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In recent years, emergency events have affected urban distribution with increasing frequency. For example, the 2019 novel coronavirus has caused a considerable impact on the supply guarantee of important urban production and living materials, such as petrol and daily necessities. On this basis, this study establishes a dual-objective mixed-integer linear programming model to formulate and solve the cooperative multidepot petrol emergency distribution vehicle routing optimization problem with multicompartment vehicle sharing and time window coordination. As a method to solve the model, genetic variation of multiobjective particle swarm optimization algorithm is considered. The effectiveness of the proposed method is analyzed and verified by first using a small-scale example and then investigating a regional multidepot petrol distribution network in Chongqing, China. Cooperation between petrol depots in the distribution network, customer clustering, multicompartment vehicle sharing, time window coordination, and vehicle routing optimization under partial road blocking conditions can significantly reduce the total operation cost and shorten the total delivery time. Meanwhile, usage of distribution trucks is optimized in the distribution network, that is, usage of single- and double-compartment trucks is reduced while that of three-compartment trucks is increased. This approach provides theoretical support for relevant government departments to improve the guarantee capability of important materials in emergencies and for relevant enterprises to improve the efficiency of emergency distribution.

The collaborative multidepot petrol distribution vehicle routing problem under emergency conditions (CMPDVRPE) is an extension of the multidepot petrol station replenishment problem (MPSRP) [

In the existing petrol distribution network, each depot is only responsible for specific petrol stations (PSs) in the region. PDs are independent of each other and lack coordination and sharing of distribution business and resources. In an emergency, roadblocks cause detours for several distribution trucks, resulting in low distribution efficiency and timeliness of the entire network. Furthermore, in such cases, petrol is an important and necessary material, such as the replenishment demand of vehicles for disaster relief and medical treatment, and thus, ensuring its efficient and timely supply is of considerable significance for rescue and recovery. Therefore, cooperation between regional PDs must be enhanced and the routing arrangement of distribution trucks should be optimized through resource sharing and business coordination of multidepots on the premise of partial road blocking. This cooperation can effectively reduce the operation cost of the entire petrol distribution network, improve the efficiency of emergency petrol distribution in the region, shorten the total distribution time in the region, and ensure the timely supply of important production and living materials such as petrol.

In this study, multicompartment truck sharing (TS), TWC, truck route detour, and a cooperation mechanism are integrated into the traditional MPSRP as CMPDVRPE. An optimal mathematical model is established to minimize the total operating cost and total delivery time to optimize the CMPDVRPE and get good results. An improved multiobjective particle swarm optimization (MOPSO) algorithm considering genetic variation (GV) is designed to achieve the near-optimal solution. Correlation results before and after optimization are compared and analyzed, and the solution of CMPDVRPE can improve the efficiency and rationality of vehicle routing arrangement of petrol distribution networks. First, petrol products have special distribution natures, such as product diversification, and cannot be mixed. Second, multidepot cooperation, multicompartment vehicle use, different TWC mechanisms, and vehicle routing optimization are comprehensively considered to propel the sustainable development of vehicle routing problem (VRP) theory [

The remaining parts of this paper are organized as follows. In Section

In the past few decades, relatively little research has been carried out on petrol replenishment in academic circles. Existing research focuses on the distribution of petrol in a single depot and the variations of PS replenishment problem. For example, the multiperiod, time window (TW), trip packing, and multidepot with TWS are separately considered for PSRP [

The above studies directly relate to the replenishment problem of PSs. However, the models mainly considered the multicompartment vehicle transportation and time window assignment (TWA). Huang [

One part of CMPDVRPE literature focuses on the cooperation in distribution networks, which largely influences the arrangement of vehicle routes and the entire network efficiency. Wang et al. [

Another part of the CMPDVRPE literature focuses on the VRP in emergency distributions. Sheu [

Generally speaking, the mathematical model of VRP is hard NP, which requires solutions using appropriate algorithms. Kuo et al. [

The above studies tackle plentiful MPSRP aspects but suffer from the following issues. (1) The vehicle routing optimized design procedure rarely considers the cooperation among PDs by regional partitioning. (2) Minimal attention is paid to distribution TS, multicompartment truck application, roadblocks, and transship transportation in a collaborative multidepot optimization network. (3) Single intelligent algorithm and heuristic approach are difficult to apply directly to a specific scale of CMPDVRPE with numerous PSs.

Combining observations in Table

Comparison between existing literature and the present study.

