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An iterative sample scenario approach for the dynamic dispatch waves problem

Leon Lan, Jasper van Doorn, Niels A. Wouda, Arpan Rijal, Sandjai Bhulai

TL;DR

This paper proposes iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach that iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided and develops two variants of ICD: one variant based on thresholds, and another variant based on similarity.

Abstract

A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery, and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper, we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch, and how to route these dispatched requests. The operator's goal is to minimize the total routing cost while ensuring that all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration. We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. Finally, we demonstrate that the threshold-based ICD variant achieves excellent results on instances from the EURO meets NeurIPS 2022 vehicle routing competition, nearly matching the performance of the winning machine learning-based strategy.

An iterative sample scenario approach for the dynamic dispatch waves problem

TL;DR

This paper proposes iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach that iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided and develops two variants of ICD: one variant based on thresholds, and another variant based on similarity.

Abstract

A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery, and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper, we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch, and how to route these dispatched requests. The operator's goal is to minimize the total routing cost while ensuring that all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration. We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. Finally, we demonstrate that the threshold-based ICD variant achieves excellent results on instances from the EURO meets NeurIPS 2022 vehicle routing competition, nearly matching the performance of the winning machine learning-based strategy.
Paper Structure (37 sections, 2 theorems, 18 equations, 6 figures, 6 tables, 2 algorithms)

This paper contains 37 sections, 2 theorems, 18 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Problem description
  4. General outline
  5. Static vehicle routing problem with dispatch windows
  6. Markov decision process formulation
  7. State space
  8. Action space
  9. State transitions
  10. Optimality conditions
  11. The iterative conditional dispatch algorithm
  12. Step I: solving sample scenarios
  13. Step II: updating dispatch and postponement using consensus functions
  14. Threshold-based consensus.
  15. Similarity-based consensus.
  16. ...and 22 more sections

Key Result

Proposition 1

Let $\sigma = (\sigma_i, \dots, \sigma_j)$ and $\sigma^{\prime} = (\sigma^{\prime}_{i^\prime}, \dots, \sigma^{\prime}_{j^{\prime}})$ be two subsequences of visits. The concatenated subsequence $\sigma \oplus \sigma^{\prime}$ is characterized by the following data: where $\Delta=D(\sigma)-T W(\sigma)+\delta_{\sigma_j \sigma^{\prime}_{i^\prime}}, \Delta_{W T}=\max \left\{E\left(\sigma^{\prime}\righ

Figures (6)

  • Figure 1: The expected number of arrivals per epoch for the homogeneous (left) and unimodal (right) arrival processes.
  • Figure 2: Two dynamic instances with ten requests per epoch and maximum time window width of two. The left figure shows an instance with deadlines and the right figure shows an instance with regular time windows.
  • Figure 3: Average percentage gaps to the hindsight solution versus the solving time in seconds per scenario.
  • Figure 4: Average percentage gaps to the hindsight solution versus the number of iterations in the ICD method.
  • Figure 5: Results for the final 100 instances of the EURO-NeurIPS competition. The lines indicate the average percentage gap to the hindsight solution obtained by ICD-double for a given time limit (120, 180, or 600 seconds).
  • ...and 1 more figures

Theorems & Definitions (2)

  • Proposition 1: Concatenation of two sequences vidal2013hgs
  • Proposition 2: vidal2013hgs