# Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study

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## Abstract

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## 1. Introduction

## 2. Literature Review

- Gradual distribution (intermediate warehousing)—each stage represents placement of a product in a warehouse. It is a system in which warehouses are used to a maximum extent. Distribution centers completing sales requirements are typical examples of such a distribution.
- Direct delivery system—products are delivered to the point of consumption directly from one or more storage locations, or directly from the production factory. The supplier has at his disposal one central warehouse to which he collects individual consignments, and from which he also handles them. This system includes cross-dock operations as well, which are mainly applied to high-volume product flows towards the retail network. The distribution center is integrated directly into the chain segment between a larger number of suppliers on one side and a retail network on another. Deliveries from all suppliers are collected to this center, stored in appropriate warehouse departments, and completed (assembled) according to retail network requirements. Consequently, the delivery itself is usually carried out at an exact time.
- Combined systems—the combination of the previous two systems is most commonly used. It determines which products will be distributed directly and which through intermediate warehousing. These systems also make it possible to deliver supplies in an alternative way.
- Postponement strategies for final operations—modern distribution systems do not only wait for the final order, but are also based on forecasting. This is also related to the risk that actual orders will differ from those anticipated. If some production distribution operations can be postponed until a specific order arrives, this risk can be substantially reduced. The basis is to keep the products in the production process in the unfinished state for as long as possible and to make the final adjustment up to confirming the customer order. The main effect of this process is to reduce the product range in stock, minimize the risk of poor inventory location and make better utilization of storage capacity for completing operations [10].
- Coupling methods—these are carried out due to an effort to cut down shipping cost. The larger the shipment, the lower the shipping cost per unit. Coupling also improves shipping cost control.

- consistent operational management according to the current needs of the network and contracted transport volumes; i.e., exact transport requirements will be assigned to a road carrier in a short-term period, within a long-term contracted capacity;
- the principle of maximum utilization of road vehicles, which leads to maximum profitability of transport;
- providing transport services directly from home to home by the relevant regional road carrier, direct contact with the customer, delivery of shipment and shipping documents are highly desirable;
- effort to minimize handling cost to a maximum extent; i.e., using appropriate transshipment mechanisms in an LC, prompt cargo transshipment to the customer with respect to an option of using a vehicle for further carriage;
- distribution by railways only when delivering (or dispatching) to the recipient’s own siding or to public reloading tracks at the destination station, i.e., without reloading and other logistics operations in relevant LC.

- tracking shipments on international and domestic routes;
- monitoring of technological processes in the LC;
- monitoring of road vehicles during collection and distribution;
- checking the collection of load and transition between routes;
- operational planning of capacities, means of transport, routes and operation of LCs and the network as a whole;
- evidence of vehicles, wagons, containers and other means, tracking the movement of means of transport in LCs, in the network, to customers;
- addressing deviations from the plan and extraordinary traffic;
- service quality management, i.e., just-in-time delivery, timeliness delivery, accuracy, flexibility and reliability;
- providing transport and logistics services;
- dispatching management of the LC and the network as a whole.

## 3. Methodology of the Addressed Problem

#### 3.1. Research Methods

- equality of the number of rows and columns (symmetric distance matrix); if this condition is not met, it is necessary to add a fictitious row with prohibitive rates (when minimizing, values are to be higher than the highest value of the distance matrix, when maximizing, we assign the value of 0);
- the distance matrix must be quantifiable;
- suppliers’ capacities and customers’ requirements must be homogeneous (any customer can be served by any supplier).