Study | Regional partitioning | Stations per trip | Time windows | Multicompartment | Fleet sharing | Emergency conditions |
---|---|---|---|---|---|---|

Cornillier et al. [ | No | Several | Yes | Yes | No | No |

Govindan et al. [ | No | Several | Yes | No | No | No |

Lahyani et al. [ | No | Several | No | Yes | No | No |

Wang et al. [ | No | Several | Yes | No | Yes | No |

Zhang et al. [ | No | Several | No | No | No | Yes |

Wang et al. [ | No | Several | No | Yes | No | No |

Xu et al. [ | Yes | One | Yes | Yes | Yes | No |

This study | Yes | Several | Yes | Yes | Yes | Yes |

CMPDVRPE integrates the problems of cooperative VRP, TS, roadblocks, and TWAs. Figure

Noncooperative petrol distribution network.

Figure

Cooperative petrol distribution network.

Based on the regional partitioning method, the transport time between PDs and stations is used to cluster corresponding PSs. Then appropriate distribution trucks are selected and distribution routes are arranged according to the demand of different petrol, demand TW, and roadblocks to each PS.

Seven assumptions underline the corresponding mathematical model. (1) In a relatively short working period, each PS only generates one distribution order for petrol demand. For each kind of petrol, the demand does not exceed the maximum loading capacity of most distribution truck compartments. (2) Each customer (PS) can only be served once in a working period, that is, only one distribution truck is used for its delivery service. (3) The petrol transfer and distribution trucks have constant transportation speed. (4) During a working period, distribution trucks may be dispatched repeatedly if time permits, regardless of the transfer time across PDs. (5) The loading and unloading service times of PDs and stations are related not to the petrol type but to the truck type and operational quantity. (6) Every 10 minutes is the time unit. (7) No consideration is given to the restriction of road geometry on multicompartment vehicles.

The proposed model is mathematically formulated as an optimization problem to minimize the total cost and delivery time when each PD is assigned to serve a group of PSs and VRP with different trucks and TWS [

Notations and definitions in CMPDVRPE.

Symbol | Description |
---|---|

Set of petrol depot, | |

Set of petrol station, | |

Set of petrol, | |

Set of petrol tanker, | |

Set of petrol distribution truck, | |

Fuel consumption per time unit of a petrol tanker, | |

Fuel consumption per time unit of petrol distribution truck, | |

Fuel price | |

Loading capacity of petrol tanker, | |

The loading capacity of single compartment of truck | |

The transport time from petrol depot g to | |

The transport time from the depot to the petrol station or from the petrol station to another, | |

The working hours of petrol depot | |

The service time window of petrol station, | |

The departure time of distribution truck | |

The time of distribution truck | |

The driving time of distribution truck | |

T | The maximum travel time allowed for each distribution truck |

The penalty cost per unit of time for distribution trucks arriving early | |

The penalty cost per unit of time for distribution trucks arriving late | |

The annual maintenance cost of a petrol tanker, | |

The annual maintenance cost of distribution truck | |

During a working period, the amount of petrol | |

During a working period, the demand of petrol station | |

During a working period, the amount of petrol | |

Integer variable, the number of compartments of distribution truck | |

Service capacity of depot | |

The fixed cost of petrol depot | |

The number of distribution trucks at petrol depot | |

The number of compartments for distribution trucks, | |

The number of working periods per year |

Judgement variables.

Decision variables | Definition |
---|---|

When the distribution truck | |

When the petrol tanker | |

When the petrol station | |

When the distribution truck | |

When the serving petrol depot of petrol station | |

When depot |

CMPDVRPE is formulated as a mixed-integer linear programming model to minimize the total cost and delivery time. The cost function contains four components, namely,

Equation (

Equation (

Equation (

Equation (

The optimization model of CMPDVRPE is defined as follows:

Equations

As a method of evolutionary computing, PSO was proposed in 1995 by Eberhart, an American electrical engineer, and Kenndey, a social psychologist. By observing the foraging behavior of birds, the authors believed that at first, the birds do not know where the food but come closer and closer to the food through a kind of information exchange. This information includes the adaptability of each bird to estimate its own position according to certain rules, ability of each bird to remember its best position, and the best position found by all the birds in the flock. The best position found by the bird group is called individual optimal “

In PSO, the entire population is called particle swarm, and each individual in the population is called a particle. The target is a search space, and the position of each particle is a potentially feasible solution. Each particle in space adjusts its flight path based on personal and group experience to find the optimal solution.

Suppose the population is composed of

The single-objective optimization problem only needs to obtain a single or a set of continuous optimal solutions, while the multiobjective optimization problem generally obtains a set of continuous solutions. For the basic PSO, all particles converge in one direction following the best particle (leader), and thus, the single-objective optimization problem can be solved. When solving the multiobjective optimization problem,

In fact, the solution of the multiobjective optimization problem is composed of a set of noninferior solutions. Different particles seek different “leaders” in the optimization. The noninferior solutions are stored in the “external container” (archive). Furthermore, by evaluating the “quality” of these solutions, the

MOPSO is a cyclic process. When the algorithm starts, the first-generation noninferior solution is found from the initialized particle swarm and stored in the external archive. Subsequently, the

Based on the generation of new nondominant solutions after each particle iteration, the external archive set size, and thereby the computation, increases after multiple iterations. Therefore, considering the effect of computational complexity, limiting the size of external collections is necessary [

In solving MOPSO, the evaluation criteria of particles, construction, and preservation of noninferior solutions, selection of optimal positions, and the processing of constraints are mainly used.

