Investments in Labor Productivity: Single Period Model

Abstract

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. In this chapter, a supply chain network optimization model is constructed, 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.