Optimization of Investments in Labor Productivity in Supply Chain Networks

Labor is an essential resource in the functionality of supply chains. The COVID19 pandemic has demonstrated the varied impacts of disruptions to supply chains because of labor issues. Shortages of labor continue even now as economies begin to open up with progress on vaccinations. Investing in labor productivity is a possible mechanism in moderating shortfalls in labor. This paper constructs a supply chain network optimization model, whose solution yields optimal product path flows to demand markets, the optimal investments in link labor productivity, as well as labor hours needed, and the optimal wages of the workers in production, transportation, storage, and distribution. The model includes a budget constraint on the investments, along with maximum bounds on investments on the supply chain network links. The theoretical framework, which includes Lagrange analysis, and the computational approach, are based on the theory of variational inequalities. Managerial insights are provided obtained via the Lagrange analysis and a series of numerical examples, which demonstrate that such investments can help both the firm and the consumers