- Step 1. Listing distances—compilation of the distance matrix.
- Step 2. Row reduction—select the lowest value in each row; this value is then subtracted in individual rows, and this step gives us the required zeros in each row. This step is not repeated in the calculation process.
- Step 3. Column reduction—this step is similar to the second step, except that the lowest number is now selected in each column and subtracted from the given values in a particular column.
- Step 4. Placement of cross rows—in this step, the independent zeros that are individually in a column or row are identified. They are marked (crossed out) by either vertical or horizontal rows to use as few crossed rows as possible.
- Step 5. Modifying a matrix and selection of a minimum value—in the matrix, non-crossed numbers are searched and the number with the lowest value is identified. This number is designated as, for example, the letter n. Values of numbers that are crossed out once do not change. Numbers that are crossed out twice are increased by a value of n. From numbers that are not crossed out, the value of n is subtracted.
- Step 6. Finding a path—in the matrix, zero-value cells are nodes. A path can pass through this place provided that the shortest path is met. Here, it applies that it is possible to pass through each site only once. The aim is to pass through all the sites so that the circuit distance is as short as possible. As a result, the route starts at site number 1 and ends at site number 1.
- Step 7. Final procedure—repeat Steps 4 and 5 until the final solution is reached. The end of the calculation process occurs at the moment of closing the entire circuit, where the route leads through all the sites. Steps 4 and 5 are carried out together, this is called iteration. After modifying the matrix by Step 5, we obtain the first iteration.
- Step 8. Route distance calculation—the calculation is based on the first unmodified matrix in which we write the distances of each route. Here, we indicate the individual values that result from the assigned route. The values are summed and the final circuit distance is calculated.

- Step 1. The basic element of this method is to compile a default symmetric (balanced) distance table among individual locations of one circuit route.
- Step 2. For each row and column of a default distance table, it is necessary to calculate the difference between the two lowest values. The difference value is written on the table’s right side for rows and at the bottom for columns.
- Step 3. The highest possible value of all the difference values is then selected. For the row or column with the highest difference value, the lowest value in the distance table is identified. This value represents the first segment of the circuit and presents the order in which the circuit will be operated.
- Step 4. Both the row and the column for the selected value must be removed (crossed out). Furthermore, it is imperative to remove a value which, with the value currently occupied, could close the circuit route without operating all the necessary locations.
- Step 5. The next step is to recalculate the differences for the remaining rows and columns, followed by the same procedure as for Step 3.
- Step 6. We repeat the above procedure until all the necessary locations are ranked in one circuit route.

- Step 1. Identify a point of origin and, in the distance matrix, the column corresponding to the given location is marked (crossed).
- Step 2. Seek a row corresponding to the given location and, in that row, find the field with a minimum value, and thereby another place to visit is determined.
- Step 3. Find a column with this new location and cross it. Search for a row corresponding to the given location and, in that row, find the field with the minimum value; thus, apply Steps 2 and 3 until all the columns are crossed out.
- Step 4. In the last row, occupy the field in a column corresponding to an origin point, so the whole circuit is actually closed.
- Step 5. Select another location as an origin point and, applying Steps 2–5, define the circuit route for this origin point.

#### 3.2. Presentation of the Addressed Problem

#### 3.2.1. Default State: Route A

#### 3.2.2. Default State: Route B

#### 3.2.3. Default State: Route C

## 4. Optimization of the Pick-Up Technology

- Creating default matrices

- Default matrix: Route A

- Speed difference coefficient

#### 4.1. Optimization of Default Routes by the Hungarian Method

- Route A

#### 4.2. Optimization of Default Routes by the Vogel Approximation Method

- Route A—route optimization by Vogel approximation method

#### 4.3. Optimization of Initial Routes by the Nearest Neighbor Method

- Route A—route optimization by the nearest neighbor method

#### 4.4. Optimization of Initial Routes Using the Routin Application

## 5. Discussion

- Technical evaluation of route A

- Technical evaluation of route C

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Number of Unloading Points | 12 |
---|---|

Length of the route | 166.6 km |

Average speed | 47.2 km/h |

Driving time | 3 h 32 min |

Average time spent at a stop | 8 min |

Preparation and loading of goods | 50 min |

Total route time | 5 h 58 min |

Number of Unloading Points | 10 |
---|---|

Length of the route | 181.2 km |

Average speed | 49.2 km/h |

Driving time | 3 h 41 min |

Average time spent at a stop | 12 min |

Preparation and loading of goods | 42 min |

Total route time | 6 h 10 min |

Number of Unloading Points | 10 |
---|---|

Length of the route | 166.2 km |

Average speed | 46.2 km/h |

Driving time | 3 h 36 min |

Average time spent at a stop | 8 min |

Preparation and loading of goods | 42 min |

Total route time | 5 h 38 min |

Unloading Points | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

Sving | A1 | 29.7 | 31.6 | 36.6 | 27.1 | 39.8 | 38 | 31.9 | 44.3 | 33.1 | 25 | 29.3 | 17.5 | |

