[Paper Review] Practical inventory routing: A problem definition and an optimization method

Martin Josef Geiger, Marc Sevaux|arXiv (Cornell University)|Feb 28, 2011

Vehicle Routing Optimization Methods6 references4 citations

TL;DR

This paper proposes a bi-objective optimization approach for practical inventory routing problems with partial demand knowledge, using frequency-based policies and improved routing heuristics. It introduces a novel method that balances routing and inventory costs, achieving non-dominated solutions through controlled random frequency strategies and record-to-record travel improvements, with results validated on instances up to 250 customers over 240 periods.

ABSTRACT

The global objective of this work is to provide practical optimization methods to companies involved in inventory routing problems, taking into account this new type of data. Also, companies are sometimes not able to deal with changing plans every period and would like to adopt regular structures for serving customers.

Motivation & Objective

• To address real-world inventory routing problems where demand is only partially known over a finite horizon.
• To develop practical, interpretable optimization methods that support long-term planning with stable delivery frequencies.
• To minimize two distinct objectives—total routing cost and total inventory cost—without assuming comparability of these costs.
• To provide decision-makers with non-dominated solutions through frequency-based delivery policies.
• To create a visual, interactive solver tool for testing and refining delivery strategies in real-time.

Proposed method

• The problem is modeled as a single-product, finite-horizon inventory routing problem with a depot, customers, and a homogeneous fleet of trucks.
• A frequency-policy is used, assigning each customer a fixed delivery frequency to ensure stable, regular service schedules.
• Initial routes are generated using savings heuristics and then improved via the Record-To-Record Travel (RRT) algorithm.
• A bi-objective optimization framework is applied, treating routing and inventory costs as separate, non-comparable objectives.
• A controlled random frequency strategy is employed to explore the solution space and fill gaps in the Pareto front.
• An interactive solver with visual feedback is developed to display inventory levels, vehicle usage, and routing tours per period.

Experimental results

Research questions

• RQ1 How can inventory routing problems be modeled when demand is only partially known over future periods?
• RQ2 What is the impact of using fixed delivery frequencies on balancing routing and inventory costs?
• RQ3 Can a bi-objective approach that treats routing and inventory costs as distinct objectives yield better practical solutions than single-objective models?
• RQ4 How effective are frequency-based policies in generating non-dominated solutions across diverse demand patterns?
• RQ5 To what extent can routing improvements via RRT enhance the quality of the Pareto front in frequency-based strategies?

Key findings

• The frequency-policy approach successfully generates a diverse set of non-dominated solutions, with the day-to-day policy minimizing inventory costs and the uniform-frequency policy reducing routing costs.
• The use of controlled random frequencies effectively fills gaps in the Pareto front, producing a dense cluster of high-quality solutions.
• Improving routing with the Record-To-Record Travel algorithm significantly reduces routing costs, especially at low delivery frequencies.
• The visual solver interface enables real-time analysis of inventory levels, vehicle usage, and routing tours, supporting practical decision-making.
• The method scales to large instances, with tested cases reaching up to 250 customers over a 240-period horizon.
• The approach demonstrates practical viability by supporting stable, regular delivery structures that align with real-world operational constraints.