On the Entropy in Last-Mile Logistics

Berry Gerrits; Wouter van Heeswijk

arxiv: 2605.00008 · v1 · submitted 2026-02-26 · 🧮 math.OC · cs.IT· math.IT

On the Entropy in Last-Mile Logistics

Berry Gerrits , Wouter van Heeswijk This is my paper

Pith reviewed 2026-05-15 19:03 UTC · model grok-4.3

classification 🧮 math.OC cs.ITmath.IT

keywords last-mile logisticsstructural entropyBoltzmann entropyroute fragmentationspatial consolidationtemporal consolidationsystem entropyShannon duality

0 comments

The pith

Structural entropy quantifies last-mile fragmentation, showing spatial consolidation increases total system entropy in practice.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes structural entropy, calculated from the number of possible delivery route configurations, as a measure of last-mile logistics complexity. Analysis of over six thousand Amazon routes reveals high entropy levels indicating near-maximal fragmentation. It establishes that ideal spatial consolidation would conserve total entropy by redistributing it from carriers to customers, but real conditions violate this and raise overall entropy. Temporal consolidation reduces entropy without creating new movements. This approach offers a new way to diagnose and optimize logistics systems beyond traditional metrics.

Core claim

We introduce structural entropy from Boltzmann's statistical mechanics to measure the cardinality of the last-mile route configuration space. Data from 6,112 Amazon routes show persistently high normalized entropy. We prove a conservation principle under idealized conditions where spatial consolidation redistributes entropy from carrier to customer without changing the total. In practice, the idealizing conditions fail and total system entropy rises. Temporal consolidation reduces entropy by lowering the number of delivery events.

What carries the argument

The structural entropy of the route configuration space, defined via Boltzmann statistics and dual to Shannon entropy, which quantifies fragmentation and operational difficulty.

If this is right

Current operations exhibit near-maximal fragmentation as indicated by high normalized entropy values.
Entropy scales non-linearly with route distance, serving as a predictor of operational difficulty.
Aggressive spatial consolidation can cut carrier entropy by up to 40 percent but raises total system entropy due to customer trips.
Trip chaining by customers can mitigate the entropy increase from spatial consolidation.
Temporal consolidation reduces system entropy by decreasing the frequency of delivery events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This entropy view suggests that last-mile optimization should aim to minimize configuration space size rather than just total distance.
The framework could be extended to model stochastic elements like variable customer availability as additional entropy sources.
Policymakers might use system-wide entropy to evaluate the net impact of consolidation strategies including customer behavior.
If the metric correlates with real costs, it could inform dynamic routing algorithms that target lower entropy configurations.

Load-bearing premise

The configuration space of last-mile routes can be meaningfully defined and its cardinality calculated using Boltzmann's statistical mechanics to correspond directly to operational difficulty.

What would settle it

Collecting data on the actual number of distinct feasible route configurations for sample delivery sets and checking whether the logarithm of that number matches the structural entropy values computed by the framework; mismatch would falsify the measure.

Figures

Figures reproduced from arXiv: 2605.00008 by Berry Gerrits, Wouter van Heeswijk.

**Figure 2.** Figure 2: Temporal consolidation through some-day delivery. System entropy is reduced as fewer transport movements are needed for the same deliveries. 2.4 Generalized Entropy under Delivery Heterogeneity We now extend the entropy definition to accommodate heterogeneous delivery mechanisms frequently observed in last-mile logistics, including failed deliveries, pickup point restrictions, direct-to-pickup flows, and c… view at source ↗

**Figure 3.** Figure 3: Distribution of Structural (Boltzmann) and Shannon entropy across routes. Table 1 [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

**Figure 4.** Figure 4: Empirical validation of the entropy-distance scaling relationship across 6,112 Amazo [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗

read the original abstract

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces structural entropy from Boltzmann stats as a new diagnostic for last-mile fragmentation and tests it on real Amazon routes, but the config-space definition stays underspecified.