Penzion Veselí nad Lužnicí | A2 | 19 | 6.7 | 7.2 | 17.4 | 27.6 | 31.7 | 25.6 | 44.9 | 33.7 | 25.9 | 18.2 | 21.2 | |

Kemp Vlkov | A3 | 20 | 7 | 5.6 | 11.3 | 21.6 | 25.7 | 19.6 | 38.9 | 27.6 | 19.9 | 12.2 | 15.2 | |

Kemp Hamr | A4 | 28 | 9 | 11 | 7.1 | 19.7 | 36.6 | 17.7 | 44.4 | 33.2 | 25.5 | 17.8 | 20.7 | |

Penzion Klec | A5 | 30 | 19 | 13 | 12 | 12.6 | 16.6 | 10.6 | 30.2 | 23.9 | 16.1 | 8.4 | 11.4 | |

Kemp Jemčina | A6 | 38 | 30 | 24 | 31 | 19 | 14.9 | 8.8 | 28.5 | 23.7 | 20.2 | 18.7 | 21.6 | |

Autokemp Dolní Lhota | A7 | 32 | 31 | 25 | 36 | 19 | 17 | 6.1 | 14.4 | 22 | 18.5 | 22.4 | 25.7 | |

Kemp Mláka | A8 | 27 | 26 | 20 | 26 | 14 | 12 | 5 | 19.6 | 15.9 | 12.4 | 16.3 | 19.6 | |

Autokemp Staňkov | A9 | 46 | 47 | 41 | 51 | 39 | 37 | 21 | 25 | 12.3 | 24.7 | 28.6 | 38.1 | |

Kemp Majdalena | A10 | 31 | 30 | 25 | 35 | 24 | 25 | 19 | 14 | 19 | 13.5 | 17.4 | 26.9 | |

Autokemp Třeboň | A11 | 23 | 24 | 18 | 29 | 19 | 23 | 16 | 12 | 31 | 14 | 9.6 | 19.1 | |

Kemp Lužnice | A12 | 27 | 17 | 11 | 22 | 12 | 23 | 20 | 15 | 34 | 18 | 11 | 11.4 | |

Kemp Dolní Slovětice | A13 | 18 | 22 | 16 | 27 | 17 | 28 | 29 | 24 | 44 | 28 | 21 | 14 |

Route A | Route B | Route C | ||

Default values from Mapy.cz | Distance (km) | 166.6 | 181.2 | 166.2 |

Time (min) | 191 | 197 | 192 | |

Speed (km/h) | 52.3 | 55.2 | 51.9 | |

The resulting velocity difference coefficient * | 1.110 | 1.122 | 1.125 | |

Real values in the company | Speed (km/h) | 47.2 | 49.2 | 46.2 |

Time (min) | 212 | 221 | 216 | |

Distance (km) | 166.6 | 181.2 | 166.2 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | Min | |

A1 | 19 | 20 | 28 | 30 | 38 | 32 | 27 | 46 | 31 | 23 | 27 | 18 | 18 | |

A2 | 19 | 7 | 9 | 19 | 30 | 31 | 26 | 47 | 30 | 24 | 17 | 22 | 7 | |

A3 | 20 | 7 | 11 | 13 | 24 | 25 | 20 | 41 | 25 | 18 | 11 | 16 | 7 | |

A4 | 28 | 9 | 11 | 12 | 31 | 36 | 26 | 51 | 35 | 29 | 22 | 27 | 9 | |

A5 | 30 | 19 | 13 | 12 | 19 | 19 | 14 | 39 | 24 | 19 | 12 | 17 | 12 | |

A6 | 38 | 30 | 24 | 31 | 19 | 17 | 12 | 37 | 25 | 23 | 23 | 28 | 12 | |

A7 | 32 | 31 | 25 | 36 | 19 | 17 | 5 | 21 | 19 | 16 | 20 | 29 | 5 | |

A8 | 27 | 26 | 20 | 26 | 14 | 12 | 5 | 25 | 14 | 12 | 15 | 24 | 5 | |

A9 | 46 | 47 | 41 | 51 | 39 | 37 | 21 | 25 | 19 | 31 | 34 | 44 | 19 | |

A10 | 31 | 30 | 25 | 35 | 24 | 25 | 19 | 14 | 19 | 14 | 18 | 28 | 14 | |

A11 | 23 | 24 | 18 | 29 | 19 | 23 | 16 | 12 | 31 | 14 | 11 | 21 | 11 | |

A12 | 27 | 17 | 11 | 22 | 12 | 23 | 20 | 15 | 34 | 18 | 11 | 14 | 11 | |

A13 | 18 | 22 | 16 | 27 | 17 | 28 | 29 | 24 | 44 | 28 | 21 | 14 | 14 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 1 | 2 | 10 | 12 | 20 | 14 | 9 | 28 | 13 | 5 | 9 | 0 | |

