Robust Capacity Expansion Model Integrating the Perspectives of Production Economics and Capacity Regret

A typical production economics theory provides some factors which should be considered in capacity expansion; for example, a production function estimates the production possibility set (PPS) and satisfies the law of diminishing marginal returns (DMR). However, an operations research (OR) model, which usually focuses on addressing demand fluctuation for cost minimization and assumes a constant marginal productivity (MP), may overestimate the capacity level, thus leading to an infeasible capacity plan. This study proposes a novel two-stage model which integrates the perspectives of production economics and operations research (OR) to solve the capacity expansion problem (CEP). The first stage, which addresses the production economics issue, estimates the production possibility set (PPS) limiting production behavior and uses the directional distance function (DDF) to find the directional marginal productivity (DMP) towards marginal profit maximization. The second stage, which addresses demand fluctuation, employs the minimax regret strategy (MMR) balancing capacity shortage and capacity surplus to generate a robust capacity expansion. The results of a numerical illustration validating the proposed approach suggest a stochastic programming model for robust capacity planning, and justify the typical OR-type approach where the two major factors affecting capacity decisions are demand variation and cost structure rather than the DMR effect