Managing Inventory and Financing Decisions Under Ambiguity

Abstract

Micro, small and medium-sized enterprises (MSMEs) face persistent challenges in raising capitals, and one of the practical reasons could be the high level of ambiguity in this sector. As many not-for-profit organizations or governmental agencies strengthen financial supports to MSMEs, the important issue of stimulating growth while protecting fund providers under ambiguity arises. We propose a robust optimization framework to jointly determine the firm's production planning and financing decisions in a principal-agent model with the presence of distributional ambiguity. We apply the notion of absolute robustness to derive a financing agreement that is both feasibility-robust and performance-robust. We assume that both the firm and the investor base their decisions on two fundamental descriptive statistics: the mean and the variance of the demand. The firm jointly determines the production quantity and financial agreement to maximize the worst-case expected profit, while the investor approves the financial agreement if the worst case expected return can cover the cost of capital. We show that equity financing is one of the robust optimal financing agreements. We also consider loan financing as an alternative. We derive the firm's robust optimal interest rate and production quantity in closed forms. Notably, the robust optimal interest rate depends on the demand variability and the asset recovery ratio, which comprehensively considers the value of collateral, initial capital, and production quantity.