# Addressing the Location Problem of a Perishables Redistribution Center in the Middle of Europe

^{*}

## Abstract

**:**

## 1. Introduction

- Certain merchandise can be returned to the supplier for a variety of reasons. The said products could then be repackaged and served again to customers. In other words, the consolidation center would receive the defective produce (e.g., packaging in poor condition) so it may be reutilized. Alternatively, the products would be disposed of due to the impossibility of returning them to the place of origin. It is estimated that 10% of exports are returned by customers due to minor defects [23]. The said reason can be framed within reverse logistics, an area which has attracted considerable attention over the past decade (see, e.g., [24]). In economic terms, for the southeast of Spain, this represents more than 550 million euros of losses for exporters.
- In the case of the previous strategy, the response time for customers would be reduced, as a portion of the repackaged produce would be served from the redistribution center rather than from the place of origin. In other words, a product that would otherwise be wasted could be sold again.
- It is important for suppliers to maintain a strategy of fast and flexible service [23]. Thus, suppliers could store produce in advance, close to the final demand and based on their estimates to serve customers throughout Europe as they receive orders. As a result, response times to customers’ orders (transit times) would be reduced by separating, albeit by a few days, transportation to the logistics center and the final shipment to the customer. Consequently, both service and customer loyalty would be improved by optimizing the cross-docking process. In the context of this strategy, supply time and its adaptation to demand would be a critical point to consider as we deal with products not apt for long storage periods [25]. This strategy would also have positive consequences on the reduction of waste both in storage centers at the place of origin and at retail points of sale (by increasing their shelf life).
- Existence of a key customer (modern distributor, e.g., Aldi or Lidl) with points of sale throughout Europe that would want to have a distribution center supplied by a priority place of origin (southeast Spain in our case). This strategy would be framed within an intensive supplier–customer collaboration in an ad hoc supply chain [26] that is easier to implement than the previous strategy (which assumes the existence of multiple customers and a more difficult demand to anticipate).
- At present, most shipping is organized by customers. This system would thus constitute a proactive strategy by suppliers, generating more stable relationships with customers.
- Improved capacity to attract more small retailers that require a more continuous service.

_{1}would be located in France near Toulouse–Montpelier–Marseille, and if only the customers’ locations are considered, GC

_{2}would be near Cologne. Currently, 98% of the shipping is carried out by means of refrigerated trucks using logistics-based multi-stop truckload shipping. This aspect is relevant because the customer (modern large distribution company) has included the European transport strategy [28] in its plans to promote the use of intermodality and reduce the environmental impact of transport [29]. For this reason, this article, after analyzing the optimal locations of redistribution centers, studied the possibility of supplying them through an intermodal option. With this aim, the multicriteria optimization [30,31] was introduced in the P-M and P-C methodology, utilizing transit time and shipping costs as decision variables.

## 2. Materials and Methods

_{ij}is 1 if customer i is served by facility j, 0—if not; h

_{i}is the demand at location i; d

_{ij}is the distance from location i to location j; p is the number of facilities to be located. The objective function (1) minimizes the demand-weighted distance between each demand node and the nearest facility. X

_{j}is 1 if a facility is located at candidate site j, 0—if not.

_{i}and Y

_{ij}have Boolean values of 0 or 1.

_{i}that is served by facility j is A

_{j}h

_{i}:

_{ij}is the utility of a facility located at node j for a customer originating at node i. The model assumes that ${u}_{ij}={\alpha}_{j}{d}_{ij}^{-\lambda},$ where ${\alpha}_{j}$ denotes the attractiveness of facility j for customer i and λ denotes the parameter of the exponential distance decay function. In this case, α

_{ij}= 1 was utilized (common in the literature) as we dealt with a centralized scheme in which customers do not decide on the location. In other words, the utility measure decreases with distance and increases the attractiveness of a facility. The larger the value of lambda, the more attached the customer is to the nearest facility. In our case, we utilized λ = 0.6 to prioritize facilities near the customers as we dealt with highly perishable products. In practical terms, priority is given to the most centrally located points.

_{j}introduced into the gravity p-median model in such a way that ${A}_{i}=\frac{{h}_{ij}^{p}}{{h}_{ij}}$, where ${h}_{i}^{p}$ is the forecast long-term demand for each of the customers. Thus, the objective function in the p-median is not $Min\text{}{{\displaystyle \sum}}_{i}{{\displaystyle \sum}}_{j}{h}_{i}{A}_{i}{d}_{ij}{Y}_{ij}$ = $Min\text{}{{\displaystyle \sum}}_{i}{{\displaystyle \sum}}_{j}{h}_{i}^{p\text{}}{d}_{ij}{Y}_{ij}$.

