An improved formulation for the inventory routing problem with time-varying demands

Abstract

The Inventory Routing Problem (IRP) is a broad class of complex routing problems where the quanti- ties of delivered products must also be determined. In this paper, we consider the classic IRP where a single supplier must determine when to visit its customers, how much to deliver and how to com- bine the customer visits in each period into routes. We propose a branch-and-cut algorithm based on a new mathematical formulation for the IRP, improving the average lower bound obtained from algorithms based on the branch-and-cut methodology. The new formulation substitutes parts of the original formula- tion with a convex combination of extreme points. We call these extreme points customer schedules and for each customer they contain information about delivery periods and corresponding delivered quanti- ties. We show that this algorithm outperforms a state-of-the-art branch-and-cut algorithm on instances with time-varying demands. The customer schedule-based algorithm obtains better lower bounds, which improves the average optimality gap by 29% and 15% on two new sets of instances with time-varying demands.