Analysis of Asymmetric Quantity Commitment in Decentralized Supply Chains

Introduction

Quantity commitment has attracted much attention in the academic community and in industry practices to mitigate price competition. The seminal work includes Nasser and Turcic (2016), Kreps and Scheinkman (1983) and Singh and Vives (1984). For instance, Singh and Vives (1984) assume that the firm that chooses quantity commitment will not set a price at a subsequent stage and the specific price is followed by default to clear the entire committed quantity. However, none of the studies considers the scenario where heterogeneous consumers on the market and product value differentiation from different channels lead to price differentiation simultaneously.

In this paper, we propose a general modeling approach: 1) There are two competing firms: one is an e-tailer which sells the product online directly and another one is a retailer which sells the product through the brick-mortar retailing store. The objectives of these two firms are to maximize their own profits, respectively. 2) The asymmetric choice of quantity commitment is adopted: it is assumed that the e-tailer never makes a quantity commitment because of its shortened lead times, or else it adopts just-in-time systems to circumvent quantity commitment while the retailer can choose to make the quantity commitment or not. This kind of model is common. For example, Dell Company which sells many of its products online normally does not make quantity commitment; rather it starts production only when the demand from consumers is received while its retailing competitor does (Guo and Iyer 2013). Dell’s approach constitutes a pull system in terms of supply chain strategy. In contrast, the competitors are employing a push supply chain strategy. The push versus pull system and level of quantity commitment has an impact on the supply chain business function known as “available to promise” (ATP). Push-based ATP is based on forecasts of future demand which can be inaccurate. Pull-based systems dynamically allocate resources in response to actual customer demand (Zhao 2005). 3) Heterogeneous consumers value the product differently. On the market, they are uniformly distributed on the interval and have a total mass of 1. This kind of consumer distribution is widely adopted and in common knowledge (Kabul and Parlaktürk 2017). 4) Firms will strategically set the prices at a subsequent stage regardless of whether it commits to a quantity or not in the earlier stage. They compete against each other.

Our study incorporates the difference between online and brick-mortar retailing sales into the model, which is widely discussed in the literature. The seminal work mainly demonstrates the main differences in the following aspects: 1) online sales require longer delivery times and additional shipping and handling fees (Hess, Gerstner and Chu 1996); 2) brick-mortar retail sales are more convenient (Liang and Huang 1998); and 3) there is less consumer acceptance of the product value through online purchases (Kacen, Hess and Chiang 2013; Chiang, Chhajed and Hess 2003 and Qin and Mambula 2018). In our study, we adopt the model of Chiang, Chhajed and Hess (2003) and assume that a consumer acceptance of online channel is θ due to the difference between the online and brick-mortar retail sales. Moreover, Chiang et al. (2003) further adopt that the acceptance of the online channel by consumers is , i.e., is the proportionate loss of benefits from an online channel purchase.