A Two-Echelon Routing Model for Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study of Pharmaceutical Distribution in Rome
Abstract
:1. Introduction
1.1. Context Description
- defining and formulating a two-echelon bi-objective routing problem with an intermediate facility to establish the delivery scheme within each urban zone with the aim of planning sustainable and cost-effective routes;
- solving the problem and conducting a what-if analysis based on the available data, assessing the benefits and drawbacks of this delivery scheme and the use of a mixed fleet.
2. Materials and Methods
2.1. Literature Review
2.2. Main Contribution
2.3. Problem Description
- n: number of nodes, consisting of customers to be visited and the depot, referred to as , from which the ICEV’s route originates and ends (hereafter also referred to as the first route);
- : a customer that also serves as a depot for the EV’s route, selected from the customers served by the ICEV. The EV’s route is hereafter referred to as the second route;
- , : length of the best route to move from node i to node j using the ICEV;
- , : length of the best route to move from node i to node j using the EV. Since the EV may be authorized to cross low-emission zones in urban areas, it generally happens that , ;
- and : CO2 emission (in kg/km) of the ICEV and EV, respectively;
- and : transportation cost (in EUR/km) of the ICEV and EV, respectively. Although the trend in future years favors a reduction in the cost per kilometer for electric vehicles, it is more realistically assumed that , which implies that
- k, : number of customers and depot served by the first route.
- the assignment of customers to the two vehicles, ensuring that each customer is served by only one vehicle. Specifically, the ICEV route starts and ends at depot , while the EV route starts and ends at depot ;
- the visiting order of the customers within each route.
- each vehicle can perform only one route that starts and ends at its designated depot;
- split deliveries are not allowed;
- the first node visited by the ICEV’s route must be node to ensure that the second tour can start as quickly as possible, thereby reducing the overall completion time for serving the customers.
Mathematical Model
3. Results
3.1. Data of the Case Study
- in Equation (1). In this scenario, there are no differences in the transportation cost per kilometer between the ICEV and the EV. This is evident from the data provided by the LSP and presented in Table A2 in Appendix A (the cost breakdown includes fuel consumption, maintenance, other operational expenses, and the purchase cost amortized over eight years). The 2-EATSP model can therefore be simplified by removing the budget constraint (18) and focusing solely on minimizing CO2 emissions (see Section 3.2);
- in Equation (1). In this more general scenario, several Pareto-optimal solutions can be generated for different values of budget B in Constraint (18). These solutions are evaluated and compared in a what-if analysis presented in Section 3.3.
3.2. Case of
3.2.1. Discussion
3.2.2. Benchmark Comparison
3.3. Case of
4. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
ID | Point of Interest | Latitude | Longitude |
---|---|---|---|
1 | Pharmacy 1 | 41.8797075 | 12.5017273 |
2 | Pharmacy 2 | 41.8815379 | 12.5131229 |
3 | Pharmacy 3 | 41.8960212 | 12.4904504 |
4 | Pharmacy 4 | 41.8889683 | 12.4964994 |
5 | Pharmacy 5 | 41.8941843 | 12.4906858 |
6 | Pharmacy 6 | 41.9025231 | 12.5016612 |
7 | Pharmacy 7 | 41.9009856 | 12.4932650 |
8 | Pharmacy 8 | 41.8984073 | 12.4905973 |
9 | Pharmacy 9 | 41.8974436 | 12.4952554 |
10 | Pharmacy 10 | 41.8951780 | 12.4997721 |
11 | Pharmacy 11 | 41.8996024 | 12.4947634 |