#### 2.1. Random Distances

^{R}and P-C

^{R}). This adjustment offered flexibility to the decision on whether to use country capitals as destination points. The new distance utilized was $d{\left(\xi \right)}_{ij}$, where ${\xi}_{ij}$ is the uncertain degree of the distance between i and j.

_{ij}and deviation (σ) to be equal to the existing distance between the capital and the second most populated city in the country: for example, in France, the distance between Paris and Marseilles; or between Berlin and Hamburg in Germany. Distances $d{\left(\xi \right)}_{ij}$ between the place of origin and the rest of the j destinations are displayed in Appendix A.

#### 2.2. Multicriteria Optimization within the P-M and P-C Problems

^{th}objective (real value). Therefore, the problem that arises from a practical point of view is:

_{ij}is the transport cost (€/kg) from location i to location j;

_{ij}is the time (hours) to transport goods from location i to location j.

## 3. Results and Discussion

^{R}model was utilized considering p = 3, the optimal locations were the original ones (Figure 7a): place of origin, Brussels, and Berlin. Furthermore, the robustness of the results is also revealed by considering random deviations at the unloading points. However, the total weighted distance would increase due to the use of new distances that include possible deviations (specifically, 11%). The random P-C

^{R}model for p = 3 (Figure 7b) underwent modifications with respect to the original. When including possible deviations, the total weighted distance would increase by 21% compared to the result calculated with deterministic distances. In general, the random models incorporate, with respect to the original ones, the uncertainty at unloading points (even including changes once the shipment process has started), an aspect that may greatly influence decision-making when choosing redistribution centers.

#### Intermodal Option

_{2}emissions, especially in the case of perishables [44].

_{2}reduction. In any case, the use of specific lines for the transport of perishables could reduce the transit times of SSS and rail freight by more than 50%, although today this option, in the case of trains, is unrealistic [45].

## 4. Conclusions

_{2}emissions, it would increase the chances of having a disposable product at destination. In any case, the creation of redistribution centers could favor the transport mode change, provided that ad hoc lines (much faster) are created. In addition, the use of intermodality will depend on the implementation of initiatives that foster a change in the perception of exporters (e.g., the poor image of SSS for door-to-door service) and favor willingness to utilize ships as a transport system (e.g., eradicate the lack of knowledge of this system among many exporters). At the same time, it would be necessary to improve the systems for preserving merchandise in order to avoid waste on ships and at cross-docking points.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Destination | d = from Southest Spain to: | Average Weighted (*) | d(ξ) = from Southest Spain to: |
---|---|---|---|

Berlin | 2403 | 726 | 2780 |

Paris | 1820 | 840 | 2828 |

London | 2221 | 900 | 2481 |

Amsterdam | 2210 | 729 | 2353 |

Warsaw | 3120 | 1191 | 3608 |

Rome | 2504 | 1580 | 3309 |

Stockholm | 3404 | 1567 | 3814 |

Prague | 2612 | 882 | 2879 |

Lisbon | 831 | 2481 | 636 |

Copenhagen | 2902 | 977 | 3145 |

Brussels | 2012 | 717 | 2090 |

Vienna | 2803 | 1095 | 2907 |

Helsinki | 4298 | 2162 | 4532 |

Bucharest | 3499 | 2050 | 4210 |

Bern | 1982 | 988 | 2021 |

Dublin | 2601 | 1474 | 2930 |

Budapest | 3006 | 1310 | 3305 |

Herend | 2268 | 1104 | 2639 |

Origin:Southest Spain | 2377 |

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**Figure 1.**The principal merchandise distribution strategies between suppliers and customers. Source: own elaboration.

**Figure 2.**Main customers of fruit and vegetable exportation from southeast Spain. Source: own elaboration.

**Figure 3.**Results of the p-median (maps

**a**–

**c**) and gravity p-median models (map

**d**). Lines: only samples of routes are shown. Each color represents customer allocation by the redistribution center. Source: own elaboration.

**Figure 5.**Results of the p-center model (p = 2 and p = 3). Lines: only samples of routes are shown. Each color represents the customer allocation by the redistribution center. Source: own elaboration.

