Collaborative Multidepot Vehicle Routing Problem with Dynamic Customer Demands and Time Windows
Abstract
:1. Introduction
2. Literature Review
2.1. VRPDCDTW
2.2. MVRPDCDTW
2.3. CMVRPDCDTW
2.4. Related Solution Methodologies
3. Problem Statement and Model Formulation
3.1. Problem Statement
3.2. Definitions
3.3. Model Formulation
4. Solution Methodology
4.1. Customer Clustering
Algorithm 1: Improved k-medoids clustering |
Input: Set of customers and depots, the number of clustering units k |
Output: k clustering units Steps: (1) Randomly select k customers as medoids (2) Repeat (i) Calculate the distance between medoids and customers (ii) Assign the customers to the nearest clusters (iii) Randomly select customer h to replace medoid i (iv) Calculate the total cost TCih when new clusters are formed (v) If TCih > 0 then Replace medoid i with the customer h and update the set of medoids End (3) Until clustering results no longer change (4) Calculate the distance between each medoid and each depot (5) Assign each clustering unit to the nearest depot (6) Output k clustering units |
4.2. IMOPSO-DIS
Algorithm 2: IMOPSO-DIS |
Input: Clustering units (coordinates, time windows, and demands), i_max (number of maximum iteration), Npop (size of the swarm), Narc (capacity of the external archive), c1 (personal learning coefficient), c2 (global learning coefficient), w (inertia weight), γ (elitist learning rate) |
Output: Nondominated particles in the external archive Steps: (1) Initialize the particles in the swarm P0 (vp,0, xp,0) (2) Evaluate each particle in P0 and Nondominated sorting (P0) (3) Initialize the external archive A0 by nondominated solution maintaining (4) Initialize pbestp,0 and gbest0 (5) While i< i_max do (6) For each particle p = 1: Npop (7) Update the velocity and position by using Equations (33) and (34) (8) Evaluate the new particle (9) Update pbestp,i (10) End for (11) Ai←External archive updating (Ai−1) (12) Select gbesti according to the crowding distance (13) If rand () < γ (14) Update Ai by ELS (15) End If (16) While DCD d appears do (17) For each particle p in Ai (18) xp,i←DIS (d, xp,i) and update Ai (19) End for (20) End while (21) i = i + 1 (22) End while (23) Output results in the external archive |
4.2.1. Particle Updating
4.2.2. Selection of pbest and Nondominated Sorting
Algorithm 3: Nondominated sorting |
Input: Particle swarm P = {p1, p2, p3, …, pj}, rank counter r |
Output: r and a set of particles in different ranks Steps: (1) Initialize rank counter r as 0 (2) Repeat (i) r←r + 1 (ii) Evaluate the particles (iii) Find the nondominated particles from P based on the dominance relationship (iv) Assign rank r to these particles (v) Remove these particles from P (3) Until the P←ø (4) Output the nondominated soring results |
4.2.3. External Archive Updating Strategy and Gbest Selection
Algorithm 4: External archive updating |
Input: External archive Ai−1, new particle swarm P = {p1, p2, p3, …, pj}, Narc |