12 | Pharmacy 12 | 41.8950950 | 12.5009679 |
13 | Pharmacy 13 | 41.8982191 | 12.5155031 |
14 | Pharmacy 14 | 41.9022693 | 12.5049111 |
15 | Pharmacy 15 | 41.8919719 | 12.5017881 |
16 | Pharmacy 16 | 41.8941144 | 12.5033891 |
17 | Pharmacy 17 | 41.8980393 | 12.4996115 |
18 | Pharmacy 18 | 41.9015448 | 12.5031056 |
19 | Pharmacy 19 | 41.8925406 | 12.5054307 |
20 | Pharmacy 20 | 41.9053853 | 12.5038711 |
21 | Pharmacy 21 | 41.8974293 | 12.5126908 |
22 | Pharmacy 22 | 41.8950682 | 12.5053476 |
23 | Pharmacy 23 | 41.8910022 | 12.5022499 |
24 | Pharmacy 24 | 41.9012792 | 12.5022033 |
25 | Pharmacy 25 | 41.8965883 | 12.5148512 |
26 | Pharmacy 26 | 41.9029806 | 12.4957247 |
27 | Pharmacy 27 | 41.8977001 | 12.5020334 |
28 | Pharmacy 28 | 41.8937245 | 12.5077524 |
29 | Pharmacy 29 | 41.8895619 | 12.5137454 |
30 | Pharmacy 30 | 41.8906894 | 12.5063857 |
31 | Regional depot | 41.8864490 | 12.5159620 |
Cost Component | ICEV [EUR/km] | EV [EUR/km] |
---|---|---|
Fuel/Electricity | 0.16 | 0.12 |
Maintenance | 0.05 | 0.06 |
Other Operational Costs | 0.03 | 0.04 |
Amortized Purchase Cost | 0.10 | 0.12 |
Total Cost | 0.34 | 0.34 |
k | CO2 [kg/km] | STC [h] |
---|---|---|
2 | 2.435 | 4.928 |
9 | 2.855 | 4.131 |
15 | 3.862 | 3.143 |
19 | 4.440 | 2.959 |
31 | 6.845 | 5.067 |
From/To | ID 1 | ID 2 | ID 3 | ID 4 | ID 5 | ID 6 | ID 7 | ID 8 |
---|---|---|---|---|---|---|---|---|
ID 1 | - | 1.274 | 3.849 | 2.738 | 3.093 | 3.619 | 4.112 | 3.723 |
ID 2 | 1.681 | - | 3.604 | 2.780 | 3.113 | 3.567 | 3.795 | 3.478 |
ID 3 | 3.237 | 3.404 | - | 1.695 | 0.264 | 1.814 | 1.104 | 0.715 |
ID 4 | 2.183 | 2.485 | 3.909 | - | 3.153 | 3.680 | 4.173 | 3.783 |
ID 5 | 3.018 | 3.330 | 1.246 | 1.475 | - | 1.595 | 1.509 | 1.120 |
ID 6 | 3.960 | 3.653 | 2.579 | 3.947 | 2.517 | - | 1.919 | 2.453 |
ID 7 | 3.931 | 3.478 | 1.136 | 2.388 | 0.957 | 0.895 | - | 0.937 |
ID 8 | 3.643 | 3.810 | 0.848 | 2.100 | 0.669 | 1.285 | 0.389 | - |
ID 9 | 3.697 | 3.194 | 0.603 | 2.154 | 0.723 | 1.133 | 0.866 | 0.477 |
ID 10 | 2.915 | 2.566 | 1.521 | 2.196 | 0.765 | 1.365 | 1.784 | 1.395 |
ID 11 | 3.613 | 3.264 | 1.032 | 2.401 | 0.970 | 1.411 | 1.112 | 0.723 |
ID 12 | 2.939 | 2.590 | 1.619 | 2.294 | 0.863 | 1.389 | 1.882 | 1.493 |
ID 13 | 3.393 | 2.714 | 3.411 | 3.380 | 3.152 | 3.197 | 2.994 | 3.285 |
ID 14 | 3.890 | 3.583 | 2.674 | 3.877 | 2.448 | 1.879 | 1.538 | 2.383 |
ID 15 | 2.513 | 2.164 | 1.923 | 1.993 | 1.167 | 1.693 | 2.186 | 1.797 |
ID 16 | 2.517 | 2.210 | 1.638 | 2.504 | 1.097 | 1.600 | 1.828 | 1.511 |
ID 17 | 3.170 | 2.862 | 1.446 | 2.815 | 1.384 | 0.935 | 1.162 | 1.320 |
ID 18 | 3.792 | 3.485 | 2.412 | 3.779 | 2.350 | 2.093 | 1.752 | 2.285 |
ID 19 | 2.257 | 1.950 | 1.897 | 2.244 | 1.357 | 1.860 | 2.087 | 1.771 |
ID 20 | 4.332 | 4.025 | 2.296 | 3.547 | 2.116 | 1.501 | 1.159 | 2.096 |
ID 21 | 3.467 | 2.787 | 2.630 | 3.453 | 2.568 | 2.416 | 2.671 | 2.504 |
ID 22 | 3.218 | 2.911 | 1.710 | 3.079 | 1.648 | 1.496 | 1.724 | 1.584 |
ID 23 | 2.399 | 2.050 | 2.037 | 1.878 | 1.281 | 1.807 | 2.300 | 1.911 |
ID 24 | 3.952 | 3.644 | 2.733 | 3.939 | 2.509 | 1.939 | 1.597 | 2.445 |
ID 25 | 3.617 | 2.938 | 3.027 | 3.604 | 3.376 | 2.813 | 3.068 | 2.900 |
ID 26 | 4.262 | 3.769 | 1.467 | 2.719 | 1.288 | 0.673 | 0.331 | 1.267 |
ID 27 | 3.289 | 2.982 | 1.793 | 3.163 | 1.732 | 1.580 | 1.807 | 1.667 |
ID 28 | 2.584 | 2.379 | 2.515 | 2.570 | 1.975 | 2.314 | 2.541 | 2.389 |
ID 29 | 2.189 | 1.561 | 2.705 | 2.392 | 2.164 | 2.503 | 2.731 | 2.579 |
ID 30 | 2.037 | 1.730 | 2.117 | 2.024 | 1.577 | 2.080 | 2.308 | 1.991 |
ID 31 | 1.924 | 1.183 | 3.202 | 2.457 | 2.661 | 3.000 | 3.228 | 3.076 |
From/To | ID 9 | ID 10 | ID 11 | ID 12 | ID 13 | ID 14 | ID 15 | ID 16 |
---|---|---|---|---|---|---|---|---|
ID 1 | 3.108 | 2.328 | 3.087 | 2.352 | 3.286 | 3.841 | 1.926 | 2.586 |