A2 | 12 | 0 | 2 | 12 | 23 | 24 | 19 | 40 | 23 | 17 | 10 | 15 | |

A3 | 13 | 0 | 4 | 6 | 17 | 18 | 13 | 34 | 18 | 11 | 4 | 9 | |

A4 | 19 | 0 | 2 | 3 | 22 | 27 | 17 | 42 | 26 | 20 | 13 | 18 | |

A5 | 18 | 7 | 1 | 0 | 7 | 7 | 2 | 27 | 12 | 7 | 0 | 5 | |

A6 | 26 | 18 | 12 | 19 | 7 | 5 | 0 | 25 | 13 | 11 | 11 | 16 | |

A7 | 27 | 26 | 20 | 31 | 14 | 12 | 0 | 16 | 14 | 11 | 15 | 24 | |

A8 | 22 | 21 | 15 | 21 | 9 | 7 | 0 | 20 | 9 | 7 | 10 | 19 | |

A9 | 27 | 28 | 22 | 32 | 20 | 18 | 2 | 6 | 0 | 12 | 15 | 25 | |

A10 | 17 | 16 | 11 | 21 | 10 | 11 | 5 | 0 | 5 | 0 | 4 | 14 | |

A11 | 12 | 13 | 7 | 18 | 8 | 12 | 5 | 1 | 20 | 3 | 0 | 10 | |

A12 | 16 | 6 | 0 | 11 | 1 | 12 | 9 | 4 | 23 | 7 | 0 | 3 | |

A13 | 4 | 8 | 2 | 13 | 3 | 14 | 15 | 10 | 30 | 14 | 7 | 0 | |

Min | 4 | 0 | 0 | 0 | 1 | 7 | 0 | 0 | 5 | 0 | 0 | 0 | 0 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 1 | 2 | 10 | 11 | 13 | 14 | 9 | 23 | 13 | 5 | 9 | 0 | |

A2 | 8 | 0 | 2 | 11 | 16 | 24 | 19 | 35 | 23 | 17 | 10 | 15 | |

A3 | 9 | 0 | 4 | 5 | 10 | 18 | 13 | 29 | 18 | 11 | 4 | 9 | |

A4 | 15 | 0 | 2 | 2 | 15 | 27 | 17 | 37 | 26 | 20 | 13 | 18 | |

A5 | 14 | 7 | 1 | 0 | 0 | 7 | 2 | 22 | 12 | 7 | 0 | 5 | |

A6 | 22 | 18 | 12 | 19 | 6 | 5 | 0 | 20 | 13 | 11 | 11 | 16 | |

A7 | 23 | 26 | 20 | 31 | 13 | 5 | 0 | 11 | 14 | 11 | 15 | 24 | |

A8 | 18 | 21 | 15 | 21 | 8 | 0 | 0 | 15 | 9 | 7 | 10 | 19 | |

A9 | 23 | 28 | 22 | 32 | 19 | 11 | 2 | 6 | 0 | 12 | 15 | 25 | |

A10 | 13 | 16 | 11 | 21 | 9 | 4 | 5 | 0 | 0 | 0 | 4 | 14 | |

A11 | 8 | 13 | 7 | 18 | 7 | 5 | 5 | 1 | 15 | 3 | 0 | 10 | |

A12 | 12 | 6 | 0 | 11 | 0 | 5 | 9 | 4 | 18 | 7 | 0 | 3 | |

A13 | 0 | 8 | 2 | 13 | 2 | 7 | 15 | 10 | 25 | 14 | 7 | 0 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 1 | 0 | 8 | 9 | 11 | 12 | 9 | 21 | 13 | 3 | 7 | 0 | |