Output: Updated external archive Ai Steps: (1) Ai←Ai−1 (2) For j= 1: |j| (3) Evaluate the new particle pj (4) If new particle pj is dominated by any particles in Ai (5) New particle pj cannot add to Ai (6) Else (7) Ai←Ai ∪ pj (8) End if (9) End for (10) If |Ai|> Narc (11) Nondominated sorting (Ai) (12) For j = 1: |Ai| (13) Calculate the CD(j) by Equation (38) (14) End for (15) Remove the particle with the lowest CD from Ai (16) End if (17) Output Ai |
4.2.4. ELS
4.2.5. DIS
Algorithm 5: DIS |
Input: External archive Ai−1, new particle swarm P = {p1, p2, p3, …, pj}, Narc |
Output: Updated external archive Ai Steps: (1) While DCDs exist, do (2) For each DCD d (3) Perform the feasibility insertion checks (4) If DCD d can be inserted into xp,i (5) Feasible insertion points in xp,i are found (6) Calculate Δfij(d) after inserting d (7) Choose the insertion point with minimum Δfij(d) as the best insertion point for DCD (8) Else (9) Plan a new route for DCD (10) xp,i←xp,i∪d (11) End If (12) End for (13) Compare the Δfij(d) of each DCD d (14) Insert DCD d with the maximum Δfij(d) into the best insertion point (15) Update xp,i and external archive Ai (16) End while (17) Output the external archive Ai |
5. Implementation and Analysis
5.1. Algorithm Comparison
5.2. Case Study
5.2.1. Data Description and Parameter Setting
5.2.2. Customer Clustering Results
5.2.3. Results of Routing Optimization with Resource Sharing and DIS
5.3. Analysis and Discussion
5.3.1. Results of Different Numbers of Service Periods
5.3.2. Results of Different Optimization Strategies
5.4. Management Insights
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Reference | Problem Features | Objectives | Solution Methods | |||
---|---|---|---|---|---|---|
MD | TW | DCD | RS | |||
Lin (2008) [60] | ✓ | ✓ | Total cost | Insertion-based construction heuristic | ||
Hong (2012) [30] | ✓ | ✓ | Total service cost | large neighborhood search (LNS) | ||
Ghannadpour et al. (2014) [61] | ✓ | ✓ | Total distance, number of vehicles | GA | ||
Li et al. (2014) [62] | ✓ | ✓ | ✓ | Total travel cost | GA with adaptive local search | |
Bae and Moon (2016) [9] | ✓ | ✓ | Total cost | Heuristic algorithm and GA | ||
Mańdziuk and Żychowski (2016) [2] | ✓ | ✓ | Total distance | GA | ||
Okulewicz and Mańdziuk (2017) [29] | ✓ | ✓ | Total cost | PSO | ||
Fernández et al. (2018) [63] | ✓ | ✓ | Total cost | Branch-and-cut algorithm | ||
Chen et al. (2018) [40] | ✓ | ✓ | Total travel cost, fixed costs of vehicles | Adaptive large neighborhood search | ||
Goel et al. (2019) [32] | ✓ | ✓ | Transportation cost | Ant colony system | ||
Li et al. (2019) [64] | ✓ | Revenue, costs, time, and emission | Improved ACO | |||
Vaziri et al. (2019) [55] | ✓ | ✓ | Total profit fairly, travel time | GA and VNS | ||
Xu et al. (2019) [7] | ✓ | Total fuel consumption, customer satisfaction | NSGA-ΙΙ | |||
Xiang et al. (2020) [23] | ✓ | Total traveling cost | ACO-CD | |||
Yang et al. (2020) [48] | ✓ | ✓ | Total cost | Branch-price-and-cut algorithm | ||
Zhang et al. (2020) [65] | ✓ | ✓ | Operating quality, reliability, cost, time | Extended VNS | ||
Wang et al. (2021) [66] | ✓ | ✓ | Total route distance, waiting time | MOEA | ||