ID 2 | 3.056 | 2.348 | 3.034 | 2.201 | 2.844 | 3.399 | 1.946 | 1.967 |
ID 3 | 1.740 | 0.985 | 1.091 | 1.082 | 3.006 | 2.335 | 1.386 | 1.317 |
ID 4 | 3.168 | 2.388 | 3.147 | 2.412 | 2.971 | 3.525 | 1.986 | 2.481 |
ID 5 | 1.520 | 0.765 | 1.496 | 0.863 | 2.786 | 2.115 | 1.167 | 1.097 |
ID 6 | 2.031 | 1.653 | 2.009 | 1.555 | 1.698 | 0.521 | 1.980 | 1.558 |
ID 7 | 0.546 | 0.943 | 0.214 | 1.038 | 3.197 | 1.416 | 1.314 | 1.298 |
ID 8 | 0.880 | 1.390 | 0.548 | 1.488 | 3.587 | 1.805 | 1.792 | 1.722 |
ID 9 | - | 0.659 | 0.853 | 0.754 | 2.704 | 1.654 | 1.030 | 1.014 |
ID 10 | 0.854 | - | 0.833 | 0.098 | 2.022 | 1.886 | 0.402 | 0.332 |
ID 11 | 1.344 | 1.932 | - | 0.824 | 2.773 | 1.932 | 1.100 | 1.084 |
ID 12 | 0.878 | 0.098 | 0.857 | - | 1.924 | 2.478 | 0.426 | 0.235 |
ID 13 | 2.862 | 2.388 | 2.841 | 2.290 | - | 1.529 | 2.547 | 2.055 |
ID 14 | 1.961 | 1.583 | 1.752 | 1.485 | 1.628 | - | 1.911 | 1.489 |
ID 15 | 1.182 | 0.402 | 1.161 | 0.426 | 2.000 | 2.555 | - | 0.660 |
ID 16 | 1.089 | 0.332 | 1.068 | 0.235 | 1.689 | 2.244 | 0.660 | - |
ID 17 | 0.897 | 0.747 | 0.876 | 0.649 | 2.342 | 1.455 | 1.075 | 0.653 |
ID 18 | 1.863 | 1.485 | 1.842 | 1.387 | 1.530 | 0.353 | 1.813 | 1.391 |
ID 19 | 1.349 | 0.592 | 1.327 | 0.494 | 1.587 | 2.142 | 0.920 | 0.260 |
ID 20 | 1.705 | 2.024 | 1.373 | 1.927 | 1.520 | 0.638 | 2.352 | 1.930 |
ID 21 | 2.081 | 1.703 | 2.060 | 1.605 | 0.306 | 1.205 | 2.031 | 1.609 |
ID 22 | 1.161 | 0.795 | 1.140 | 0.697 | 1.659 | 2.214 | 1.123 | 0.701 |
ID 23 | 1.296 | 0.516 | 1.275 | 0.540 | 1.886 | 2.441 | 0.114 | 0.774 |
ID 24 | 2.022 | 1.644 | 1.811 | 1.547 | 1.690 | 0.513 | 1.972 | 1.550 |
ID 25 | 2.478 | 2.612 | 2.457 | 2.514 | 0.388 | 1.602 | 2.771 | 2.279 |
ID 26 | 0.877 | 1.234 | 0.545 | 1.329 | 2.370 | 1.193 | 1.605 | 1.450 |
ID 27 | 1.245 | 0.867 | 1.223 | 0.769 | 1.973 | 2.528 | 1.195 | 0.772 |
ID 28 | 1.967 | 1.210 | 1.945 | 1.112 | 1.215 | 1.770 | 1.538 | 0.878 |
ID 29 | 2.156 | 1.400 | 2.135 | 1.302 | 1.633 | 2.187 | 1.728 | 1.067 |
ID 30 | 1.569 | 0.812 | 1.547 | 0.714 | 1.650 | 2.204 | 1.140 | 0.480 |
ID 31 | 2.653 | 1.897 | 2.632 | 1.799 | 2.146 | 2.701 | 1.624 | 1.564 |
From/To | ID 17 | ID 18 | ID 19 | ID 20 | ID 21 | ID 22 | ID 23 | ID 24 |
---|---|---|---|---|---|---|---|---|
ID 1 | 3.067 | 3.777 | 2.425 | 4.139 | 2.981 | 2.772 | 1.812 | 3.723 |
ID 2 | 3.015 | 3.866 | 1.707 | 4.149 | 2.538 | 2.055 | 1.832 | 3.812 |
ID 3 | 1.262 | 1.972 | 1.577 | 2.334 | 2.701 | 1.767 | 1.501 | 1.918 |
ID 4 | 3.127 | 3.837 | 2.221 | 4.275 | 2.665 | 2.569 | 1.872 | 3.783 |
ID 5 | 1.042 | 1.752 | 1.357 | 2.114 | 2.481 | 1.547 | 1.281 | 1.698 |
ID 6 | 1.989 | 0.158 | 1.818 | 1.204 | 1.262 | 1.463 | 2.095 | 0.103 |
ID 7 | 0.898 | 1.053 | 1.558 | 1.422 | 2.157 | 1.748 | 1.428 | 0.999 |
ID 8 | 1.232 | 1.442 | 1.982 | 1.811 | 2.547 | 2.172 | 1.906 | 1.388 |
ID 9 | 0.581 | 1.291 | 1.274 | 1.653 | 2.398 | 1.464 | 1.144 | 1.237 |
ID 10 | 0.813 | 1.523 | 0.592 | 1.885 | 1.716 | 0.782 | 0.516 | 1.469 |
ID 11 | 0.684 | 1.569 | 1.344 | 1.931 | 2.468 | 1.534 | 1.214 | 1.515 |
ID 12 | 0.837 | 1.547 | 0.494 | 1.909 | 1.618 | 0.684 | 0.540 | 1.493 |
ID 13 | 2.821 | 1.996 | 2.005 | 2.279 | 0.306 | 1.701 | 2.433 | 1.942 |
ID 14 | 1.920 | 0.465 | 1.748 | 0.822 | 1.193 | 1.394 | 2.025 | 0.411 |
ID 15 | 1.141 | 1.851 | 0.848 | 2.213 | 1.695 | 1.110 | 0.114 | 1.797 |
ID 16 | 1.048 | 1.758 | 0.260 | 2.120 | 1.384 | 0.450 | 0.774 | 1.704 |
ID 17 | - | 1.092 | 0.912 | 1.454 | 2.036 | 1.103 | 1.189 | 1.038 |
ID 18 | 1.822 | - | 1.650 | 1.036 | 1.094 | 1.296 | 1.927 | 0.766 |
ID 19 | 1.307 | 2.018 | - | 2.380 | 1.281 | 0.348 | 1.034 | 1.964 |
ID 20 | 1.623 | 0.581 | 2.190 | - | 1.351 | 1.835 | 2.466 | 0.527 |
ID 21 | 2.040 | 1.673 | 1.869 | 1.955 | - | 1.514 | 2.145 | 1.618 |
