Fertilizer is an essential commodity traded in international and domestic markets and spatial competition is important feature impacting interfirm rivalry. In the case of North American fertilizer, numerous plants have been announced to either expand or open new plants (nitrogen-based fertilizer plants), exerting competitive pressures on an industry with surplus capacity but highly competitive in terms of production costs and technology. Proposed new plants and expansions are being induced by changes in the composition of crops, changes in the price of natural gas which affects the cost of producing domestic anhydrous ammonia. Developments in the fertilizer industry have become more volatile in the post-COVID period, and concurrent with the escalation in fuel prices, the Ukraine invasion, related embargoes on Russian trade, the world's largest exporter, and operations of the Grain Corridor. The purpose of this study is to quantify risks for plant expansion (brownfield and greenfield) of nitrogen fertilizer plants in North America, given the spatial competition and the corresponding dynamic market boundaries. Specifically, we quantify risks associated with fertilizer plant expansions, identify the optimal locations of new plants, and characterize spatial competition as a result of new entrants. A model is specified that integrates Geographical Information Systems (GIS) data into a stochastic mixed-integer network spatial optimization model using Monte Carlo simulations to account for risk in the random variables. The results are reprocessed into GIS for interpretation. The impact of risk in these variables results in market boundaries that are random. Specifically, competition for these new plants has embedded risks for new entrants on the probability of production and market penetration.

化肥是国际国内市场交易的重要商品，空间竞争是影响企业间竞争的重要特征。就北美肥料而言，许多工厂已经宣布扩建或开设新工厂（氮肥工厂），对产能过剩但在生产成本和技术方面具有高度竞争力的行业施加竞争压力。由于农作物成分的变化、天然气价格的变化影响了国内无水氨的生产成本，因此拟建的新工厂和扩建厂正受到影响。在后 COVID 时期，化肥行业的发展变得更加不稳定，同时燃料价格上涨、乌克兰入侵、俄罗斯贸易相关禁运、世界” 最大的出口商，以及粮食走廊的运营。本研究的目的是在考虑到空间竞争和相应的动态市场边界的情况下，量化北美氮肥工厂扩张（棕地和绿地）的风险。具体来说，我们量化了与化肥厂扩张相关的风险，确定了新工厂的最佳位置，并描述了新进入者带来的空间竞争。指定了一个模型，该模型将地理信息系统 (GIS) 数据集成到一个随机混合整数网络空间优化模型中，使用蒙特卡罗模拟来考虑随机变量中的风险。结果被重新处理到 GIS 中以供解释。风险对这些变量的影响导致市场边界是随机的。具体来说，