Optimizing Inventory Routing: A Decision-Focused Learning Approach using Neural Networks

TL;DR: This paper introduces a decision-focused learning approach that seamlessly integrates inventory prediction and routing optimization to address the Inventory Routing Problem, incorporating optimization feedback into neural network training.

Abstract

Inventory Routing Problem (IRP) is a crucial challenge in supply chain management as it involves optimizing efficient route selection while considering the uncertainty of inventory demand planning. IRP addresses the challenge of accurately predicting inventory levels. To solve IRP, usually a two-stage approach is employed, where demand is predicted using machine learning techniques firstly, and then an optimization algorithm is used to minimize routing costs. However, machine learning models often fall short of achieving perfect accuracy because inventory levels are influenced by the dynamic business environment, which, in turn, affects the optimization problem in the next stage, resulting in sub-optimal decisions. In this paper, we formulate and propose decision-focused learning based approach to solve real-world IRPs. This approach directly integrates inventory prediction and routing optimization within an end-to-end system. Mathematical formulations exhibit promise in effectively addressing uncertainties and accurately predicting inventory levels, potentially influencing global supply chain systems significantly.

Architecture

Formulation.

The inventory routing problem integrates inventory management and vehicle routing decisions, improving supply chain solutions by jointly addressing inventory levels and customer delivery routing. Various approaches, including branch and cut, genetic algorithms, and heuristics/meta-heuristics, aim to find optimal or near-optimal solutions in most models. In the dynamic business environment, where demand fluctuations significantly affect overall profit, few models focus on integrating demand prediction with optimal decision-making. To address uncertainty, the problem is typically tackled using a two-stage method. In the first stage, demand prediction is performed, and in the second stage, the predicted value is used in an optimization algorithm to make decisions. But enhancing prediction accuracy doesn’t always guarantee optimal decision-making. Moreover, in the dynamic business landscape, improving accuracy can be challenging, often resulting in sub-optimal decisions. Decision-focused learning (DFL) takes a unique approach by not segregating predictive modeling and optimization. Instead, it integrates them by connecting the machine learning model directly to decision quality. In DFL, the loss function relies on the solution of an optimization model, effectively embedding the optimization solver as part of the machine learning model, leading to more effective decision-making.

Model.

Discussion

In our paper, we introduce a novel idea to tackle the intricate Inventory Routing Problems (IRP) using decision-focused learning.Our experiments highlight a critical insight: simply increasing model accuracy doesn’t guarantee improved profitability or optimal decisions. This discovery has motivated us to embrace a decision-focused perspective. However, challenges emerge when calculating gradients for optimal solutions with respect to model parameters. To address this, we’ve introduced the concept of regularizers and logarithmic barriers. Traditional regularization demonstrates promise in smoothing the objective function, while the logarithmic barrier method proves useful for managing constraints. It’s essential to recognize that IRPs are NP-hard and become particularly computationally demanding at a large scale. Finding optimal decisions through objective function differentiation can be counterproductive if the methodology isn’t chosen wisely for objective function transformation. In the realm of IRP, the logarithmic barrier method stands out as a robust choice for efficiently handling capacity constraints. However, to smoothen the objective and ensure differentiability for gradientbased optimization, regularization may be the more suitable path. Further research is imperative to determine the most effective approach among these two or any hybridized method for integrating decisions and predictions into a single model, ensuring the optimal selection of inventory and routing for establishing a resilient supply chain strategy.

BibTeX


      # Preferred
      @inproceedings{
        islam2023optimizing,
        title={Optimizing Inventory Routing: A Decision-Focused Learning Approach using Neural Networks},
        author={MD Shafikul Islam and Azmine Toushik Wasi},
        booktitle={New in Machine Learning Workshop, NeurIPS 2023},
        year={2023},
        url={https://openreview.net/forum?id=r0fzjB8f7f}
      }
  
  
    
      @article{
        islam2023optimizing,
        title={Optimizing Inventory Routing: A Decision-Focused Learning Approach using Neural Networks}, 
        author={MD Shafikul Islam and Azmine Toushik Wasi},
        year={2023},
        eprint={2311.00983},
        archivePrefix={arXiv},
        primaryClass={cs.LG}
      }