ID 22 | 1.120 | 1.654 | 0.961 | 2.016 | 1.354 | - | 1.237 | 1.600 |
ID 23 | 1.255 | 1.965 | 0.734 | 2.327 | 1.581 | 1.082 | - | 1.911 |
ID 24 | 1.981 | 0.149 | 1.810 | 0.881 | 1.254 | 1.455 | 2.086 | - |
ID 25 | 2.437 | 2.069 | 2.230 | 2.352 | 0.397 | 1.925 | 2.657 | 2.015 |
ID 26 | 0.795 | 0.830 | 1.710 | 1.199 | 1.935 | 1.569 | 1.719 | 0.776 |
ID 27 | 1.203 | 1.737 | 1.032 | 2.099 | 1.668 | 0.911 | 1.309 | 1.683 |
ID 28 | 1.925 | 2.237 | 0.822 | 2.520 | 0.909 | 0.817 | 1.652 | 2.183 |
ID 29 | 2.115 | 2.655 | 1.012 | 2.937 | 1.327 | 1.007 | 1.445 | 2.600 |
ID 30 | 1.527 | 2.238 | 0.220 | 2.954 | 1.344 | 0.568 | 1.254 | 2.184 |
ID 31 | 2.612 | 3.168 | 1.509 | 3.451 | 1.840 | 1.504 | 1.509 | 3.114 |
From/To | ID 25 | ID 26 | ID 27 | ID 28 | ID 29 | ID 30 | ID 31 |
---|---|---|---|---|---|---|---|
ID 1 | 3.250 | 5.143 | 3.249 | 2.787 | 2.392 | 2.205 | 2.401 |
ID 2 | 2.441 | 4.214 | 2.532 | 2.069 | 1.195 | 1.487 | 0.807 |
ID 3 | 2.970 | 2.234 | 1.856 | 1.781 | 2.384 | 1.797 | 3.098 |
ID 4 | 2.935 | 4.987 | 3.045 | 2.583 | 2.420 | 2.001 | 2.883 |
ID 5 | 2.750 | 2.748 | 1.636 | 1.562 | 2.164 | 1.577 | 3.024 |
ID 6 | 1.532 | 2.112 | 1.177 | 1.496 | 2.241 | 1.978 | 3.354 |
ID 7 | 2.427 | 1.132 | 1.272 | 1.763 | 2.365 | 1.778 | 3.172 |
ID 8 | 2.816 | 1.628 | 1.662 | 2.187 | 2.789 | 2.202 | 3.503 |
ID 9 | 2.667 | 2.105 | 1.175 | 1.479 | 2.082 | 1.494 | 2.888 |
ID 10 | 1.986 | 3.023 | 1.259 | 0.797 | 1.400 | 0.812 | 2.259 |
ID 11 | 2.737 | 2.351 | 1.106 | 1.549 | 2.151 | 1.564 | 2.957 |
ID 12 | 1.888 | 2.036 | 1.161 | 0.699 | 1.302 | 0.714 | 2.786 |
ID 13 | 0.508 | 3.309 | 1.552 | 2.010 | 1.362 | 1.785 | 2.313 |
ID 14 | 1.462 | 1.731 | 1.108 | 1.427 | 2.172 | 1.909 | 3.285 |
ID 15 | 1.964 | 2.340 | 1.587 | 1.125 | 1.251 | 0.628 | 1.858 |
ID 16 | 1.653 | 2.247 | 0.927 | 0.465 | 1.067 | 0.480 | 2.551 |
ID 17 | 2.306 | 1.581 | 0.604 | 1.117 | 1.720 | 1.132 | 3.204 |
ID 18 | 1.364 | 1.945 | 1.010 | 1.329 | 2.074 | 1.811 | 3.187 |
ID 19 | 1.551 | 2.507 | 0.824 | 0.362 | 0.965 | 0.220 | 2.449 |
ID 20 | 1.620 | 1.352 | 1.549 | 1.868 | 2.613 | 2.350 | 3.726 |
ID 21 | 0.347 | 2.985 | 1.228 | 1.547 | 1.436 | 1.859 | 2.386 |
ID 22 | 1.623 | 2.143 | 0.477 | 0.602 | 1.347 | 1.181 | 2.580 |
ID 23 | 1.850 | 2.454 | 1.558 | 1.096 | 1.137 | 0.514 | 1.743 |
ID 24 | 1.523 | 1.790 | 1.169 | 1.488 | 2.233 | 1.970 | 3.346 |
ID 25 | - | 3.382 | 1.625 | 2.234 | 1.587 | 2.010 | 2.537 |
ID 26 | 2.204 | - | 1.049 | 1.602 | 2.517 | 1.930 | 3.580 |
ID 27 | 1.937 | 2.226 | - | 0.944 | 1.689 | 1.252 | 2.922 |
ID 28 | 1.179 | 2.960 | 1.294 | - | 1.027 | 0.602 | 1.978 |
ID 29 | 1.399 | 3.150 | 1.484 | 1.022 | 100 - | 0.792 | 1.484 |
ID 30 | 1.614 | 2.727 | 1.044 | 0.582 | 0.682 | - | 1.423 |
ID 31 | 1.743 | 3.647 | 1.981 | 1.519 | 0.497 | 1.289 | - |
From/To | ID 1 | ID 2 | ID 3 | ID 4 | ID 5 | ID 6 | ID 7 | ID 8 |
---|---|---|---|---|---|---|---|---|
ID 1 | - | 1.274 | 2.848 | 1.774 | 2.112 | 2.548 | 3.187 | 2.885 |
ID 2 | 1.681 | - | 2.586 | 1.960 | 2.467 | 2.507 | 2.932 | 2.746 |
ID 3 | 2.494 | 2.195 | - | 1.695 | 0.264 | 1.814 | 1.104 | 0.715 |
ID 4 | 1.632 | 1.833 | 2.957 | - | 2.104 | 2.734 | 3.150 | 2.698 |
ID 5 | 2.106 | 2.191 | 1.246 | 1.475 | - | 1.595 | 1.509 | 1.120 |
ID 6 | 2.897 | 2.907 | 2.018 | 3.138 | 1.758 | - | 1.919 | 1.839 |
ID 7 | 3.097 | 2.621 | 1.136 | 1.848 | 0.957 | 0.895 | - | 0.937 |
ID 8 | 2.805 | 2.504 | 0.848 | 1.499 | 0.669 | 1.285 | 0.389 | - |
ID 9 | 2.954 | 2.294 | 0.603 | 1.579 | 0.723 | 1.133 | 0.866 | 0.477 |
ID 10 | 2.004 | 1.904 | 1.521 | 1.416 | 0.765 | 1.365 | 1.784 | 1.395 |
ID 11 | 2.716 | 2.462 | 1.032 | 1.907 | 0.970 | 1.411 | 1.112 | 0.723 |
ID 12 | 2.283 | 1.869 | 1.619 | 1.473 | 0.863 | 1.389 | 1.882 | 1.493 |