Wang et al. (2021) [12] | ✓ | ✓ | ✓ | Logistics operating cost | GA and tabu search (TS) | |
Niu et al. (2021) [24] | ✓ | ✓ | Total cost and customer satisfaction | Membrane-inspired multi-objective algorithm | ||
Zhang et al. (2022) [56] | ✓ | ✓ | ✓ | Total travel cost | branch-and-cut algorithm | |
This study | ✓ | ✓ | ✓ | ✓ | Total operating cost, number of vehicles | IMOPSO-DIS |
Case | TC ($) | DC ($) | PC ($) | IC ($) | MC ($) | TOC ($) | NST | NV |
---|---|---|---|---|---|---|---|---|
Before optimization | 0 | 2160 | 260 | 0 | 1300 | 3720 | 0 | 13 |
After optimization | 480 | 1110 | 0 | 160 | 600 | 2350 | 1 | 4 |
Sets | Definitions |
---|---|
L | Set of depots, L = {i|i = 1, 2, 3, …, a} and a is the total number of depots |
S | Set of SCDs, S = {s|s = 1,2,3, …, h} and h is total number of SCD |
D | Set of DCDs, D = {d|d = 1, 2, 3, …, c} and c is total number of DCD |
C | Set of total customer demands, C = S∪D = {j|j = 1, 2, 3, …, n} n is total number of customer demands |
T | Set of semitrailer trucks, T = {t|t = 1, 2, 3, …, b} and b is total number of trucks |
V | Set of delivery vehicles, V = {v|v = 1, 2, 3, …, g} and g is total number of vehicles |
R | Set of service periods, R = {r|r = 1, 2, 3, …, h} and h is total number of service periods |
, t∈T, r∈R | |
, v∈V, r∈R | |
, r∈R | |
, r∈R | |
Parameters | |
Fi | Fixed cost of depot i, i∈L |
Mt | Average annual maintenance cost of each semitrailer truck |
Mv | Average annual maintenance cost of each vehicle |
Service time windows of the depot i within rth service period, i∈L, r∈R | |
[aj, bj] | Service time windows of the customer j, j∈C |
Qi | Capacity of depot i, i∈L |
Ct | Capacity of semitrailer truck t, t∈T |
Cv | Capacity of delivery vehicle v, v∈V |
Demand of depot i within rth service period, i∈L, r∈R | |
qjv | Demand of customer j for vehicle v, j∈C, v∈V |
dij | Distance from depots or customer i to customer j, i, j∈L∪C |
ft | Diesel fuel consumption per kilometer of semitrailer truck t, t∈T |
fv | Gasoline fuel consumption per kilometer of delivery vehicle v, v∈V |
pt | Diesel price (dollar/gallon) |
pv | Gasoline price (dollar/gallon) |
λd | Insert cost coefficient of DCD |
N | Number of working periods in one year |
ρe | Penalty cost per time unit for early arrival |
ρl | Penalty cost per time unit for delayed arrival |
, r∈R | |
, r∈R | |
, r∈R | |
Request submit time of DCD d within rth service period, d∈D, r∈R | |
Travel time of vehicle v between node i and node j in the kth route, v∈V, i, j∈L∪C, r∈R | |
Decision variables | |
, r∈R | |
, r∈R | |
, t∈T, r∈R | |
, v∈V, r∈R | |
, i∈L, j∈C, v∈V, r∈R |
Instance | Datasets | Number of Depots | Number of SCDs | Number of DCDs | Capacity of Vehicles |
---|---|---|---|---|---|
1 | Pr01-1 | 4 | 41 | 7 | 200 |
2 | Pr01-2 | 4 | 36 | 12 | 200 |
3 | Pr02-1 | 4 | 82 | 14 | 195 |
4 | Pr02-2 | 4 | 72 | 24 | 195 |
5 | Pr03-1 | 4 | 122 | 22 | 190 |
6 | Pr03-2 | 4 | 108 | 36 | 190 |
7 | Pr04-1 | 4 | 163 | 29 | 185 |
8 | Pr04-2 | 4 | 144 | 48 | 185 |
9 | Pr05-1 | 4 | 204 | 36 | 180 |