A2 | 8 | 0 | 2 | 11 | 16 | 24 | 21 | 35 | 25 | 17 | 10 | 17 | |

A3 | 7 | 0 | 2 | 3 | 8 | 16 | 13 | 27 | 18 | 9 | 4 | 9 | |

A4 | 13 | 0 | 0 | 0 | 13 | 25 | 17 | 35 | 26 | 18 | 11 | 18 | |

A5 | 14 | 9 | 1 | 0 | 0 | 7 | 4 | 22 | 14 | 7 | 0 | 7 | |

A6 | 20 | 18 | 10 | 17 | 4 | 3 | 0 | 18 | 13 | 9 | 9 | 16 | |

A7 | 21 | 26 | 18 | 29 | 11 | 3 | 0 | 9 | 14 | 9 | 13 | 24 | |

A8 | 18 | 23 | 15 | 21 | 8 | 0 | 0 | 15 | 11 | 7 | 10 | 21 | |

A9 | 21 | 28 | 20 | 30 | 17 | 9 | 0 | 6 | 0 | 10 | 13 | 25 | |

A10 | 13 | 18 | 11 | 21 | 9 | 4 | 5 | 2 | 0 | 0 | 4 | 16 | |

A11 | 8 | 15 | 7 | 18 | 7 | 5 | 5 | 3 | 15 | 5 | 0 | 12 | |

A12 | 12 | 8 | 0 | 11 | 0 | 5 | 9 | 6 | 18 | 9 | 0 | 5 | |

A13 | 0 | 10 | 2 | 13 | 2 | 7 | 15 | 12 | 25 | 16 | 7 | 0 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 1 | 0 | 8 | 9 | 11 | 12 | 12 | 15 | 13 | 3 | 7 | 0 | |

A2 | 6 | 0 | 0 | 9 | 14 | 22 | 22 | 27 | 23 | 15 | 8 | 10 | |

A3 | 7 | 0 | 2 | 3 | 8 | 16 | 16 | 21 | 18 | 9 | 4 | 4 | |

A4 | 13 | 0 | 0 | 0 | 13 | 25 | 20 | 29 | 26 | 18 | 11 | 13 | |

A5 | 14 | 9 | 1 | 0 | 0 | 7 | 7 | 16 | 14 | 7 | 0 | 2 | |

A6 | 17 | 15 | 7 | 14 | 1 | 0 | 0 | 9 | 10 | 6 | 6 | 8 | |

A7 | 21 | 23 | 15 | 26 | 8 | 0 | 0 | 0 | 11 | 6 | 10 | 16 | |

A8 | 18 | 23 | 15 | 21 | 8 | 0 | 0 | 9 | 11 | 7 | 10 | 16 | |

A9 | 21 | 28 | 20 | 30 | 17 | 9 | 0 | 9 | 0 | 10 | 13 | 20 | |

A10 | 13 | 18 | 11 | 21 | 9 | 4 | 5 | 5 | 0 | 0 | 4 | 11 | |

A11 | 8 | 15 | 7 | 18 | 7 | 5 | 5 | 6 | 9 | 5 | 0 | 7 | |

A12 | 12 | 8 | 0 | 11 | 0 | 5 | 9 | 9 | 12 | 9 | 0 | 0 | |

A13 | 0 | 10 | 2 | 13 | 2 | 7 | 15 | 15 | 19 | 16 | 7 | 0 |

Length of the Route (km) | 158.8 |
---|---|

Operating time (min) | 181 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | Min | Dif | |

