A logistics ratio-optimised inventory routing problem with lateral transhipment using mixed-integer robust fractional programming

This study addresses a single-period multi-product inventory routing problem (IRP) considering reactive lateral transhipment with the optimisation objective of logistics ratio, defined as logistics cost per unit of product value. The problem is modelled in two stages: in the first stage, the distribution is planned based on imperfect forecasted demand. In the second stage, actual demand is revealed, and reactive lateral transhipment is executed based on first-stage decisions. We develop a basic fractional programming (BFP) model with deterministic demand for both stages. Considering demand uncertainty, we extend a robust fractional programming (RFP) model and a two-stage robust fractional programming (TSRFP) model for first-stage IRP and propose structural uncertainty sets. We apply Dinkelbach's algorithm and the robust counterpart transformation to tackle the RFP model. We employ the column and constraint generation algorithm to address the TSRFP model with Dinkelbach's algorithm. The results indicate that the proposed TSRFP is suits scenarios with high stockout penalties and at medium demand uncertainty levels. Managers can select between TSRFP, RFP, and BFP to optimise inventory management based on demand uncertainty and product attributes.