# Combining Parcel Lockers with Staffed Collection and Delivery Points: An Optimization Case Study Using Real Parcel Delivery Data (London, UK)

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## Abstract

**:**

## 1. Introduction

- (1)
- The paper differentiates from previous research publications as it uses real parcel delivery data collected for every day over one year as opposed to probabilistic scenarios.
- (2)
- The paper evaluates the variability and inhomogeneity of parcel deliveries over one year. This is especially relevant for researchers who are doing stochastic optimization.
- (3)
- The paper also differs from previous studies as it compares modular lockers (i.e., lockers adjusted once per month depending on the demand) with combining fixed lockers and staffed CDPs. Modular lockers have been proposed as a solution to the inhomogeneous demand [25,26]. Combining fixed lockers with staffed CDPs enables advantage to be taken of the low cost per parcel for lockers and low investment costs of staffed CDPs. It is assumed that parcels are placed in fixed lockers and undeliverable parcels due to insufficient locker space are placed in staffed CDPs. Both are at the same place.
- (4)
- The paper applies the decision support method to determine the optimal number of parcels being delivered to a parcel locker, while the remaining parcels are delivered to a staffed CDP if the number of lockers is insufficient. Given that parcel lockers and staffed CDPs require financial investments at different time points (e.g., high initial investment for parcel lockers and low investment for staffed CDPs), the decision support method considers the net present value (NPV) of the investment. The decision support method can be applied to any delivery trip data set, like the one used in this study.

## 2. Literature

## 3. Materials and Methods

#### 3.1. Dataset

- ${n}_{{p}_{CDP}{}_{d}}$: Number of parcels delivered to or already in a specific CDP on day d
- ${n}_{{d}_{CDP}{}_{d}}$: Number of successful parcel deliveries on day d
- ${n}_{{r}_{CDP}{}_{d+1}}$: Number of pickups by a delivery driver on the following day (i.e., parcels returned by customer)
- ${n}_{{f}_{CDP}{}_{d-1}}$: Number of parcels not picked up by customers on the previous day.

#### 3.2. NPV/Investment

- ${c}_{{L}_{NPV}}$: Cost per locker in today’s value
- ${c}_{{L}_{i}}$: Initial investment to set up one parcel locker
- ${C}_{{C}_{i}}$: Initial investment to set up one computer at a CDP
- ${n}_{c}$: Number of lockers per computer
- ${c}_{{L}_{o}}$: Yearly operating cost (e.g., land rent, maintenance, and driver training) per locker
- $T$: Number of years
- $t$: Year.

- ${c}_{{S}_{NPV}}$: Cost to send one parcel to a staffed CDP in today’s monetary value
- ${c}_{S}$: Cost to send one parcel to a staffed CDP
- $T$: Number of years considered in the study
- $r$: Increase in the fees paid to staffed CDP (0%)
- $t$: Year.

#### 3.3. Optimized Number of Lockers at Each Staffed CDP

- ${c}_{{L}_{NPV}}$: Cost per locker in today’s value
- ${c}_{{S}_{NPV}}$: Cost to send one parcel to a staffed CDP in today’s monetary value
- ${n}_{s}$: Number of parcels sent to a staffed CDP per year
- $D$: Number of days in a year
- ${n}_{CDP}$: Number of CDPs
- ${n}_{{p}_{CDP}{}_{d}}$: Number of parcels delivered to or are already in a specific CDP on day d
- ${n}_{{L}_{CDP}}$: Number of lockers at a specific CDP

- ${c}_{{L}_{NPV}}$: Cost per locker in today’s value
- ${c}_{{S}_{NPV}}$: Cost to send one parcel to a staffed CDP in today’s monetary value
- ${n}_{s}$: Number of parcels sent to a staffed CDP per year
- $D$: Number of days in a year
- ${n}_{CDP}$: Number of CDPs
- ${n}_{{p}_{CDP}{}_{d}}$: Number of parcels delivered to or are already in a specific CDP on day d
- ${n}_{{L}_{CDP}}$: Number of lockers at a specific CDP.

## 4. Results

#### 4.1. Number of Locker Spaces Required per Day

#### 4.2. Total Number of Locker Spaces

#### 4.3. Optimal Number of Lockers

#### 4.4. Example Calculation

#### 4.5. Modular Lockers vs. Fixed Lockers

## 5. Suggestions for Future Work and Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Comparison of the maximum number of locker spaces per month between all parcels picked up and 30% of parcels not picked up (Density 1.0).

**Figure 5.**Comparison of the mean number of locker spaces per month between all parcels picked up and 30% of parcels not picked up (Density 1.0).

**Figure 8.**Percentage of parcels that could not be delivered per year due to a lack of locker availability if the number of parcel lockers is equal to the 80-percentile, 90-percentile, etc. (Density 1.0).

**Figure 10.**Optimal number of lockers depending on the costs and variation in the demand for parcel lockers (512 CDPs).

**Figure 11.**Comparison of the average utilization of fixed lockers with modular lockers, which are adjusted in the beginning of each month.

Modular Locker | Fixed Locker & Staffed CDP | |
---|---|---|

Number of lockers | High demand season | Medium demand season |

Land rent at CDP | More or similar to medium demand depending on season | Medium demand season |

Locker storage space | During low demand season | N/A |

Transport of lockers | E.g., monthly adjustments | N/A |

Fee for staffed CDP | N/A | Ca. £0.50 per parcel [18] |

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**MDPI and ACS Style**

Schnieder, M.; Hinde, C.; West, A.
Combining Parcel Lockers with Staffed Collection and Delivery Points: An Optimization Case Study Using Real Parcel Delivery Data (London, UK). *J. Open Innov. Technol. Mark. Complex.* **2021**, *7*, 183.
https://doi.org/10.3390/joitmc7030183

**AMA Style**

Schnieder M, Hinde C, West A.
Combining Parcel Lockers with Staffed Collection and Delivery Points: An Optimization Case Study Using Real Parcel Delivery Data (London, UK). *Journal of Open Innovation: Technology, Market, and Complexity*. 2021; 7(3):183.
https://doi.org/10.3390/joitmc7030183

**Chicago/Turabian Style**

Schnieder, Maren, Chris Hinde, and Andrew West.
2021. "Combining Parcel Lockers with Staffed Collection and Delivery Points: An Optimization Case Study Using Real Parcel Delivery Data (London, UK)" *Journal of Open Innovation: Technology, Market, and Complexity* 7, no. 3: 183.
https://doi.org/10.3390/joitmc7030183