A1 | 19 | 20 | 28 | 30 | 38 | 32 | 27 | 46 | 31 | 23 | 27 | 18 | 18 | 1 | |

A2 | 19 | 7 | 9 | 19 | 30 | 31 | 26 | 47 | 30 | 24 | 17 | 22 | 7 | 2 | |

A3 | 20 | 7 | 11 | 13 | 24 | 25 | 20 | 41 | 25 | 18 | 11 | 16 | 7 | 4 | |

A4 | 28 | 9 | 11 | 12 | 31 | 36 | 26 | 51 | 35 | 29 | 22 | 27 | 9 | 2 | |

A5 | 30 | 19 | 13 | 12 | 19 | 19 | 14 | 39 | 24 | 19 | 12 | 17 | 12 | 0 | |

A6 | 38 | 30 | 24 | 31 | 19 | 17 | 12 | 37 | 25 | 23 | 23 | 28 | 12 | 5 | |

A7 | 32 | 31 | 25 | 36 | 19 | 17 | 5 | 21 | 19 | 16 | 20 | 29 | 5 | 11 | |

A8 | 27 | 26 | 20 | 26 | 14 | 12 | 5 | 25 | 14 | 12 | 15 | 24 | 5 | 7 | |

A9 | 46 | 47 | 41 | 51 | 39 | 37 | 21 | 25 | 19 | 31 | 34 | 44 | 19 | 2 | |

A10 | 31 | 30 | 25 | 35 | 24 | 25 | 19 | 14 | 19 | 14 | 18 | 28 | 14 | 5 | |

A11 | 23 | 24 | 18 | 29 | 19 | 23 | 16 | 12 | 31 | 14 | 11 | 21 | 11 | 1 | |

A12 | 27 | 17 | 11 | 22 | 12 | 23 | 20 | 15 | 34 | 18 | 11 | 14 | 11 | 1 | |

A13 | 18 | 22 | 16 | 27 | 17 | 28 | 29 | 24 | 44 | 28 | 21 | 14 | 14 | 2 | |

Min | 18 | 7 | 7 | 9 | 12 | 12 | 5 | 5 | 19 | 14 | 11 | 11 | 14 | ||

Dif | 1 | 2 | 4 | 2 | 0 | 5 | 11 | 7 | 2 | 5 | 1 | 0 | 2 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | Min | Dif | |

A1 | 19 | 20 | 28 | 30 | 38 | 27 | 46 | 31 | 23 | 27 | 18 | 18 | 1 | ||

A2 | 19 | 7 | 9 | 19 | 30 | 26 | 47 | 30 | 24 | 17 | 22 | 7 | 2 | ||

A3 | 20 | 7 | 11 | 13 | 24 | 20 | 41 | 25 | 18 | 11 | 16 | 7 | 4 | ||

A4 | 28 | 9 | 11 | 12 | 31 | 26 | 51 | 35 | 29 | 22 | 27 | 9 | 2 | ||

A5 | 30 | 19 | 13 | 12 | 19 | 14 | 39 | 24 | 19 | 12 | 17 | 12 | 0 | ||

A6 | 38 | 30 | 24 | 31 | 19 | 12 | 37 | 25 | 23 | 23 | 28 | 12 | 7 | ||

A7 | 32 | 31 | 25 | 36 | 19 | 17 | 21 | 19 | 16 | 20 | 29 | 16 | 1 | ||

A8 | 5 | ||||||||||||||

A9 | 46 | 47 | 41 | 51 | 39 | 37 | 25 | 19 | 31 | 34 | 44 | 19 | 6 | ||

A10 | 31 | 30 | 25 | 35 | 24 | 25 | 14 | 19 | 14 | 18 | 28 | 14 | 5 | ||

A11 | 23 | 24 | 18 | 29 | 19 | 23 | 12 | 31 | 14 | 11 | 21 | 11 | 1 | ||

A12 | 27 | 17 | 11 | 22 | 12 | 23 | 15 | 34 | 18 | 11 | 14 | 11 | 1 | ||

A13 | 18 | 22 | 16 | 27 | 17 | 28 | 24 | 44 | 28 | 21 | 14 | 14 | 2 | ||

Min | 18 | 7 | 7 | 9 | 12 | 17 | 12 | 19 | 14 | 11 | 11 | 14 | |||

Dif | 1 | 2 | 4 | 2 | 0 | 2 | 2 | 2 | 5 | 3 | 0 | 2 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | Min | Dif | |