10 | Pr05-2 | 4 | 180 | 60 | 180 |
11 | Pr06-1 | 4 | 245 | 43 | 175 |
12 | Pr06-2 | 4 | 216 | 72 | 175 |
13 | Pr07-1 | 6 | 61 | 11 | 200 |
14 | Pr07-2 | 6 | 54 | 18 | 200 |
15 | Pr08-1 | 6 | 122 | 22 | 190 |
16 | Pr08-2 | 6 | 108 | 36 | 190 |
17 | Pr09-1 | 6 | 184 | 32 | 180 |
18 | Pr09-2 | 6 | 162 | 54 | 180 |
19 | Pr10-1 | 6 | 245 | 43 | 170 |
20 | Pr10-2 | 6 | 216 | 72 | 170 |
21 | Pr11-1 | 4 | 41 | 7 | 200 |
22 | Pr11-2 | 4 | 36 | 12 | 200 |
23 | Pr12-1 | 4 | 82 | 14 | 195 |
24 | Pr12-2 | 4 | 72 | 24 | 195 |
25 | Pr13-1 | 4 | 122 | 22 | 190 |
26 | Pr13-2 | 4 | 108 | 36 | 190 |
Instance | IMOPSO-DIS | MOPSO | NSGA-ΙΙ | MOEA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
TOC ($) | NV | WT (min) | TOC ($) | NV | WT (min) | TOC ($) | NV | WT (min) | TOC ($) | NV | WT (min) | |
1 | 3133 | 4 | 33.44 | 3760 | 4 | 36.44 | 6819 | 5 | 48.44 | 4222 | 4 | 37.62 |
2 | 3983 | 4 | 41 | 4381 | 4 | 46.00 | 7245 | 5 | 58.00 | 5062 | 5 | 46.04 |
3 | 5985 | 5 | 65.47 | 6584 | 6 | 66.47 | 10,810 | 7 | 67.47 | 9071 | 7 | 65.92 |
4 | 5564 | 5 | 62.23 | 6677 | 6 | 61.23 | 9480 | 8 | 74.23 | 9213 | 7 | 63.49 |
5 | 7315 | 9 | 77.98 | 8046 | 10 | 82.98 | 11,616 | 10 | 81.98 | 10,342 | 10 | 78.56 |
6 | 8156 | 10 | 74.48 | 9787 | 11 | 89.48 | 18,952 | 12 | 93.48 | 12,931 | 11 | 81.02 |
7 | 11,171 | 15 | 86.14 | 13,405 | 16 | 106.14 | 20,060 | 16 | 102.14 | 21,895 | 16 | 100.08 |
8 | 12,205 | 16 | 97.66 | 13,425 | 17 | 101.66 | 17,209 | 19 | 101.66 | 22,250 | 17 | 109.14 |
9 | 15,869 | 18 | 88.70 | 17,456 | 18 | 95.70 | 24,179 | 20 | 106.70 | 27,893 | 20 | 98.15 |
10 | 16,163 | 20 | 91.47 | 19,396 | 20 | 92.47 | 25,026 | 22 | 116.47 | 26,180 | 21 | 97.61 |
11 | 17,452 | 23 | 141.07 | 19,197 | 23 | 146.07 | 27,738 | 25 | 152.07 | 25,464 | 25 | 155.74 |
12 | 18,674 | 24 | 146.19 | 20,541 | 25 | 150.19 | 28,563 | 26 | 159.19 | 26,738 | 26 | 159.27 |
13 | 7873 | 6 | 59.65 | 8660 | 7 | 68.65 | 11,049 | 11 | 76.65 | 10,896 | 11 | 70.27 |
14 | 7955 | 6 | 64.79 | 9546 | 7 | 81.79 | 11,934 | 11 | 87.79 | 11,991 | 11 | 73.12 |
15 | 10,132 | 10 | 91.37 | 12,159 | 13 | 94.37 | 20,535 | 15 | 102.37 | 22,193 | 15 | 95.44 |
16 | 10,999 | 11 | 84.53 | 13,199 | 14 | 87.53 | 25,576 | 16 | 101.53 | 23,085 | 16 | 109.82 |
17 | 23,275 | 14 | 160.55 | 25,602 | 16 | 164.55 | 28,697 | 18 | 179.55 | 28,372 | 17 | 164.92 |
18 | 24,105 | 16 | 167.33 | 26,516 | 17 | 186.33 | 26,124 | 17 | 174.33 | 29,190 | 18 | 178.90 |
19 | 30,852 | 25 | 213.27 | 33,937 | 25 | 219.27 | 36,706 | 26 | 232.27 | 37,866 | 25 | 221.19 |
20 | 33,945 | 25 | 204.97 | 37,339 | 26 | 213.97 | 36,461 | 27 | 205.97 | 38,975 | 26 | 236.64 |
21 | 3149 | 4 | 32.58 | 3788 | 4 | 36.48 | 6832 | 5 | 50.96 | 4363 | 5 | 38.30 |
22 | 4075 | 4 | 45.76 | 4475 | 4 | 49.84 | 7269 | 5 | 53.84 | 5153 | 5 | 47.78 |
23 | 6084 | 5 | 66.46 | 6620 | 6 | 63.36 | 10,794 | 7 | 66.67 | 9167 | 7 | 63.77 |
24 | 5960 | 5 | 63.51 | 6657 | 6 | 64.37 | 9477 | 7 | 74.54 | 9665 | 7 | 73.07 |
25 | 7326 | 9 | 79.21 | 8121 | 10 | 89.79 | 11,508 | 10 | 89.50 | 10,364 | 11 | 87.59 |
26 | 7893 | 9 | 81.67 | 9861 | 11 | 94.59 | 18,977 | 11 | 90.57 | 15,971 | 11 | 96.18 |
