Applying Fixed Order Commitment Contracts in a Capacitated Supply Chain

Past event — 27 May 2020

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Christina Imdahl, PhD

Assistant Professor of Machine Learning in Operations Management

Eindhoven University of Technology

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Problem definition: Demand uncertainty can lead to excess inventory holdings, capacity creation, emergency deliveries, and stock-outs. Under a base-stock policy, the costs of demand uncertainty are borne by upstream suppliers, but can propagate downstream in the form of higher prices. To address these problems, we investigate a practical application of a fixed order commitment contract (FOCC) in which a manufacturer commits to a minimum fixed order quantity each period and receives a per unit price discount from the supplier for the commitment.

Academic/practical relevance: We show that a FOCC can smooth the orders received by the supplier and offset the negative consequences of demand uncertainty for the supplier, the manufacturer, and the supply chain. We extend the theoretical literature by solving for an endogenous price discount instead of treating it as an exogenous value, and analyze the impact on supply chain performance in a practical setting.

Methodology: We model a FOCC as a Stackelberg game in which the supplier offers a price discount anticipating the manufacturer's response, and the manufacturer subsequently decides on the optimal commitment quantity. Using data for 863 parts from a large international materials handling equipment manufacturer, we evaluate the relationships between the model parameters, contract parameters, and the contract effectiveness in terms of cost savings.


Christina Imdahl joined Kühne Logistics University as a PhD Candidate in the field of Supply Chain Management in June 2016. Her research will concentrate on the reduction of delivery times along the supply chain.

Christina received her Master degree in Mathematics from the Georg-August University Göttingen in May 2016 and a B.Sc. degree in Business Administration with strong focus on logistics and operations management. The bachelor thesis examines different visualization approaches for multidimensional data that are often needed in the field of Multi-criteria Decision Analysis. During her studies Christina worked as a student assistant at the Department of Production and Logistics at the Georg-August University Göttingen, where she gained first insights to academic research.

Results: We show that the FOCC generates greater savings for the manufacturer and supplier if (i) the holding costs of the manufacturer is low, (ii) the supplier's capacity utilization is high, or (iii) the supplier's cost of excess capacity production is high. We also show that when the supplier's demand uncertainty is high, the FOCC generates greater savings for the supplier. The manufacturer's cost savings initially increase as the supplier's demand uncertainty increases, but moderate when the demand uncertainty increases too much.

Managerial Implications: Our results help operations managers better understand how to obtain the optimal contract parameters for a FOCC and the circumstances under which such a contract is most beneficial for the supply chain partners.

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Bärbel Wegener

Assistant to Resident Faculty