read the letter

The main thing here is a new metric for last-mile complexity that treats route options as a configuration space and borrows S = k ln W from statistical mechanics. They apply it to 6112 Amazon routes in five cities, report persistently high normalized entropy, and claim a non-linear link to route distance that they treat as validation. They also build a system-wide version that includes customer movements and argue that under ideal conditions spatial consolidation just shifts entropy from carriers to customers without changing the total, while temporal consolidation actually lowers it. The data application and the conservation idea are the clearest additions over standard distance or cost KPIs. The framework is applied at scale and produces concrete numbers like a 40% carrier entropy drop under aggressive consolidation. That part is useful for anyone thinking about network design or policy. The soft spot is the missing step on how W is actually counted. Customer locations are continuous, yet the paper gives no discretization rule, no enumeration procedure for feasible routes, and no derivation showing why ln W tracks operational difficulty rather than just counting combinations. Without that, the duality with Shannon entropy and the redistribution claim rest on an assumption that is not shown to hold. The non-linear scaling fit also risks being post-hoc on the same data. The work is aimed at researchers and planners working on last-mile consolidation and optimization. It deserves peer review because the core idea is new and the empirical application is concrete, even though the mathematical grounding needs tightening before the conservation principle can be taken as established.

Referee Report

3 major / 2 minor

Summary. The paper introduces a structural entropy framework derived from Boltzmann statistical mechanics to quantify fragmentation and complexity in last-mile logistics, establishes a formal duality with Shannon entropy, applies the metric to 6,112 Amazon routes across five U.S. cities, identifies a non-linear entropy-distance scaling, and develops a system-wide entropy measure to analyze spatial and temporal consolidation effects, including a theoretical conservation principle that spatial consolidation redistributes entropy under idealized conditions but increases total system entropy in practice.

Significance. If the configuration-space definition and derivations can be made rigorous, the entropy measure could provide a new diagnostic for inherent system disorder beyond distance or cost KPIs and guide consolidation policy evaluation.

major comments (3)

[theoretical framework (structural entropy definition)] Definition of structural entropy: the cardinality W of the last-mile route configuration space is invoked via S = k ln W without an explicit discretization rule for continuous customer locations, enumeration procedure for feasible routes, or derivation showing why ln W maps to operational difficulty; this is load-bearing for the claimed duality with Shannon entropy and the redistribution principle.
[empirical application and scaling relationship] Non-linear scaling validation: the stable non-linear relationship between entropy and route distance is presented as validating the metric as a predictive indicator, yet the coefficients appear fitted to the same 6,112-route dataset, reducing the claim to a post-hoc fit by the paper's own description and undermining the predictive status.
[system-wide entropy and consolidation analysis] Conservation principle: the idealizing conditions under which spatial consolidation merely redistributes entropy from carrier to customer (with total system entropy conserved) are stated but lack explicit mathematical derivation or precise statement of when they are violated, so the conclusion that practice increases total entropy cannot be assessed.

minor comments (2)

[empirical results] Data processing details (exclusion criteria, normalization procedure, error bars on entropy values) are not reported for the 6,112 routes, reducing reproducibility of the high normalized entropy finding.
[system-wide measure] Notation for the system-wide entropy measure and its decomposition into carrier and customer components should be introduced with an equation to clarify the accounting for all movements.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which identify important areas for strengthening the theoretical foundations and empirical claims. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: Definition of structural entropy: the cardinality W of the last-mile route configuration space is invoked via S = k ln W without an explicit discretization rule for continuous customer locations, enumeration procedure for feasible routes, or derivation showing why ln W maps to operational difficulty; this is load-bearing for the claimed duality with Shannon entropy and the redistribution principle.

Authors: We agree that the definition requires greater rigor. In the revised manuscript we will add an explicit discretization rule that partitions the service region into a uniform grid of resolution δ (calibrated to average inter-stop distance), define W as the cardinality of feasible route sequences respecting vehicle capacity and time windows on this grid, and supply a dynamic-programming bound for enumeration. We will also derive the operational interpretation by showing that ln W equals the log of the number of distinct routing decisions a planner must consider, thereby grounding the duality with Shannon entropy (recovered when the distribution over configurations is uniform) and the redistribution principle. revision: yes
Referee: Non-linear scaling validation: the stable non-linear relationship between entropy and route distance is presented as validating the metric as a predictive indicator, yet the coefficients appear fitted to the same 6,112-route dataset, reducing the claim to a post-hoc fit by the paper's own description and undermining the predictive status.

Authors: The referee correctly notes that the scaling coefficients were estimated on the full dataset. We will revise the text to describe the relationship as a robust, cross-city empirical scaling law rather than a predictive model. We will explicitly acknowledge the post-hoc character of the fit and add a sentence noting that out-of-sample validation on additional routes remains future work. The observed stability across five cities nevertheless supports the metric’s usefulness as a diagnostic indicator. revision: partial
Referee: Conservation principle: the idealizing conditions under which spatial consolidation merely redistributes entropy from carrier to customer (with total system entropy conserved) are stated but lack explicit mathematical derivation or precise statement of when they are violated, so the conclusion that practice increases total entropy cannot be assessed.

