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Forecasting the load of Parcel Pickup Points using a Markov Jump Process

Thi-Thu-Tam Nguyen, Adnane Cabani, Iyadh Cabani, Koen De Turck, Michel Kieffer

Abstract

The growth of e-commerce has resulted in a surge in parcel deliveries, increasing transportation costs and pollution issues. Alternatives to home delivery have emerged, such as the delivery to so-called parcel pick-up points (PUPs), which eliminates delivery failure due to customers not being at home. Nevertheless, parcels reaching overloaded PUPs may need to be redirected to alternative PUPs, sometimes far from the chosen ones, which may generate customer dissatisfaction. Consequently, predicting the PUP load is critical for a PUP management company to infer the availability of PUPs for future orders and better balance parcel flows between PUPs. This paper proposes a new approach to forecasting the PUP load evolution using a Markov jump process that models the parcel life cycle. The latest known status of each parcel is considered to estimate its contribution to the future load of its target PUP. This approach can account for the variability of activity, the various parcel preparation delays by sellers, and the diversity of parcel carriers that may result in different delivery delays. Here, results are provided for predicting the load associated with parcels ordered from online retailers by customers (Business-to-Customer, B2C). The proposed approach is generic and can also be applied to other parcel flows to PUPs, such as second-hand products (Customer-to-Customer, C2C) sent via a PUP network.

Forecasting the load of Parcel Pickup Points using a Markov Jump Process

Abstract

The growth of e-commerce has resulted in a surge in parcel deliveries, increasing transportation costs and pollution issues. Alternatives to home delivery have emerged, such as the delivery to so-called parcel pick-up points (PUPs), which eliminates delivery failure due to customers not being at home. Nevertheless, parcels reaching overloaded PUPs may need to be redirected to alternative PUPs, sometimes far from the chosen ones, which may generate customer dissatisfaction. Consequently, predicting the PUP load is critical for a PUP management company to infer the availability of PUPs for future orders and better balance parcel flows between PUPs. This paper proposes a new approach to forecasting the PUP load evolution using a Markov jump process that models the parcel life cycle. The latest known status of each parcel is considered to estimate its contribution to the future load of its target PUP. This approach can account for the variability of activity, the various parcel preparation delays by sellers, and the diversity of parcel carriers that may result in different delivery delays. Here, results are provided for predicting the load associated with parcels ordered from online retailers by customers (Business-to-Customer, B2C). The proposed approach is generic and can also be applied to other parcel flows to PUPs, such as second-hand products (Customer-to-Customer, C2C) sent via a PUP network.
Paper Structure (20 sections, 4 theorems, 60 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 20 sections, 4 theorems, 60 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem description
  4. Model of the life-cycle of a parcel
  5. Problem formulation
  6. Prediction of $L$
  7. Sets of parcels contributing to the load of the PUP
  8. Contribution to the load for each set of parcels
  9. Load prediction algorithm
  10. Application
  11. Model
  12. Estimation of the pmf $f_{n}$
  13. Prediction of the number of parcel orders
  14. Results
  15. Conclusion
  16. ...and 5 more sections

Key Result

Proposition 1

At time $k$, consider a parcel $\tau$ with current status $S_{k}=N-1$, i.e., that has been delivered at time $t_{N-1}\leqslant k$ and that has not yet been picked up time $k$. The pickup time $T_{N}$ depends on the delivery time $T_{N-1}$, and implicitly on the opening hours of the PUP $\rho$. The p

Figures (6)

  • Figure 1: Statuses and possible transitions between statuses for a parcel; From time $k$ to $k+1$, the parcel can stay in status $n$ or switch to the status $n+1$; When the status $N$ is reached (picked-up parcel), parcels stay in this status and do not contribute to the PUP load anymore.
  • Figure 2: Illustration of parcels contributing to the load $L$$\left(k+j\right)$ for a prediction performed at time $k$. One has to account for parcels delivered before time $k$ (cases 1 and 2) as well as parcels taken over by a carrier before time $k$ and not yet delivered (cases 3 and 4). Only parcels expected to be picked up after time $k+j$ will actually contribute to the load at time $k+j$ (cases 2 and 3). Products that are expected to be ordered between time $k$ and time $k+j$ (case 5) may also contribute to the load at time $k+j$.
  • Figure 3: Life-cycle of a parcel
  • Figure 4: Evolution of the load at 13:00 of the considered PUP from July 2017 to December 2019.
  • Figure 5: Predicted and actual value of $L\left(k+13\right)$ (top) and $L\left(k+37\right)$ (bottom) and prediction errors
  • ...and 1 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4