Capacity games with supply function competition
File(s)OR Note 2021-07-21.pdf (428.04 KB)
Accepted version
Author(s)
Anderson, Edward
Chen, Bo
Shao, Lusheng
Type
Journal Article
Abstract
We introduce a general model for suppliers competing for a buyer’s procurement business. The buyer faces uncertain demand, and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two-dimensional, with some capacity costs incurred prior to production and some production costs incurred at the time of delivery. These costs are general functions of quantity, and this naturally leads us to a supply function competition framework in which each supplier offers a schedule of prices and quantities. We show that there is an equilibrium of a particular form: the buyer makes a reservation choice that maximizes the overall supply chain profit, each supplier makes a profit equal to their marginal contribution to the supply chain, and the buyer takes the remaining profit. This is a natural equilibrium for the suppliers to coordinate on, since no supplier can do better in any other equilibrium. These results make use of a submodularity property for the supply chain optimal profits as a function of the suppliers available and build on the assumption that the buyer breaks a tie in favor of the solutions that give the largest supply chain profit. We demonstrate the applications of our model in three operations management problems: a newsvendor problem with unreliable suppliers, a portfolio procurement problem with supply options and a spot market, and a bundling problem with nonsubstitutable products.
Date Issued
2022-07-01
Date Acceptance
2021-10-14
Citation
Operations Research, 2022, 70 (4), pp.1969-1983
ISSN
0030-364X
Publisher
Institute for Operations Research and Management Sciences
Start Page
1969
End Page
1983
Journal / Book Title
Operations Research
Volume
70
Issue
4
Copyright Statement
© 2022 INFORMS
Identifier
https://pubsonline.informs.org/doi/10.1287/opre.2021.2221
Subjects
Social Sciences
Science & Technology
Technology
Management
Operations Research & Management Science
Business & Economics
capacity game
supply function
option contract
submodularity
Nash equilibrium
ELECTRICITY
AUCTIONS
DEMAND
Operations Research
0102 Applied Mathematics
0802 Computation Theory and Mathematics
1503 Business and Management
Publication Status
Published
Date Publish Online
2022-02-02