Authors: We accept that the conservation principle needs an explicit derivation. The revision will state the three idealizing assumptions—(i) fixed total number of movements, (ii) no activation of new customer collection trips, and (iii) additive entropy across carrier and customer subsystems—and prove that under these conditions S_total = S_carrier + S_customer is invariant while entropy is merely redistributed. We will then enumerate the practical violations (primarily the induction of customer trips) and show, using the system-wide measure, how these violations produce a net entropy increase. This material will appear in a new subsection. revision: yes

Circularity Check

1 steps flagged

Non-linear entropy-distance scaling presented as validation reduces to fit on same dataset

specific steps

fitted input called prediction [Abstract]
"A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty."

Entropy is computed directly on the 6,112 routes; the reported scaling with distance is therefore an empirical relationship extracted from that same collection. Labeling the observed (and likely parameterized) scaling as external validation of the entropy metric's predictive power makes the claim tautological rather than an independent test.

full rationale

The paper defines structural entropy via Boltzmann S = k ln W on last-mile route configurations and applies it to 6,112 Amazon routes. It then reports a stable non-linear scaling between this entropy and route distance on the identical data, claiming this 'validates the metric as a predictive indicator of operational difficulty.' This step matches the fitted-input-called-prediction pattern: the scaling relationship is observed and parameterized from the same empirical instances used to compute and apply the entropy values, rendering the validation non-independent. The conservation principle and duality claims rest on the initial W definition but do not exhibit further self-reduction in the provided text; the primary circularity is localized to the validation claim.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim rests on an analogy from statistical mechanics to logistics configuration spaces without independent prior validation, introduces structural entropy as a new entity, and relies on an empirical scaling relationship whose parameters appear fitted to the study data.

free parameters (1)

coefficients in non-linear entropy-distance scaling
Stable non-linear scaling relationship is used to validate the metric as predictive, implying fitted parameters from the 6112-route dataset.

axioms (2)

domain assumption Boltzmann's statistical mechanics can be applied to define the cardinality of last-mile route configuration spaces
Framework is derived from Boltzmann's statistical mechanics as stated in the abstract.
domain assumption A formal duality exists between structural entropy and Shannon entropy linking complexity burden to distributional balance
Established in the abstract as part of the framework.

invented entities (2)

structural entropy no independent evidence
purpose: Quantifies cardinality of the configuration space as a diagnostic of inherent system disorder in LML
New metric introduced to replace or augment traditional KPIs.
system-wide entropy measure no independent evidence
purpose: Accounts for all movements by carriers and customers to evaluate spatial consolidation effects
Developed in the paper to reveal total system entropy changes.

pith-pipeline@v0.9.0 · 5571 in / 1721 out tokens · 84609 ms · 2026-05-15T19:03:11.392756+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We adopt the Boltzmann definition of entropy to measure the number of ways a system’s states can be arranged... W = N! / ∏ p_k! ... G = ln(W) = ln(N!) − ∑ ln(p_k!).
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Under the symmetric conditions... G_delivery + G_customer = ln(N!) is invariant to the degree of spatial partitioning K (Proposition 2).

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

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Procedia Computer Science , volume=

Performance evaluation and explainability of last-mile delivery , author=. Procedia Computer Science , volume=. 2024 , publisher=

work page 2024
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Transportation Science , volume=

The delivery dispatching problem with time windows for urban consolidation centers , author=. Transportation Science , volume=. 2019 , publisher=

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1879 , address =

Clausius, Rudolf , title =. 1879 , address =

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Scientific Reports , volume =

Entropy and Order in Urban Street Networks , author =. Scientific Reports , volume =. 2013 , publisher =. doi:10.1038/srep03324 , url =

work page doi:10.1038/srep03324 2013
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Research in Transportation Business & Management , volume=

Last-mile logistics fulfilment: A framework for energy efficiency , author=. Research in Transportation Business & Management , volume=. 2020 , publisher=

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Operations Research , volume =

Maximum Entropy Utility , author =. Operations Research , volume =. 2006 , publisher =. doi:10.1287/opre.1050.0253 , url =

work page doi:10.1287/opre.1050.0253 2006
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Entropy , VOLUME =

Sharp, Kim and Matschinsky, Franz , TITLE =. Entropy , VOLUME =. 2015 , NUMBER =

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[8]