ID 13 | 2.585 | 1.855 | 2.528 | 2.362 | 2.202 | 2.284 | 2.352 | 2.189 |
ID 14 | 3.026 | 2.671 | 2.090 | 2.528 | 1.614 | 1.879 | 1.538 | 1.808 |
ID 15 | 1.797 | 1.647 | 1.923 | 1.993 | 1.167 | 1.693 | 1.716 | 1.797 |
ID 16 | 1.877 | 1.645 | 1.638 | 1.712 | 1.097 | 1.600 | 1.828 | 1.511 |
ID 17 | 2.493 | 2.216 | 1.446 | 1.847 | 1.384 | 0.935 | 1.162 | 1.320 |
ID 18 | 3.031 | 2.698 | 1.718 | 2.605 | 1.635 | 1.599 | 1.752 | 1.568 |
ID 19 | 1.536 | 1.950 | 1.897 | 1.562 | 1.357 | 1.860 | 1.386 | 1.771 |
ID 20 | 3.297 | 2.593 | 1.693 | 2.332 | 1.479 | 1.501 | 1.159 | 1.410 |
ID 21 | 2.416 | 2.151 | 1.708 | 2.235 | 1.678 | 1.790 | 2.130 | 1.631 |
ID 22 | 2.411 | 2.250 | 1.710 | 2.189 | 1.648 | 1.496 | 1.724 | 1.584 |
ID 23 | 1.683 | 1.315 | 1.584 | 1.878 | 1.281 | 1.807 | 1.649 | 1.911 |
ID 24 | 2.718 | 2.705 | 2.058 | 2.641 | 1.682 | 1.939 | 1.597 | 1.617 |
ID 25 | 2.518 | 2.020 | 2.037 | 2.370 | 2.518 | 2.081 | 2.408 | 2.052 |
ID 26 | 3.048 | 2.689 | 1.467 | 1.898 | 1.288 | 0.673 | 0.331 | 1.267 |
ID 27 | 2.213 | 2.257 | 1.793 | 2.308 | 1.732 | 1.580 | 1.807 | 1.667 |
ID 28 | 1.779 | 1.747 | 1.942 | 1.992 | 1.975 | 1.758 | 1.810 | 1.638 |
ID 29 | 1.557 | 1.561 | 1.899 | 1.753 | 1.645 | 1.859 | 1.854 | 2.057 |
ID 30 | 1.476 | 1.730 | 1.635 | 1.479 | 1.577 | 1.531 | 1.619 | 1.991 |
ID 31 | 1.924 | 1.183 | 2.123 | 1.707 | 2.060 | 2.366 | 2.250 | 2.448 |
From/To | ID 9 | ID 10 | ID 11 | ID 12 | ID 13 | ID 14 | ID 15 | ID 16 |
---|---|---|---|---|---|---|---|---|
ID 1 | 2.457 | 1.539 | 2.173 | 1.615 | 2.618 | 2.477 | 1.926 | 1.725 |
ID 2 | 1.981 | 1.515 | 2.035 | 1.654 | 2.231 | 2.347 | 1.946 | 1.967 |
ID 3 | 1.740 | 0.985 | 1.091 | 1.082 | 2.032 | 1.517 | 1.386 | 1.317 |
ID 4 | 2.463 | 1.604 | 2.480 | 1.549 | 2.010 | 2.708 | 1.986 | 1.983 |
ID 5 | 1.520 | 0.765 | 1.496 | 0.863 | 2.018 | 1.652 | 1.167 | 1.097 |
ID 6 | 1.460 | 1.653 | 1.315 | 1.555 | 1.698 | 0.521 | 1.980 | 1.558 |
ID 7 | 0.546 | 0.943 | 0.214 | 1.038 | 2.082 | 1.416 | 1.314 | 1.298 |
ID 8 | 0.880 | 1.390 | 0.548 | 1.488 | 2.407 | 1.805 | 1.792 | 1.722 |
ID 9 | - | 0.659 | 0.853 | 0.754 | 2.067 | 1.654 | 1.030 | 1.014 |
ID 10 | 0.854 | - | 0.833 | 0.098 | 1.307 | 1.886 | 0.402 | 0.332 |
ID 11 | 0.332 | 0.729 | - | 0.824 | 1.948 | 1.932 | 1.100 | 1.084 |
ID 12 | 0.878 | 0.098 | 0.857 | - | 1.924 | 1.886 | 0.426 | 0.235 |
ID 13 | 2.143 | 1.839 | 2.254 | 1.615 | - | 1.529 | 1.762 | 1.639 |
ID 14 | 1.961 | 1.583 | 1.752 | 1.485 | 1.628 | - | 1.911 | 1.489 |
ID 15 | 1.182 | 0.402 | 1.161 | 0.426 | 2.000 | 1.677 | - | 0.660 |
ID 16 | 1.089 | 0.332 | 1.068 | 0.235 | 1.689 | 1.473 | 0.660 | - |
ID 17 | 0.897 | 0.747 | 0.876 | 0.649 | 1.647 | 1.455 | 1.075 | 0.653 |
ID 18 | 1.863 | 1.485 | 1.842 | 1.387 | 1.530 | 0.353 | 1.813 | 1.391 |
ID 19 | 1.349 | 0.592 | 1.327 | 0.494 | 1.587 | 1.489 | 0.920 | 0.260 |
ID 20 | 1.705 | 1.456 | 1.373 | 1.927 | 1.520 | 0.638 | 1.665 | 1.930 |
ID 21 | 1.522 | 1.703 | 1.329 | 1.605 | 0.306 | 1.205 | 1.312 | 1.609 |
ID 22 | 1.161 | 0.795 | 1.140 | 0.697 | 1.659 | 1.439 | 1.123 | 0.701 |
ID 23 | 1.296 | 0.516 | 1.275 | 0.540 | 1.886 | 1.610 | 0.114 | 0.774 |
ID 24 | 1.322 | 1.644 | 1.811 | 1.547 | 1.690 | 0.513 | 1.972 | 1.550 |
ID 25 | 1.968 | 1.895 | 1.753 | 1.896 | 0.388 | 1.602 | 1.955 | 1.812 |
ID 26 | 0.877 | 1.234 | 0.545 | 1.329 | 1.621 | 1.193 | 1.605 | 1.450 |
ID 27 | 1.245 | 0.867 | 1.223 | 0.769 | 1.973 | 1.990 | 1.195 | 0.772 |
ID 28 | 1.967 | 1.210 | 1.945 | 1.112 | 1.215 | 1.770 | 1.538 | 0.878 |
ID 29 | 1.685 | 1.400 | 1.692 | 1.302 | 1.633 | 1.736 | 1.728 | 1.067 |
ID 30 | 1.569 | 0.812 | 1.547 | 0.714 | 1.650 | 1.539 | 1.140 | 0.480 |
ID 31 | 1.873 | 1.897 | 1.710 | 1.799 | 1.519 | 1.993 | 1.624 | 1.564 |
From/To | ID 17 | ID 18 | ID 19 | ID 20 | ID 21 | ID 22 | ID 23 | ID 24 |
---|---|---|---|---|---|---|---|---|
