inventory of all products, and hence the dimensionality of the dynamic program can be significantly reduced. For both models, we suggest several packaging/pricing heuristics and test their effectiveness numerically.

Keywords

dynamic programming/optimal control, models, marketing, pricing ; buyer behavior

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Date Posted: 27 November 2017

This document has been peer reviewed.