An adjusted branch-and-bound algorithm for solving cyclical long-term inventory routing problems

The SV-CIRP is an optimization problem consisting of finding a recurring distribution plan, from a single depot to a selected subset of retailers, that maximizes the collected rewards from the visited retailers while minimizing transportation and inventory costs. It appears as fundamental building block for all variants of the cyclic inventory routing problem (CIRP). One of the main complications in developing solution methods for the SV-CIRP is the non-convexity of the objective function. We demonstrate how the problem can be reformulated so that its continuous relaxation is a convex optimization problem. We propose an adjusted branch-and-bound algorithm that solves the SV-CIRP more effectively