**Figure 6.**Summary of results applying variations in demand to the gravity p-median (GP-M’), p-median (P-M’), and p-center models (P-C’) for p = 3. Source: own elaboration using the [1] data.

**Figure 7.**Results of the p-median (map

**a**) and p-center models (map

**b**) with random distances (p = 3). Lines: only samples of routes are shown. Each color represents the customer allocation by redistribution center. Source: own elaboration.

f_{1} | f_{2} | … | f_{n} | |

f_{1} | ${f}_{1}^{*}$ = f_{11} | f_{12} | ,,, | f_{1n} |

… | … | … | … | … |

f_{n} | f_{n1} | f_{n2} | … | f_{nn} |

**Table 2.**Examples of the results for intermodal transport for P-C2 (Figure 5, map 1).

SSS–Road | SSS, Southest Spain–Rotterdam | Road, Rotterdam–Brusells | Road, Brusells–End Clients | Total | % Variat. on the Road |

Km | 2740 | 143 | 545 | 3428 | 24 |

Time (h) (1) | 240 | 1.4 | 5.0 | 246 | 782 |

Time (h) (2) | 106 | 1.4 | 5.0 | 112 | 304 |

Cost (€/kg) (1) | 0.10 | 0.01 | 0.02 | 0.13 | –38 |

Cost (€/kg) (2) | 0.19 | 0.01 | 0.02 | 0.22 | 6 |

tCO^{2} (trip) | 1.10 | 0.23 | 0.87 | 2.20 | –50 |

Train–road | SSS, southest Spain–Rotterdam | Train, southest Spain–Brusells | Road, Brusells–end clients | Total | % variat. on the road |

Km | - | 1610 | 545 | 2155 | –22 |

Time (h) (1) | - | 240 | 5 | 245 | 775 |

Cost (€) (1) | - | 0.16 | 0.02 | 0.18 | –14 |

tCO^{2} (trip) | - | 1.61 | 0.87 | 2.48 | –44 |

Road | SSS, southest Spain–Rotterdam | Road, southest Spain–Brusells | Road, Brusells–end clients | Total | |

Km | - | 2210 | 545 | 2755 | - |

Time (h) | - | 23 | 5.0 | 28 | - |

Cost (€) (3) | - | 0.19 | 0.02 | 0.21 | - |

tCO^{2} (trip) | - | 3.53 | 0.87 | 4.41 | - |

Cost (€/kg) | Time (h) | |
---|---|---|

Cost (€/kg) | 0.13 * | 72 |

Time (h) | 0.21 | 28 * |

Values Tested in the Sensitivity Analysis | Importance the Decisionmaker Gives to the Variables Based on the Tested Values: | Real Results | Calculated Results | |||
---|---|---|---|---|---|---|

Cost (€/kg) | Time (h) | Weight (Cost) | Weight (Time) | Cost (€/kg) | Time (h) | With the p-Center Model (Two Facilities) |

0.13 | 72 | 100% | 0% | 0.13 | 72 | Brusells (I) |

0.15 | 60 | 87% | 13% | 0.13 | 72 | Brusells (I) |

0.16 | 52 | 81% | 19% | 0.21 | 28 | Brusells (T) |

0.17 | 45 | 52% | 48% | 0.21 | 28 | Brusells (T) |

0.19 | 35 | 23% | 77% | 0.21 | 28 | Brusells (T) |

0.21 | 28 | 0% | 100% | 0.21 | 28 | Brusells (T) |

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**MDPI and ACS Style**

Pérez-Mesa, J.C.; Serrano-Arcos, M.M.; Jiménez-Guerrero, J.F.; Sánchez-Fernández, R.
Addressing the Location Problem of a Perishables Redistribution Center in the Middle of Europe. *Foods* **2021**, *10*, 1091.
https://doi.org/10.3390/foods10051091

**AMA Style**

Pérez-Mesa JC, Serrano-Arcos MM, Jiménez-Guerrero JF, Sánchez-Fernández R.
Addressing the Location Problem of a Perishables Redistribution Center in the Middle of Europe. *Foods*. 2021; 10(5):1091.
https://doi.org/10.3390/foods10051091

**Chicago/Turabian Style**

Pérez-Mesa, Juan Carlos, M. Mar Serrano-Arcos, José Felipe Jiménez-Guerrero, and Raquel Sánchez-Fernández.
2021. "Addressing the Location Problem of a Perishables Redistribution Center in the Middle of Europe" *Foods* 10, no. 5: 1091.
https://doi.org/10.3390/foods10051091