The Optimal Number of Suppliers in the Presence of Volume Discounts and Different Compensation Potentials - An Analytical and Numerical Analysis

Abstract

Supplier selection is becoming more and more critical for purchasing managers. The ongoing integration of supply chains increases dependencies within the supply chain and therefore requires a thorough decision on the right number and set of suppliers. In choosing the optimal number of suppliers and allocating purchasing volumes, companies face a fundamental tradeoff: while the costs of managing supplier relationships and purchasing costs may increase with the number of suppliers, buyers may also realize the benefit of lower supply risks. We extend existing models to account for volume discounts and the compensation that a set of multiple suppliers may provide if individual suppliers fail. We propose a model with volume-dependent prices to determine the optimal number of suppliers in the presence of risks, volume discounts, and different compensation potentials. We use our model to provide analytical insights into the complex decision problem that managers face when choosing a set of suppliers and determining purchasing volumes for individual suppliers. More specifically, we identify a "purchasing cost effect" and a "compensation effect" that together drive the optimal purchasing decision, and we show how these effects interact in different situations. While volume discounts favor a concentration of the purchasing volume, compensation between suppliers may suggest at a first glance a more balanced allocation of purchasing volumes across suppliers. However, we show in this paper that under certain conditions both the purchasing cost effect and the compensation effect favor a volume concentration - a counter-intuitive result. Our analytical insights are supported by numerical analyses in which we highlight the sensitivity of the optimal purchasing decision to relevant problem parameters.

Keywords: supply chain management, purchasing, supplier selection