ID 1 | 2.350 | 2.912 | 1.869 | 3.110 | 2.135 | 2.026 | 1.812 | 2.805 |
ID 2 | 2.200 | 3.018 | 1.707 | 2.990 | 2.016 | 1.345 | 1.832 | 2.892 |
ID 3 | 1.262 | 1.972 | 1.577 | 1.533 | 1.903 | 1.767 | 1.501 | 1.918 |
ID 4 | 2.094 | 2.636 | 1.518 | 2.892 | 2.100 | 1.908 | 1.872 | 2.956 |
ID 5 | 1.042 | 1.752 | 1.357 | 1.450 | 1.683 | 1.547 | 1.281 | 1.698 |
ID 6 | 1.989 | 0.158 | 1.818 | 1.204 | 1.262 | 1.463 | 1.592 | 0.103 |
ID 7 | 0.898 | 1.053 | 1.558 | 1.422 | 1.447 | 1.748 | 1.428 | 0.999 |
ID 8 | 1.232 | 1.442 | 1.982 | 1.811 | 1.673 | 1.627 | 1.906 | 1.388 |
ID 9 | 0.581 | 1.291 | 1.274 | 1.653 | 1.872 | 1.464 | 1.144 | 1.237 |
ID 10 | 0.813 | 1.523 | 0.592 | 1.885 | 1.716 | 0.782 | 0.516 | 1.469 |
ID 11 | 0.684 | 1.569 | 1.344 | 1.931 | 1.776 | 1.534 | 1.214 | 1.515 |
ID 12 | 0.837 | 1.547 | 0.494 | 1.909 | 1.618 | 0.684 | 0.540 | 1.493 |
ID 13 | 2.026 | 1.996 | 1.531 | 1.588 | 0.324 | 1.701 | 1.878 | 1.942 |
ID 14 | 1.920 | 0.465 | 1.748 | 0.822 | 1.193 | 1.394 | 1.406 | 0.411 |
ID 15 | 1.141 | 1.851 | 0.848 | 1.451 | 1.695 | 1.110 | 0.114 | 1.797 |
ID 16 | 1.048 | 1.758 | 0.260 | 1.395 | 1.384 | 0.450 | 0.774 | 1.704 |
ID 17 | - | 1.092 | 0.912 | 1.454 | 1.626 | 1.103 | 1.189 | 1.038 |
ID 18 | 1.822 | - | 1.650 | 1.036 | 1.094 | 1.296 | 1.927 | 0.766 |
ID 19 | 1.307 | 1.431 | - | 1.868 | 1.281 | 0.348 | 1.034 | 1.964 |
ID 20 | 1.623 | 0.581 | 1.579 | - | 1.351 | 1.835 | 1.896 | 0.527 |
ID 21 | 1.354 | 1.673 | 1.869 | 1.955 | - | 1.514 | 1.615 | 1.618 |
ID 22 | 1.120 | 1.654 | 0.961 | 1.388 | 1.354 | - | 1.237 | 1.600 |
ID 23 | 1.255 | 1.965 | 0.734 | 1.586 | 1.581 | 1.082 | - | 1.911 |
ID 24 | 1.981 | 0.149 | 1.810 | 0.881 | 1.254 | 1.455 | 1.498 | - |
ID 25 | 1.935 | 1.383 | 1.655 | 1.834 | 0.397 | 1.925 | 1.904 | 1.364 |
ID 26 | 0.795 | 0.830 | 1.710 | 1.199 | 1.935 | 1.569 | 1.719 | 0.776 |
ID 27 | 1.203 | 1.737 | 1.032 | 1.670 | 1.668 | 0.911 | 1.309 | 1.683 |
ID 28 | 1.925 | 1.554 | 0.822 | 1.903 | 0.909 | 0.817 | 1.652 | 1.413 |
ID 29 | 1.403 | 1.825 | 1.012 | 2.127 | 1.327 | 1.007 | 1.445 | 2.039 |
ID 30 | 1.527 | 1.774 | 0.220 | 2.186 | 1.344 | 0.568 | 1.254 | 1.528 |
ID 31 | 1.821 | 2.302 | 1.509 | 2.460 | 1.840 | 1.504 | 1.509 | 2.022 |
From/To | ID 25 | ID 26 | ID 27 | ID 28 | ID 29 | ID 30 | ID 31 |
---|---|---|---|---|---|---|---|
ID 1 | 2.282 | 3.999 | 2.447 | 2.067 | 1.739 | 1.487 | 1.844 |
ID 2 | 1.694 | 3.161 | 1.815 | 1.474 | 1.195 | 1.487 | 0.807 |
ID 3 | 1.938 | 1.755 | 1.856 | 1.781 | 1.832 | 1.797 | 2.456 |
ID 4 | 1.943 | 3.493 | 2.275 | 2.04 | 1.816 | 1.497 | 1.97 |
ID 5 | 1.953 | 1.859 | 1.636 | 1.562 | 1.56 | 1.577 | 2.166 |
ID 6 | 1.532 | 1.551 | 1.177 | 1.496 | 1.522 | 1.978 | 2.56 |
ID 7 | 1.696 | 1.132 | 1.272 | 1.763 | 1.562 | 1.778 | 2.13 |
ID 8 | 2.203 | 1.628 | 1.662 | 1.67 | 2.04 | 1.474 | 2.32 |
ID 9 | 1.99 | 1.366 | 1.175 | 1.479 | 1.558 | 1.494 | 2.07 |
ID 10 | 1.986 | 2.296 | 1.259 | 0.797 | 1.4 | 0.812 | 1.627 |
ID 11 | 2.167 | 1.776 | 1.106 | 1.549 | 1.408 | 1.564 | 2.253 |
ID 12 | 1.888 | 1.41 | 1.161 | 0.699 | 1.302 | 0.714 | 1.889 |
ID 13 | 0.508 | 2.281 | 1.552 | 1.484 | 1.362 | 1.785 | 1.503 |
ID 14 | 1.462 | 1.731 | 1.108 | 1.427 | 1.454 | 1.909 | 2.336 |
ID 15 | 1.964 | 1.635 | 1.587 | 1.125 | 1.251 | 0.628 | 1.858 |
ID 16 | 1.653 | 1.518 | 0.927 | 0.465 | 1.067 | 0.48 | 1.779 |
ID 17 | 1.808 | 1.581 | 0.604 | 1.117 | 1.72 | 1.132 | 2.223 |
ID 18 | 1.364 | 1.945 | 1.01 | 1.329 | 1.58 | 1.811 | 2.384 |
ID 19 | 1.551 | 1.858 | 0.824 | 0.362 | 0.965 | 0.22 | 1.855 |
ID 20 | 1.62 | 1.352 | 1.549 | 1.868 | 1.788 | 1.774 | 2.967 |
ID 21 | 0.347 | 2.204 | 1.228 | 1.547 | 1.436 | 1.859 | 1.584 |
ID 22 | 1.623 | 1.519 | 0.477 | 0.602 | 1.347 | 1.181 | 2.024 |
ID 23 | 1.85 | 1.689 | 1.558 | 1.096 | 1.137 | 0.514 | 1.743 |
