Abstract: Labor constraints caused by COVID-19 has produced enormous capacity pressure on labor-intensive enterprise. Using shared employees is a method to relieve capacity pressure of enterprises during the COVID-19 pandemic. For a supply chain network system consisting of several competing heterogeneous supply chains, a variational inequality approach is used to develop an equilibrium model of a supply chain network considering labor flowing constraints. Euler algorithm is used to solve the problem, and the impact of labor resources on the equilibrium decision of a supply chain network is analyzed. Furthermore, the impact of "shared employees" on the efficiency of supply chain operation is also discussed. Results show that insufficient labor resources may reduce the production and profits of a supply chain; "shared employees" can help a supply chain better allocate limited labor according to its industrial structure and demand; in some cases, "shared employees" may reduce the operational efficiency of a supply chain.