Attracting international migrant labor: Investment optimization to alleviate supply chain labor shortages

The COVID-19 pandemic has disrupted supply chains globally with a major shortfall being that of labor shortages from production through distribution activities. In this paper, we construct a new supply chain network optimization model that includes both domestic labor and international migrant labor from multiple countries, with the latter made possible through investments in attracting labor subject to a budget constraint. We allow for different wage settings for domestic versus migrant labor and also have the flexibility of providing true information as to the wages of migrants or not. We derive variational inequality formulations of the model, along with qualitative properties, and present an algorithm that yields closed form expressions for the underlying problem variables at each iteration. The model is one of the very few variational inequality operations research models with nonlinear constraints. Three series of algorithmically solved numerical examples, motivated by a high value agricultural product — that of truffles, demonstrate the insights in terms of profits, prices, product path flows, and investments, with variations in the data including that of truthful and untruthful wages being used to attract migrant labor.