Proceedings of the 36th International Conference on Machine Learning , pages =

Understanding the Impact of Entropy on Policy Optimization , author =. Proceedings of the 36th International Conference on Machine Learning , pages =. 2019 , editor =

work page 2019
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MIT Sloan Management Review , volume=

Cutting Last-Mile Delivery Costs , author=. MIT Sloan Management Review , volume=. 2025 , publisher=

work page 2025
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Transportation Science , volume=

Evaluating urban logistics schemes using agent-based simulation , author=. Transportation Science , volume=. 2020 , publisher=

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Transportation Science , volume=

50th anniversary invited article—city logistics: Challenges and opportunities , author=. Transportation Science , volume=. 2016 , publisher=

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, title =

Shannon, Claude E. , title =. Bell System Technical Journal , volume =. 1948 , doi =

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2021 Amazon Last Mile Routing Research Challenge: Data Set , journal =

Merch. 2021 Amazon Last Mile Routing Research Challenge: Data Set , journal =. 2024 , doi =

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Facility Location Under Uncertainty: A Review , volume =

Snyder, Lawrence , year =. Facility Location Under Uncertainty: A Review , volume =. IIE Transactions , doi =

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and Hartl, R

Matl, P. and Hartl, R. F. and Vidal, T. , title =. Transportation Science , volume =. 2017 , publisher=

work page 2017
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Transportation Research Part A: Policy and Practice , volume=

Investigating the theoretical cost-relationships of urban consolidation centres for their users , author=. Transportation Research Part A: Policy and Practice , volume=. 2017 , publisher=

work page 2017
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What is Freight Consolidation? , year =

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Transportation Research , volume=

A statistical theory of spatial distribution models , author=. Transportation Research , volume=. 1967 , publisher=

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Logistics Research , volume=

Toward a Physical Internet , author=. Logistics Research , volume=. 2011 , publisher=

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2014 , publisher=

Vehicle routing: Problems, methods, and applications , author=. 2014 , publisher=

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Sustainability , VOLUME =

Zennaro, Ilenia and Finco, Serena and Calzavara, Martina and Persona, Alessandro , TITLE =. Sustainability , VOLUME =. 2022 , NUMBER =

work page 2022
[22]

International Journal of Physical Distribution & Logistics Management , volume =

Mangiaracina, Riccardo and Perego, Alessandro and Seghezzi, Arianna and Tumino, Angela , title =. International Journal of Physical Distribution & Logistics Management , volume =. 2019 , month =. doi:10.1108/IJPDLM-02-2019-0048 , url =

work page doi:10.1108/ijpdlm-02-2019-0048 2019
[23]

The International Journal of Logistics Management , volume=

An innovation diffusion perspective of e-consumers’ initial adoption of self-collection service via automated parcel station , author=. The International Journal of Logistics Management , volume=. 2018 , publisher=

work page 2018
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Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review , journal =

Vega-Mej. Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review , journal =. 2019 , doi =

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Causal Discovery in Multi-Echelon Supply Networks: Leveraging Foundation Models for Demand Propagation Analysis , volume =

Anderson, Michael and Müller, Anna , year =. Causal Discovery in Multi-Echelon Supply Networks: Leveraging Foundation Models for Demand Propagation Analysis , volume =. Frontiers in Applied Physics and Mathematics , doi =

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Cunha , keywords =

Julia Coutinho Amaral and Claudio B. Cunha , keywords =. An exploratory evaluation of urban street networks for last mile distribution , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.cities.2020.102916 , url =

work page doi:10.1016/j.cities.2020.102916 2020

[1] [1]

Procedia Computer Science , volume=

Performance evaluation and explainability of last-mile delivery , author=. Procedia Computer Science , volume=. 2024 , publisher=

work page 2024

[2] [2]

Transportation Science , volume=

The delivery dispatching problem with time windows for urban consolidation centers , author=. Transportation Science , volume=. 2019 , publisher=

work page 2019

[3] [3]

1879 , address =

Clausius, Rudolf , title =. 1879 , address =

work page

[4] [4]

Scientific Reports , volume =

Entropy and Order in Urban Street Networks , author =. Scientific Reports , volume =. 2013 , publisher =. doi:10.1038/srep03324 , url =

work page doi:10.1038/srep03324 2013

[5] [5]

Research in Transportation Business & Management , volume=

Last-mile logistics fulfilment: A framework for energy efficiency , author=. Research in Transportation Business & Management , volume=. 2020 , publisher=

work page 2020

[6] [6]

