Article
Agent-Based Modeling for By-Product Metal Supply—A Case
Study on Indium
Jinjian Cao
1
, Chul Hun Choi
2
and Fu Zhao
1,3,
*
Citation: Cao, J.; Choi, C.H.; Zhao, F.
Agent-Based Modeling for By-Product
Metal Supply—A Case Study on
Indium. Sustainability 2021, 13, 7881.
https://doi.org/10.3390/su13147881
Academic Editor: João Carlos de
Oliveira Matias
Received: 1 June 2021
Accepted: 25 June 2021
Published: 14 July 2021
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1
Environmental and Ecological Engineering, Purdue University, 500 Central Dr,
West Lafayette, IN 47907, USA; cao164@purdue.edu
2
Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47907, USA;
chrischoi1979@gmail.com
3
Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA
* Correspondence: fzhao@ecn.purdue.edu
Abstract:
With rapid development and deployment of clean energy technology, demand for certain
minor metals has increased significantly. However, many such metals are by-products of various
host metals and are economically infeasible to extract independently. Meanwhile, by-product metals
present in the mined ores may not be extracted even if they are sent to smelters along with host
metal concentrates if it is not economically favorable for the producers. This dependency poses
potential supply risks to by-product metals. Indium is a typical by-product metal, mainly from
zinc mining and refining, and is important for flat panel displays, high efficiency lighting, and
emerging thin-film solar panel production. Current indium supply–demand forecast models tend
to overlook the volatile and competitive nature of minor metal market and are mostly based on
top-down approaches. Therefore, a bottom-up agent-based model can shed new light on the market
dynamics and possible outcome of future indium supply–demand relationship. A multi-layered
model would also be helpful for identifying possible bottlenecks of indium supply and finding
solutions. This work takes indium as an example of minor metal market and sets up an agent-based
model to predict future market situation and supply–demand balance. The market is modeled as
a Cournot competition oligopolistic market by refineries with capacity restriction based on host
metal production. The model maintains active Nash equilibrium each year to simulate competitions
between suppliers. The model is validated and verified by historical data and sensitivity analysis.
Several scenarios are also explored to illustrate possible uncertainties of the market.
Keywords: indium; agent-based modeling; Cournot equilibrium
1. Introduction
Energy is a fundamental element of economic growth. Global primary energy con-
sumption has increased by 2.9% in 2018, which is the fastest for the decade [
1
]. To avoid
dependency on fossil fuels, which still count for 64% of world energy generation [
1
], non-
fossil resources, especially renewable energy from wind and solar power, have been heavily
promoted by governments. Between 2005 and 2015, the US government spent $51.2 billion
US dollars on incentives to solar and wind power industries, including tax, credit, and
R&D grants [
2
]. As a result, renewable energy consumption has increased by four times
between 2008 and 2018, to a total of 561.3 million tons oil equivalent [
1
]. With an imminent
need for renewable energy development and technology advancement, minor metals have
become increasingly important. The US Department of Energy has identified 14 materials
as critical to the clean energy economy [
3
]. Meanwhile, Joint Research Centre of European
Commission addressed 32 significant materials toward clean energy sector [
4
]. One major
issue for these materials is the potential supply risk caused by the increasing demands.
Many of the so-called critical materials are by-product metals. By-product metals are
those minor metals that are mined mostly or solely as companion of other major metals [
5
].
Sustainability 2021, 13, 7881. https://doi.org/10.3390/su13147881 https://www.mdpi.com/journal/sustainability