A1 | 19 | 20 | 28 | 30 | 38 | 46 | 31 | 23 | 27 | 18 | 18 | 1 | |||

A2 | 19 | 7 | 9 | 19 | 30 | 47 | 30 | 24 | 17 | 22 | 7 | 2 | |||

A3 | 20 | 7 | 11 | 13 | 24 | 41 | 25 | 18 | 11 | 16 | 7 | 4 | |||

A4 | 28 | 9 | 11 | 12 | 31 | 51 | 35 | 29 | 22 | 27 | 9 | 2 | |||

A5 | 30 | 19 | 13 | 12 | 19 | 39 | 24 | 19 | 12 | 17 | 12 | 0 | |||

A6 | 12 | ||||||||||||||

A7 | 32 | 31 | 25 | 36 | 19 | 17 | 21 | 19 | 16 | 20 | 29 | 16 | 1 | ||

A8 | 5 | ||||||||||||||

A9 | 46 | 47 | 41 | 51 | 39 | 37 | 19 | 31 | 34 | 44 | 19 | 12 | |||

A10 | 31 | 30 | 25 | 35 | 24 | 25 | 19 | 14 | 18 | 28 | 14 | 4 | |||

A11 | 23 | 24 | 18 | 29 | 19 | 23 | 31 | 14 | 11 | 21 | 11 | 3 | |||

A12 | 27 | 17 | 11 | 22 | 12 | 23 | 34 | 18 | 11 | 14 | 11 | 0 | |||

A13 | 18 | 22 | 16 | 27 | 17 | 28 | 44 | 28 | 21 | 14 | 14 | 2 | |||

Min | 18 | 7 | 7 | 9 | 12 | 17 | 19 | 14 | 11 | 11 | 14 | ||||

Dif | 1 | 2 | 4 | 2 | 0 | 2 | 2 | 5 | 3 | 0 | 2 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | Min | Dif | |

A1 | 20 | 30 | 20 | 10 | |||||||||||

A2 | 9 | ||||||||||||||

A3 | 7 | ||||||||||||||

A4 | 11 | 12 | 11 | 1 | |||||||||||

A5 | 19 | ||||||||||||||

A6 | 12 | ||||||||||||||

A7 | 21 | ||||||||||||||

A8 | 5 | ||||||||||||||

A9 | 19 | ||||||||||||||

A10 | 14 | ||||||||||||||

A11 | 11 | ||||||||||||||

A12 | 14 | 14 | 1 | ||||||||||||

A13 | 18 | ||||||||||||||

Min | 11 | 12 | 14 | ||||||||||||

Dif | 9 | 18 | 13 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 20 | ||||||||||||