Average | 11,896 | 12 | 93 | 13,428 | 13 | 100 | 18,063 | 14 | 105.71 | 17,635 | 14 | 101.91 |
t-test | −8.63 | −9.34 | −8.00 | |||||||||
p-value | 2.85× 10−9 | 6.31 × 10−10 | 1.17 × 10−8 |
Symbols | Depots/Customers | Number of Customers | Type of Demands |
---|---|---|---|
| D1 and its customers | 44 | SCD |
| D2 and its customers | 36 | DCD |
| D3 and its customers | 43 | SCD |
| D4 and its customers | 34 | DCD |
| D5 and its customers | 43 | SCD |
Notation | Definition | Value |
---|---|---|
Parameters in the proposed model | ||
Ct | Capacity of the semitrailer truck | 2000 |
Cv | Capacity of the delivery vehicle | 200 |
Mt | MC of semitrailer truck | 1000 |
Mv | MC of delivery vehicle | 200 |
ρe | PC of early arrival per unit time | 10 |
ρl | PC of late arrival per unit time | 15 |
ft | Fuel consumption of semitrailer truck | 0.25 |
fv | Fuel consumption of delivery vehicle | 0.2 |
pt | Diesel price | 40 |
pv | Gasoline price | 30 |
Parameters in the proposed algorithm | ||
Npop | Swarm size | 100 |
run_max | Maximum number of runs | 500 |
i_max | Maximum number of iterations | 100 |
Narc | The external archive size | 40 |
c1 | Personal acceleration coefficient | 1 |
c2 | Global acceleration coefficient | 1.5 |
wmin | Lower bound of inertia weight | 0.4 |
wmax | Upper bound of inertia weight | 0.9 |
Depots | DC ($) | PC ($) | MC ($) | FC ($) | TOC ($) | NV |
---|---|---|---|---|---|---|
D1 | 12,010.51 | 762.14 | 900 | 200 | 13,872.65 | 9 |
D2 | 9236.37 | 847.83 | 700 | 300 | 11,084.2 | 7 |
D3 | 11,840.33 | 777.37 | 900 | 200 | 13,717.7 | 9 |
D4 | 8965.2 | 971.98 | 700 | 300 | 10,937.18 | 7 |
D5 | 9844.87 | 1454.58 | 900 | 200 | 12,399.45 | 9 |
Total | 51,897.28 | 4813.9 | 4100 | 1200 | 62,011.18 | 41 |
Depots | Service Periods | DC ($) | PC ($) | IC ($) | Number of Routes |
---|---|---|---|---|---|
D1 | 1st | 2830.86 | 59.49 | 850 | 3 |
2nd | 1025.47 | 9.43 | 85 | 2 | |
3rd | 2179.1 | 122.92 | 337.5 | 3 | |
Total | 6035.43 | 191.84 | 1272.5 | 8 | |
D2 | 1st | 2779.11 | 46.97 | 645 | 3 |
2nd | 1975.38 | 129.94 | 370 | 2 | |
3rd | 336.5 | 39.5 | 290 | 2 | |
Total | 5090.99 | 216.41 | 1305 | 7 | |
D3 | 1st | 1278.1 | 2.077 | 207.5 | 1 |
2nd | 1540.87 | 41.56 | 370 | 2 | |
3rd | 2100.61 | 333.03 | 357.5 | 3 | |
Total | 4919.58 | 376.66 | 935 | 6 | |
D4 | 1st | 303.02 | 22.18 | 377.5 | 1 |
2nd | 1816 | 129.02 | 877.5 | 2 | |
3rd | 2018.05 | 212.87 | 177.5 | 2 | |
Total | 4137.07 | 364.07 | 1432.5 | 5 | |
D5 | 1st | 2587.51 | 67.87 | 517.5 | 2 |
2nd | 3438.3 | 162.46 | 765 | 3 | |
3rd | 2267.1 | 130.3 | 172.5 | 2 | |
Total | 8292.91 | 360.63 | 1455 | 7 | |
Total | 28,475.98 | 1509.61 | 6400 | 33 |
Depots | Optimized Vehicle Routes | Number of Routes |
---|---|---|
D1 | R1: D1→C87→C31 *→C143→C30 *→C85→C168 *→D1 R2: D1→C6 *→C129→C128→C75→C1 *→D1 R3: D1→C140→C7 *→C27 *→C139→C72→D1 R4: D1→C71→C86→C23 *→C167 *→C141→D1 R5: D1→C5 *→C142→C84→C73→D1 R6: D1→C60→C2 *→C147→C150→C13 *→D1 R7: D1→C148→C28 *→C149→C177 *→C29 *→C146→D1 R8: D1→C151→C152→C92→C63→D1 | 8 |