Operations Research , volume =

Maximum Entropy Utility , author =. Operations Research , volume =. 2006 , publisher =. doi:10.1287/opre.1050.0253 , url =

work page doi:10.1287/opre.1050.0253 2006

[7] [7]

Entropy , VOLUME =

Sharp, Kim and Matschinsky, Franz , TITLE =. Entropy , VOLUME =. 2015 , NUMBER =

work page 2015

[8] [8]

Proceedings of the 36th International Conference on Machine Learning , pages =

Understanding the Impact of Entropy on Policy Optimization , author =. Proceedings of the 36th International Conference on Machine Learning , pages =. 2019 , editor =

work page 2019

[9] [9]

MIT Sloan Management Review , volume=

Cutting Last-Mile Delivery Costs , author=. MIT Sloan Management Review , volume=. 2025 , publisher=

work page 2025

[10] [10]

Transportation Science , volume=

Evaluating urban logistics schemes using agent-based simulation , author=. Transportation Science , volume=. 2020 , publisher=

work page 2020

[11] [11]

Transportation Science , volume=

50th anniversary invited article—city logistics: Challenges and opportunities , author=. Transportation Science , volume=. 2016 , publisher=

work page 2016

[12] [12]

, title =

Shannon, Claude E. , title =. Bell System Technical Journal , volume =. 1948 , doi =

work page 1948

[13] [13]

2021 Amazon Last Mile Routing Research Challenge: Data Set , journal =

Merch. 2021 Amazon Last Mile Routing Research Challenge: Data Set , journal =. 2024 , doi =

work page 2021

[14] [14]

Facility Location Under Uncertainty: A Review , volume =

Snyder, Lawrence , year =. Facility Location Under Uncertainty: A Review , volume =. IIE Transactions , doi =

work page

[15] [15]

and Hartl, R

Matl, P. and Hartl, R. F. and Vidal, T. , title =. Transportation Science , volume =. 2017 , publisher=

work page 2017

[16] [16]

Transportation Research Part A: Policy and Practice , volume=

Investigating the theoretical cost-relationships of urban consolidation centres for their users , author=. Transportation Research Part A: Policy and Practice , volume=. 2017 , publisher=

work page 2017

[17] [17]

What is Freight Consolidation? , year =

work page

[18] [18]

Transportation Research , volume=

A statistical theory of spatial distribution models , author=. Transportation Research , volume=. 1967 , publisher=

work page 1967

[19] [19]

Logistics Research , volume=

Toward a Physical Internet , author=. Logistics Research , volume=. 2011 , publisher=

work page 2011

[20] [20]

2014 , publisher=

Vehicle routing: Problems, methods, and applications , author=. 2014 , publisher=

work page 2014

[21] [21]

Sustainability , VOLUME =

Zennaro, Ilenia and Finco, Serena and Calzavara, Martina and Persona, Alessandro , TITLE =. Sustainability , VOLUME =. 2022 , NUMBER =

work page 2022

[22] [22]

International Journal of Physical Distribution & Logistics Management , volume =

Mangiaracina, Riccardo and Perego, Alessandro and Seghezzi, Arianna and Tumino, Angela , title =. International Journal of Physical Distribution & Logistics Management , volume =. 2019 , month =. doi:10.1108/IJPDLM-02-2019-0048 , url =

work page doi:10.1108/ijpdlm-02-2019-0048 2019

[23] [23]

The International Journal of Logistics Management , volume=

An innovation diffusion perspective of e-consumers’ initial adoption of self-collection service via automated parcel station , author=. The International Journal of Logistics Management , volume=. 2018 , publisher=

work page 2018

[24] [24]

Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review , journal =

Vega-Mej. Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review , journal =. 2019 , doi =

work page 2019

[25] [25]

Causal Discovery in Multi-Echelon Supply Networks: Leveraging Foundation Models for Demand Propagation Analysis , volume =

Anderson, Michael and Müller, Anna , year =. Causal Discovery in Multi-Echelon Supply Networks: Leveraging Foundation Models for Demand Propagation Analysis , volume =. Frontiers in Applied Physics and Mathematics , doi =

work page

[26] [26]

Cunha , keywords =

Julia Coutinho Amaral and Claudio B. Cunha , keywords =. An exploratory evaluation of urban street networks for last mile distribution , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.cities.2020.102916 , url =

work page doi:10.1016/j.cities.2020.102916 2020