Distributionally robust inventory routing problem to maximize the service level under limited budget

This paper studies a stochastic inventory routing problem with alternative handling modules and limited capital budget, under partial distributional information (i.e., the mean and covariance matrix of customer demands). The objective is to maximize the service level, i.e., the probability of jointly ensuring no stockout and respecting the warehouse capacities for all customers at the end of each period. A novel distributionally robust chance constrained formulation is proposed. The sample average approximation method and a model-based hierarchical approach based on problem analysis are developed. Computational results show that the latter approach is more efficient. We also draw some managerial insights.