D2 | R9: D2→C94→C105→C137→C80→C43 *→C34 *→D2 R10: D2→C136→C39→C40→C9 *→C4 *→C124→D2 R11: D2→C35 *→C132→C74→C77→C33 *→D2 R12: D2→C178 *→C135→C81→C179 *→C83→C138→C127→D2 R13: D2→C90→C26 *→C59→C25 *→C123→C42→D2 R14: D2→C130→C3 *→C125→C8 *→C133→C37→D2 R15: D2→C82→C131→C134→C10 *→C38→C91→C180 *→C126→C52→D2 | 7 |
D3 | R16: D3→C51→C104→C184 *→C106→C69→C122→C120→D3R 17: D3→C44→C46→C107→C164→C166→C79→D3 R18: D3→C48→C175 *→C183 *→C121→D3 R19: D3→C47→C108→C110→C32 *→D3 R20: D3→C57→C20 *→C162→C109→C200→C68→C119→D3 R21: D3→C196 *→C198 *→C195 *→D3 | 6 |
D4 | R22: D4→C111→C67→C159→C117→C118→C193 *→C78→D4 R23: D4→C186 *→C116→C197 *→C66→C19 *→C161→C172 *→D4 R24: D4→C54→C112→C113→C190 *→C103→C187 *→C18 *→C163→D4 R25: D4→C174 *→C61→C157→C188 *→C158→C189 *→D4 R26: D4→C53→C114→C191 *→C115→C194 *→C192 *→C160→D4 | 5 |
D5 | R27: D5→C65→C97→C45→C182 *→C12 *→C95→C58→C176 *→D5 R28: D5→C165→C181 *→C41→C55→C76→C62→C170 *→C21 *→C96→D5 R29: D5→C89→C171 *→C11 *→C88→C199 *→C70→C22 *→D5 R30: D5→C145→C14 *→C98→C144→C169 *→C99→D5 R31: D5→C50→C153→C36 *→C154→C155→C49→C185 *→D5 R32: D5→C17 *→C93→C15 *→C156→C16 *→C100→C173 *→D5 R33: D5→C56→C102→C64→C24 *→C101→D5 | 7 |
Cases | TC ($) | DC ($) | PC ($) | IC ($) | FC ($) | MC ($) | TOC ($) | NT | NV |
---|---|---|---|---|---|---|---|---|---|
Before optimization | 0 | 51,897.29 | 4813.9 | 0 | 1200 | 4100 | 62,011.18 | 0 | 41 |
After optimization | 5147.36 | 28,475.98 | 1509.61 | 3840 | 1200 | 1700 | 41,872.97 | 1 | 12 |
Case | tn(h) | Time Windows | |||
---|---|---|---|---|---|
r = 1 | r = 2 | r = 3 | r = 4 | ||
1 | 20 | [0, 24] | -- | -- | -- |
2 | 10 | [0, 12] | [12, 24] | -- | -- |
3 | 6 | [0, 8] | [8, 16] | [16, 24] | -- |
4 | 5 | [0, 6] | [6, 12] | [12, 18] | [18, 24] |
Service Period | r = 1 | r = 2 | r = 3 | r = 4 | ||||
---|---|---|---|---|---|---|---|---|
TOC ($) | NV | TOC ($) | NV | TOC ($) | NV | TOC ($) | NV | |
1st | 53,729.84 | 38 | 22,930.3 | 18 | 14,788.66 | 10 | 13,099.91 | 9 |
2nd | -- | -- | 21,193.69 | 20 | 12,871.24 | 11 | 10,968.88 | 8 |
3rd | -- | -- | -- | -- | 14,213.07 | 12 | 11,513.1 | 8 |
4th | -- | -- | -- | -- | -- | -- | 10,903.7 | 9 |
Total | 53,729.84 | 38 | 44,123.99 | 20 | 41,872.97 | 12 | 46,485.59 | 9 |
Case | TOC | NV | NST | CSS | TRS | DIS |
---|---|---|---|---|---|---|
1 | 62,011.18 | 41 | 0 | |||
2 | 46,440.32 | 37 | 3 | ✓ | ||
3 | 43,240.32 | 15 | 1 | ✓ | ✓ | |
4 | 41,872.97 | 12 | 1 | ✓ | ✓ | ✓ |
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Wang, Y.; Zhe, J.; Wang, X.; Sun, Y.; Wang, H. Collaborative Multidepot Vehicle Routing Problem with Dynamic Customer Demands and Time Windows. Sustainability 2022, 14, 6709. https://doi.org/10.3390/su14116709
Wang Y, Zhe J, Wang X, Sun Y, Wang H. Collaborative Multidepot Vehicle Routing Problem with Dynamic Customer Demands and Time Windows. Sustainability. 2022; 14(11):6709. https://doi.org/10.3390/su14116709
Chicago/Turabian StyleWang, Yong, Jiayi Zhe, Xiuwen Wang, Yaoyao Sun, and Haizhong Wang. 2022. "Collaborative Multidepot Vehicle Routing Problem with Dynamic Customer Demands and Time Windows" Sustainability 14, no. 11: 6709. https://doi.org/10.3390/su14116709