ID 24 | 1.523 | 1.79 | 1.169 | 1.488 | 1.607 | 1.97 | 2.25 |
ID 25 | - | 2.589 | 1.625 | 1.564 | 1.587 | 1.581 | 2.009 |
ID 26 | 1.419 | - | 1.049 | 1.602 | 1.806 | 1.93 | 2.679 |
ID 27 | 1.937 | 1.438 | - | 0.944 | 1.689 | 1.252 | 1.947 |
ID 28 | 1.179 | 2.019 | 1.294 | - | 1.027 | 0.602 | 1.978 |
ID 29 | 1.399 | 2.272 | 1.484 | 1.022 | - | 0.792 | 1.484 |
ID 30 | 1.614 | 1.962 | 1.044 | 0.582 | 0.682 | - | 1.423 |
ID 31 | 1.743 | 2.693 | 1.981 | 1.519 | 0.497 | 1.289 | - |
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Reference | Problem | Application/Area of Application | Features | Objective |
---|---|---|---|---|
Yuan and Gao, 2017 [18] | Location routing | Medical logistic company | Long-haul distribution, uncertainty | Minimization of operational costs |
Kramer et al., 2019 [23] | Rich vehicle routing | Tuscany (Italy) | Regional distribution | Minimization of operational costs |
Campelo et al., 2019 [25] | Consistent Vehicle Routing | Pharmaceutical distribution company | Pharmaceutical cold chain | Minimization of total distance traveled |
Hamdan and Diabat, 2020 [20] | Bi-objective robust design | Jordan | Blood supply chain under disasters | Minimization of time and delivery cost |
Bouziyane et al., 2020 [22] | Multi-objective Disrupted Vehicle Routing with Soft Time Windows | - | Disruption | Minimization of transportation time and delay |
Ahlaqqach et al., 2020 [27] | Multi-objective location | Casablanca (Morocco) | Closed-loop routing supply chain | Maximization of profit and job creation, minimization of risk |
Li and Zhou, 2021 [19] | Multi-objective location | Lianyungang (China) | Regional distribution | Minimization of operational costs, emissions and customer unsatisfaction |
Wu et al., 2021 [21] | Vehicle assingment and routing | Tianjin (China) | Urban distribution (mega-city) | Minimization of total vehicle cost |
Shahparvari et al., 2022 [29] | Allocation and distribution | Melbourne (Australia) | Covid-19 Vaccines distribution | Minimization of risk of infection, vaccine degradation and service time |
Habibi et al., 2022 [30] | Location of distribution centers, inventory policies, and routing decisions | Iran | Covid-19 Vaccines distribution | Minimization of total procurement, inventory, and distribution costs |
Ramos and Vigo, 2023 [31] | Dynamic Parallel Drone Scheduling Vehicle Routing with Lead Time | Portugal | Rural delivery with drones | Minimization of transportation cost |
De Maio et al., 2024 [32] | Autonomous Delivery Robot Routing Problem with Public Transportation | Rome (Italy) | Urban distribution | Minimization of transportation cost |
Lee and Kim, 2024 [24] | Vehicle routing and scheduling with order acceptance | - | Pharmaceutical cold chain | Maximization of profit |
Li et al., 2024 [28] | Vehicle routing | - | Pharmaceutical distribution | Minimization of customer priority, costs, and carbon emissions |
Repolho et al., 2019 [26] | Vehicle routing | Brazil | Pharmaceutical distribution in high-theft-risk areas | Minimization of total costs |
First Tour | Second Tour | Total | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
k | Length | SCT | Emission | Length | SCT | Emission | Length | SCT | Emission | Time |
[km] | [h] | [kg/km] | [km] | [h] | [kg/km] | [km] | [h] | [kg/km] | [s] | |
2 | 4.156 | 0.712 | 1.317 | 19.202 | 4.928 | 1.119 | 23.358 | 4.928 | 2.435 | 1.11 |
3 | 4.132 | 0.792 | 1.309 | 19.202 | 4.844 | 1.119 | 23.334 | 4.844 | 2.428 | 4.75 |
4 | 4.156 | 0.878 | 1.317 | 18.502 | 4.683 | 1.078 | 22.658 | 4.683 | 2.394 | 4.00 |
5 | 4.132 | 0.959 | 1.309 | 18.952 | 4.650 | 1.104 | 23.084 | 4.650 | 2.413 | 3.00 |
6 | 4.133 | 1.043 | 1.309 | 18.830 | 4.553 | 1.097 | 22.963 | 4.553 | 2.406 | 2.57 |
