Capacity allocation with competitive retailers

Abstract

This paper addresses a problem in supply chain management that how scarce resources can be efficiently allocated among competing interests. We present a formal model of allocation mechanisms for such settings that a supplier with limited production capacity allocates its products to a set of competitive retailers. In contrary to the existing allocation mechanisms in which retailers are local monopolists, the new model exhibits much more complicated market behaviors. We show that the widely-used proportional allocation mechanism is no longer necessarily Pareto optimal, even if all retailers are in a symmetric situation. A necessary and sufficient condition for the proportional allocation to be Pareto optimal is given. We propose a truthinducing allocation mechanism based on our capacity allocation model, which is more intuitive and applicable than the existing truth-inducing mechanisms.

Mechanism design for capacity allocation with price competition

“…Under proportional allocation, the retailers inflate orders to be allocated more than competitors. Contrary, we showed that uniform allocation induces truthful order quantity from the retailers under which we have the same equilibrium price as Furuhata and Zhang [11].…”

“…In this case, according to Theorem 6, we are easily able to obtain the equilibrium order quantity m * i =m i . The interesting case of the capacity range is K ≤ and the equilibrium price p * = P (K), which is the same price as the quantity competition shown in [11]. If it is asymmetric, we obtain allocation g i (m…”

“…A main goal of this model with respect to mechanism design aspect is to obtain a truth-inducing mechanism. We investigate market behaviors under uniform allocation presented in [28], which is a truth-inducing mechanism in [6] and [11]. Under uniform allocation, the retailers are indexed in ascending order of their order quantity, i.e., m1 ≤ m2 ≤ .…”

“…If the maximum order quantities are heterogeneous and the allocation for the largest allocated retailer exceeds its best response quantity, the retailers set their resale price greater than P (K) which is a unique phenomenon in this model compared to the quantity competition in [11].…”

“…Furuhata and Zhang [11] consider the problem by introducing competition into the downstream market. They consider a simple case where the downstream market is in quantity competition.…”