1. Introduction

In international iron ore market, Asian countries, mainly China, Korea, and Japan, are the major importers, who accounted for 85.7% of global iron ore import in 2016, while Australia and Brazil are two major exporters who took up 77.33% of market share of global iron ore export in 2016 (World Steel Association Report, 2018). Due to its closer transport distance to Asia, Australia dominates the Asian iron ore imports, accounted for 63.12% of market share in 2016 (World Steel Association Report, 2018). Being located far away from its major importers, Brazil competes with Australia for Asian market by initiating a series of shipping strategies. For example, Brazil miners (the Valley, Companhia Siderúrgica Nacional) have deployed very lager bulk ships (400,000 tons Valemax) for its iron ore transportation, cooperating with Chinese giant carriers, e.g., China Merchants Group and China Ocean Shipping Company since 2012. At the same time, those Brail miners also built self-owned specialized terminals for iron ore handling in order to increase the iron ore sea handling capacity and reduce the shipping cost in the East Asia trade. However, these strategies seem not effective. As an evidence, from 2012 to 2015, the iron ore exported from Brazil to East Asian countries only grew by 10.2%, while Australian export increased by 54.6%. This raises a doubt on whether it is worthwhile for Brazil miners to put so many efforts in improving the sea transportation of iron ore. In this study, we develop an analytical tool to evaluate the impact of shipping sector on international iron ore trade. 
    Computable equilibrium model is one of the widely applied approaches for strategy (as well as policy) analysis in international resource commodity markets. Based on the assumption of market structure and individual behavior, the optimization problems of stakeholders and market clearing conditions are formulated into an equilibrium framework to simulate the interrelations of the stakeholders in an economic system. 
    Compared to the analysis of other major resource commodities, e.g., LNG, electricity, the equilibrium analysis of iron ore market only attracts limited attentions. The existing equilibrium studies are mainly based on the assumption that the market is in perfect competition (e.g., Toweh and Newcomb, 1991; Wang et al., 2007), which may not be efficient to reflect the reality of iron ore trade. In addition, since the shipping demand is derived from the international iron ore trade, those studies focus less on the role of shipping sector. In most cases, the iron ore shipping cost is implicitly modeled as an exogenous, and is taken as given in the trade cost function of iron ore exporters and importers. However, some researchers present evidences which suggest the importance of the shipping cost in the international trade. For example, Martínez-Zarzoso et al. (2003) points out that higher transportation cost is a significant barrier in the export of Spanish Ceramic. Furthermore, some operational strategies e.g., fleet deployment, steaming strategy and technique development in shipping sector can influence the capacity of the fleet, which may also deter the trade growth. Therefore, knowing the impacts from shipping sector is an essential piece of jigsaw in terms of in-depth studies on the international iron ore trade. With these research gaps in mind, we propose a general iron ore trade equilibrium model, incorporating an imperfect competition trade market model and a transportation optimization model of the shipping sector.
   Due to the exist of the integer variables (e.g., ship number), this model is a Discretely Constrained Mixed Complementarity Problem (DC-MCP), which is hard to find a solution satisfying both complementarity and integer constraints. In this paper, we designed a solution procedure for finding the nearly complementarity solutions of the model by applying a mixed integer nonlinear programming (MINLP) formulation and convexification techniques. A case study with real data is conducted to validate this model and the proposed procedure.
   The main contribution of this paper is to provide a framework for the equilibrium analysis of international iron ore trade by developing an equilibrium model capturing the interrelationship of stakeholders. Depending on the previous studies, we modify the modeling of market structure and capacity restrictions with more practical features of the trade. In particular, the endogenous modeling of the shipping sector makes it available to capture the interrelationship between sea transportation activities and the trade. Practically, this model is an evaluation tool for more nuanced shipping-related strategies and policies, e.g., fleet capacity expansion, voyage cost fluctuation, the opening of new routes, etc., in the international iron ore trade. The results from strategy or policy simulation can provide systematic insights of all stakeholders’ responses, which contribute to a more comprehensive judgment for the shipping strategies or policies in iron ore shipping.
    The rest of the paper is organized as follows: in section 2, we summarize the literature regarding resource commodity market analysis and computable equilibrium models. Section 3 develops a mixed-complementarity based equilibrium model for the proposed international iron ore market. Section 4 provides the solving method for the proposed model. In section 5, we validate our model with real data through analyzing the impact of big ship adoption on international iron ore trade. Finally, in section 6, we make conclusions.