Simulation Approach to Analyse Deterministic IRP Solution of the Stochastic Fuel Delivery Problem

Two components of a supply chain with a significant impact on its performances are inventories and transportation costs. Mutual dependences between the activities of inventory allocation and vehicle routing have recently motivated some authors to model them simultaneously. This practical and challenging logistical problem is known as the integrated Inventory Routing Problem (IRP). The IRP assumes application of vendor management inventory (VMI) concept where suppliers determine an order quantity and the time of its delivery. The IRP is usually formulated and solved under the assumptions of deterministic consumption and delivery times which, in turn, provide an opportunity of obtaining a solution of the problem regardless of its NP hardness, even in this simplified form. However, since fuel consumption is stochastic in its nature, delivery plans based on a deterministic assumption, particularly covering longer planning periods, may introduce certain problems in real life applications, imposing shortages, higher inventories levels, or even the necessity of changing delivery routes. This paper presents a simulation approach to the analysis of the applicability of deterministic IRP solution to real life stochastic fuel consumption and delivery process. The applicability of deterministic IRP solutions to stochastic problems with planning periods of different lengths is analyzed through observing different process performances. From obtained results it can be concluded that solutions based on deterministic consumption can be applied in stochastic IRP by applying and balancing two additional measures: emergency deliveries and safety stocks.