A2 | 9 | ||||||||||||

A3 | 7 | ||||||||||||

A4 | 12 | ||||||||||||

A5 | 19 | ||||||||||||

A6 | 12 | ||||||||||||

A7 | 21 | ||||||||||||

A8 | 5 | ||||||||||||

A9 | 19 | ||||||||||||

A10 | 14 | ||||||||||||

A11 | 11 | ||||||||||||

A12 | 14 | ||||||||||||

A13 | 18 |

Length of the Route (km) | 158.8 |
---|---|

Operating time (min) | 181 |

Route from the Point | Value of the Purpose Function |
---|---|

A1 | 202 |

A1–variant 2 | 214 |

A2 | 221 |

A2—variant 2 | 236 |

A3 | 211 |

A4 | 227 |

A5 | 220 |

A6 | 205 |

A7 | 206 |

A7—variant 2 | 213 |

A7—variant 3 | 226 |

A8 | 205 |

A9 | 211 |

A10 | 209 |

A10—variant 2 | 222 |

A10—variant 3 | 211 |

A11 | 215 |

A12 | 204 |

A12—variant 2 | 210 |

A13 | 220 |

A13—variant 2 | 214 |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | |

A1 | 19 | 20 | 28 | 30 | 38 | 32 | 27 | 46 | 31 | 23 | 27 | 18 | |

A2 | 19 | 7 | 9 | 19 | 30 | 31 | 26 | 47 | 30 | 24 | 17 | 22 | |

A3 | 20 | 7 | 11 | 13 | 24 | 25 | 20 | 41 | 25 | 18 | 11 | 16 | |

A4 | 28 | 9 | 11 | 12 | 31 | 36 | 26 | 51 | 35 | 29 | 22 | 27 | |

A5 | 30 | 19 | 13 | 12 | 19 | 19 | 14 | 39 | 24 | 19 | 12 | 17 | |

A6 | 38 | 30 | 24 | 31 | 19 | 17 | 12 | 37 | 25 | 23 | 23 | 28 | |

A7 | 32 | 31 | 25 | 36 | 19 | 17 | 5 | 21 | 19 | 16 | 20 | 29 | |

A8 | 27 | 26 | 20 | 26 | 14 | 12 | 5 | 25 | 14 | 12 | 15 | 24 | |

A9 | 46 | 47 | 41 | 51 | 39 | 37 | 21 | 25 | 19 | 31 | 34 | 44 | |

A10 | 31 | 30 | 25 | 35 | 24 | 25 | 19 | 14 | 19 | 14 | 18 | 28 | |

A11 | 23 | 24 | 18 | 29 | 19 | 23 | 16 | 12 | 31 | 14 | 11 | 21 | |

A12 | 27 | 17 | 11 | 22 | 12 | 23 | 20 | 15 | 34 | 18 | 11 | 14 | |

A13 | 18 | 22 | 16 | 27 | 17 | 28 | 29 | 24 | 44 | 28 | 21 | 14 |

Length of the Route (km) | 178.2 |

Operating time (min) | 202 |

Route Name | Operating Time (min) | Length of the Route (km) |
---|---|---|

Route A | 184 | 154.8 |

Route B | 198 | 177.9 |

Route C | 187 | 154.3 |

Route A | Length of the Route (km) | Percentage Saving Compared to the Length of the Initial Route | Operating Time (min) | Speed Difference Coefficient | Final Operating Time (min) | Percentage Saving Compared to the Operating Time of the Initial Route |
---|---|---|---|---|---|---|

Initial route | 166.6 | 212 | ||||

Hungarian method | 158.8 | 4.68% | 181 | 1.11 | 201 | 5.23% |

VAM | 158.8 | 4.68% | 181 | 1.11 | 201 | 5.23% |

Nearest neighbor method | 178.2 | −6.96% | 202 | 1.11 | 224 | −5.76% |

Routin application | 154.8 | 7.08% | 184 | 1.11 | 204 | 3.66% |

Route B | Length of the Route (km) | Percentage Saving Compared to the Length of the Initial Route | Operating Time (min) | Speed Difference Coefficient | Final Operating Time (min) | Percentage Saving Compared to the Operating Time of the Initial Route |
---|---|---|---|---|---|---|

Initial route | 181.2 | 221 | ||||

Hungarian method | 178.3 | 1.60% | 199 | 1.122 | 223 | −1.03% |

VAM | 178.3 | 1.60% | 199 | 1.122 | 223 | −1.03% |

Nearest neighbor method | 177.9 | 1.82% | 198 | 1.122 | 222 | −0.52% |

Routin application | 177.9 | 1.82% | 198 | 1.122 | 222 | −0.52% |

Route C | Length of the Route (km) | Percentage Saving Compared to the Length of the Initial Route | Operating Time (min) | Speed Difference Coefficient | Final Operating Time (min) | Percentage Saving Compared to the Operating Time of the Initial Route |
---|---|---|---|---|---|---|

Initial route | 166.2 | 216 | ||||

Hungarian method | 155.5 | 6.44% | 183 | 1.125 | 206 | 4.69% |

VAM | 170.1 | −2.35% | 191 | 1.125 | 215 | 0.52% |

Nearest neighbor method | 155 | 6.74% | 184 | 1.125 | 207 | 4.17% |

Routin application | 154.3 | 7.16% | 187 | 1.125 | 210 | 2.60% |

Route | Total Fuel Costs | Total Fuel Costs for Each Route | Total Fuel Cost Savings for Each Route | Percentage Fuel Cost Savings on Each Route |
---|---|---|---|---|

A | EUR 3280.21 | EUR 3047.88 | EUR 232.33 | 7.08% |

B | EUR 3548.45 | EUR 3483.83 | EUR 64.62 | 1.82% |

C | EUR 3314.65 | EUR 3077.32 | EUR 237.33 | 7.16% |

Total fuel costs in 2019 | Total fuel costs in 2020 | Total expected financial savings after optimization | ||

EUR 10,143.31 | EUR 9609.03 | EUR 534.28 | 5.27% |

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## Share and Cite

**MDPI and ACS Style**

Stopka, O.; Gross, P.; Pečman, J.; Hanzl, J.; Stopková, M.; Jurkovič, M.
Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study. *Technologies* **2022**, *10*, 84.
https://doi.org/10.3390/technologies10040084

**AMA Style**

Stopka O, Gross P, Pečman J, Hanzl J, Stopková M, Jurkovič M.
Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study. *Technologies*. 2022; 10(4):84.
https://doi.org/10.3390/technologies10040084

**Chicago/Turabian Style**

Stopka, Ondrej, Patrik Gross, Jan Pečman, Jiří Hanzl, Mária Stopková, and Martin Jurkovič.
2022. "Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study" *Technologies* 10, no. 4: 84.
https://doi.org/10.3390/technologies10040084