Equilibrium analysis of capacity allocation with demand competition

Abstract

This article examines the capacity allocation decisions in a supply chain in which a supplier sells a common product to two retailers at a fixed wholesale price. The retailers order the supplier's product subject to an allocation mechanism preannounced by the supplier, and compete for the customer demand. We perform an equilibrium analysis of the retailers' ordering decisions under uniform and individually responsive allocations. Uniform allocation guarantees equilibrium orders, but is not necessarily truth inducing in the presence of demand competition. Further, we find that (1) neither the supplier nor either one of the retailers sees its profits necessarily increasing with the supplier's capacity, and the supplier may sell more with a lower capacity level, and (2) capacity allocation may not only affect the supply chain members' profits but also change the supply chain structure by driving a retailer out of the market. This article provides managerial insights on the capacity and ordering decisions for the supplier, the retailers, and the supply chain.

The bullwhip effect: Progress, trends and directions

“…When retailers are local monopolists (that is, when they don't compete for customer demand), the uniform policy is truth-inducing (Cachon and Lariviere, 1999a). If retailers are not monopolists, then all IR policies, as well as the uniform and lexicographic policies, are not truth-inducing (Liu, 2012;Cho and Tang, 2014). Further, when competing retailers have asymmetric market power, competitive allocation eliminates the gaming effect (Cho and Tang, 2014).…”

Allocation with demand competition: Uniform, proportional, and lexicographic mechanisms

“…Cho and Tang [6] and Liu [10] also study equilibrium ordering under uniform allocation. Cho and Tang [6], mostly study whether the gaming effect presents under uniform allocation and does not provide complete equilibrium orders under different conditions of K and w. The analysis in Lemma 1 and Theorem 1 makes the following major distinctions comparing with [10]: (1) we assume an upper bound (supplier's capacity K) on order size, while Liu (2012) assumes no upper bound on order size; (2) Liu [10] assumes z 2 > (z 1 + w)/2, while in our problem w is a decision variable of the supplier, and it would be artificial to impose a lower bound on w other than 0, thus our article, relax the assumption as z 2 > z 1 /2; (3) we provide complete and precise structures for retailers' ordering decisions in Nash and dominant equilibrium in Theorem 1, while Liu [10] focuses on allocations in stead of equilibrium orders and only provides a representative equilibrium when multiple equilibria result in the same allocation. In addition, Liu [10] classifies equilibria based on capacity level K, while we classify equilibria based on wholesale price w, for the ease of subsequent analysis of the supplier's wholesale pricing decision, which [10] does not consider.…”

How Precious Are Scarce Products? An Experimental Study on a Turn‐and‐Earn Allocation Mechanism

“…Further, Hall and Liu (2010) investigate supply chain coordination under a proportional or linear allocation mechanism when retailers operate in independent markets. Cho and Tang (2011), Liu (2012), and Chen, Li, and Zhang (2013) investigate uniform and lexicographic rules, respectively, when retailers engage in demand competition. The above allocation rules serve as one-period mechanisms such that capacity assignments are influenced by decisions made in the current period.…”