Optimization of Physical and Financial Flows in the Inventory Routing Problem

Abstract

Although supply chain optimization has traditionally focused on operational efficiency, financial dimensions often receive less attention. In particular, standard formulations of the Inventory Routing Problem (IRP) aim to minimize transportation and inventory costs, without accounting for financial flows or their impact on overall financial viability. To address this gap, we introduce the Operational Cash Requirement (OCR) as a dynamic indicator that captures the influence of financing strategies on inventory and routing decisions over time. This paper presents a new mixed-integer linear programming (MILP) formulation that integrates OCR into the IRP by explicitly modeling payment and collection delays. The model captures the interaction between physical and financial flows and extends the objective function to account for the financial resources required to support operational activities. Computational experiments on small-scale instances using an exact method demonstrate that incorporating financial constraints can significantly affect operational decisions, highlighting the importance of considering cash flow dynamics in logistics planning to better align operational and financial performance.