7 | 4.876 | 1.208 | 1.545 | 17.973 | 4.374 | 1.047 | 22.849 | 4.374 | 2.592 | 10.55 |
8 | 5.091 | 1.316 | 1.613 | 18.135 | 4.309 | 1.056 | 23.226 | 4.309 | 2.669 | 9.10 |
9 | 5.834 | 1.482 | 1.848 | 17.278 | 4.131 | 1.006 | 23.112 | 4.131 | 2.855 | 11.67 |
10 | 6.423 | 1.630 | 2.035 | 16.775 | 3.991 | 0.977 | 23.198 | 3.991 | 3.012 | 36.31 |
11 | 7.092 | 1.788 | 2.247 | 15.875 | 3.808 | 0.925 | 22.967 | 3.808 | 3.171 | 27.24 |
12 | 7.842 | 1.955 | 2.484 | 15.027 | 3.630 | 0.875 | 22.869 | 3.630 | 3.360 | 42.00 |
13 | 8.484 | 2.109 | 2.688 | 14.063 | 3.440 | 0.819 | 22.547 | 3.440 | 3.507 | 477.26 |
14 | 9.071 | 2.258 | 2.874 | 14.056 | 3.356 | 0.819 | 23.127 | 3.356 | 3.692 | 234.38 |
15 | 9.821 | 2.425 | 3.111 | 12.889 | 3.143 | 0.751 | 22.710 | 3.143 | 3.862 | 218.47 |
16 | 10.002 | 2.528 | 3.169 | 14.541 | 3.243 | 0.847 | 24.543 | 3.243 | 4.016 | 450.54 |
17 | 10.291 | 2.643 | 3.260 | 14.980 | 3.209 | 0.873 | 25.271 | 3.209 | 4.133 | 800.44 |
18 | 10.918 | 2.796 | 3.459 | 14.206 | 3.039 | 0.827 | 25.124 | 3.039 | 4.286 | 347.18 |
19 | 11.632 | 2.959 | 3.685 | 12.962 | 2.818 | 0.755 | 24.594 | 2.959 | 4.440 | 204.61 |
20 | 12.127 | 3.097 | 3.842 | 12.270 | 2.657 | 0.715 | 24.397 | 3.097 | 4.557 | 120.87 |
21 | 12.634 | 3.237 | 4.002 | 12.003 | 2.544 | 0.699 | 24.637 | 3.237 | 4.702 | 108.72 |
22 | 13.194 | 3.383 | 4.180 | 11.319 | 2.385 | 0.659 | 24.513 | 3.383 | 4.839 | 50.18 |
23 | 13.916 | 3.546 | 4.409 | 9.977 | 2.153 | 0.581 | 23.893 | 3.546 | 4.990 | 35.57 |
24 | 14.659 | 3.712 | 4.644 | 9.224 | 1.986 | 0.537 | 23.883 | 3.712 | 5.181 | 31.78 |
25 | 15.428 | 3.881 | 4.888 | 8.431 | 1.814 | 0.491 | 23.859 | 3.881 | 5.379 | 27.77 |
26 | 16.242 | 4.055 | 5.145 | 7.011 | 1.573 | 0.408 | 23.253 | 4.055 | 5.554 | 26.87 |
27 | 16.685 | 4.187 | 5.286 | 7.315 | 1.524 | 0.426 | 24.000 | 4.187 | 5.712 | 26.10 |
28 | 17.407 | 4.351 | 5.515 | 5.837 | 1.276 | 0.340 | 23.244 | 4.351 | 5.855 | 7.58 |
29 | 18.291 | 4.532 | 5.795 | 4.587 | 1.054 | 0.267 | 22.878 | 4.532 | 6.062 | 3.86 |
30 | 20.193 | 4.827 | 6.397 | 3.020 | 0.796 | 0.176 | 23.213 | 4.827 | 6.573 | 1.29 |
31 | 21.606 | 5.067 | 6.845 | 0.000 | 0.000 | 0.000 | 21.606 | 5.067 | 6.845 | 0.59 |
k | α | β | B | SCT | GAPSCT | CO2 | GAPCO2 | cost | GAPcost |
---|---|---|---|---|---|---|---|---|---|
[EUR] | [h] | [%] | [kg/km] | [%] | [EUR] | [%] | |||
9 | 0.25 | 0.75 | 8.95 | 3.917 | −5.18 | 3.171 | 11.07 | 8.90 | 15.32 |
9 | 0.50 | 0.75 | 10.16 | 3.791 | −8.21 | 3.385 | 18.56 | 9.92 | 28.57 |
15 | 0.25 | 0.75 | 8.95 | 3.143 | 0.00 | 3.862 | 0.00 | 8.75 | 15.39 |
15 | 0.50 | 0.75 | 10.16 | 3.143 | 0.00 | 3.862 | 0.00 | 9.84 | 29.72 |
19 | 0.25 | 0.75 | 8.95 | 3.026 | 2.25 | 4.533 | 2.10 | 8.90 | 8.32 |
19 | 0.50 | 0.75 | 10.16 | 2.988 | 0.97 | 4.453 | 0.29 | 9.97 | 21.44 |
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De Maio, A. A Two-Echelon Routing Model for Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study of Pharmaceutical Distribution in Rome. Mathematics 2024, 12, 2679. https://doi.org/10.3390/math12172679
De Maio A. A Two-Echelon Routing Model for Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study of Pharmaceutical Distribution in Rome. Mathematics. 2024; 12(17):2679. https://doi.org/10.3390/math12172679
Chicago/Turabian StyleDe Maio, Annarita. 2024. "A Two-Echelon Routing Model for Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study of Pharmaceutical Distribution in Rome" Mathematics 12, no. 17: 2679. https://doi.org/10.3390/math12172679
APA StyleDe Maio, A. (2024). A Two-Echelon Routing Model for Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study of Pharmaceutical Distribution in Rome. Mathematics, 12(17), 2679. https://doi.org/10.3390/math12172679