A robust capacity expansion integrating the perspectives of marginal productivity and capacity regret

This study addresses a capacity expansion problem (CEP). A typical CEP model usually focuses on addressing demand fluctuation for cost minimization and assumes a constant marginal productivity, which may overestimate the capacity level, thus leading to an infeasible capacity plan. However, the marginal productivity theory has some merits which can complement the CEP; for example, a production function estimates the production possibility set limiting the production behavior and characterizes the law of diminishing marginal returns (DMR). To integrate the perspective of marginal productivity factors in the CEP model, we propose a two-stage model to solve the CEP. The first stage estimates the production possibility set and finds the directional marginal productivity (DMP) towards marginal profit maximization. The second stage, which addresses demand fluctuation, develops the minimax regret model, balancing capacity shortage and capacity surplus to build a robust capacity plan. The results of a numerical illustration validate the robust decision generated by the proposed model and correct a typical CEP model without considering marginal productivity, where the major factor affecting capacity decisions is the ability to raise/leverage resource for marginal productivity rather than demand variation and cost structure.