A simulation optimization approach to apply value at risk analysis on the inventory routing problem with backlogged demand

Inventory Routing Problem (IRP) is defined as the combination of vehicle routing, inventory management and delivery scheduling decisions. In this study, a model for a basic inventory routing problem is proposed, which controls the risk of exceeding capital dedicated to an IRP with a value at risk (VaR) measure. It is assumed that the structure of the basic model is one to many, the time horizon is single period and fleet composition is homogeneous. The objective of the model is to minimize the expected total cost over a planning horizon at the same time considering the affordable risk. Since a stochastic IRP is an NP-hard problem and considering VaR makes it more complex, it is not feasible to solve the large-scale problems through an exact model. Hence, a new simulation optimization procedure is proposed to solve the problem. Finally, a numerical example is presented to demonstrate its accuracy and applicability.