PSO is characterized by rapid convergence speed, but for a multiobjective optimization problem, too fast convergence speed may cause particles to fall into the local optimal. Thus, achieving the global optimal becomes difficult. This problem may be prevented by introducing the mutation operation of particles.

In the early stage of the algorithm, the particle needs to search the entire target space to ensure the escape from the local optimal state and enhance the global search capability; in the late stage, a quick convergence is necessary to find the optimal solution. Thus, this study carries out mutation operation on particles through mutation probability. At the beginning of the algorithm, mutation should be carried out on all particles, and with the increase of iteration, the number of particles undergoing mutation should be gradually reduced. According to the variation operation requirements, the variation probability of particle swarm after each update is set as follows [

In equation (

In addition, to balance the global and local search capability of basic PSO, adding inertia weight is necessary [

Combined with the basic PSO algorithm and MOPSO, Figure

Initialization: set the particle swarm size, parameter coefficient, threshold, maximum number of iterations, and initial velocity and initial position of each particle.

Use equations (

Calculate the fitness value of each particle.

Construct the set of noninferior solutions of particle swarm according to the construction algorithm of noninferior solutions.

Update the

Update the external archive set according to the saving algorithm of noninferior solution.

Calculate the crowding distance of particles in the external archive. If the number of particles entering the external archive reaches the upper limit of the external archive size, the particles beyond the upper limit of the external archive size are removed in ascending crowding distance order.

Update the

Update the particle velocity and position according to equations (

Flowchart of the IMOPSO algorithm.

The quality of the proposed heuristic algorithm in solving the problem of multidepot vehicle routing with emergency effects is further demonstrated by a small example analysis. In this case, the petrol distribution network consists of two PDs and 31 PSs in the region. Under noncooperation, PD

For the convenience of calculation, the following assumption is made for this example: the demand of petrol product of PSs is divided into three categories, namely, nos. 92, 95, and 98. The distribution trucks have three types: single compartment with a capacity of 2,000 gallons, double compartment with a capacity of 1,500 gallons, and three compartments with a capacity of 1,500 gallons. Each time unit represents 10 minutes, and the transportation cost per unit time is $50 for a single-compartment truck, $70 for a double-compartment truck, and $80 for a three-compartment truck. The fixed cost of single-compartment truck, double-compartment truck, and three-compartment truck is $20, $30, and $40, respectively. In addition, considering the customer demand TW, the penalty cost of the distribution truck arriving early per unit time is $10, and the penalty cost of the distribution truck arriving late per unit time is $15. The single assignment cost of the distribution truck is $20. For example, the vehicle route P ⟶ Q4 ⟶ P7 ⟶ P6 ⟶ P uses a three-compartment vehicle, the entire route vehicle needs to run 11 time units, transportation cost is $880, fixed cost is $40, and the vehicle assignment cost is $20. According to (

Table

Comparison of relative indexes of multidepot petrol distribution network in a small-scale example.

Condition | Total delivery time (minutes) | Number of trucks required for distribution | Fixed cost (USD) | Transportation cost (USD) | Penalty cost (USD) | Total cost (USD) | ||
---|---|---|---|---|---|---|---|---|

Single-compartment | Double-compartment | Three-compartment | ||||||

Noncooperative | 2240 | 12 | 15 | 4 | 1470 | 15180 | — | 16650 |

Cooperative | 1080 | 2 | 4 | 8 | 760 | 7800 | 350 | 8910 |

In this section, a numerical experiment is applied to a large-scale multidepot petrol distribution network in Chongqing, China. The urban petrol distribution network in Chongqing municipality, which is directly under the jurisdiction of western China, is selected as the experimental object to demonstrate the effectiveness of IMOPSO in solving the vehicle routing optimization for the emergency joint distribution of multidepot. In this case, the petrol distribution network consists of five PDs (PD1, PD2, …, PD5) and 86 PSs (PS1, PS2, …, PS86). Figure

Distribution network diagram of multidepot and multistation.

PSs served by different PDs before optimization.

PD | PS |
---|---|

PD1 | PS1 PS2 PS3 PS4 PS5 PS6 PS7 PS19 PS20 PS29 PS30 PS57 PS58 PS59 PS66 PS67 PS68 PS69 PS70 |

PD2 | PS8 PS9 PS14 PS15 PS16 PS17 PS18 PS31 PS32 PS33 PS71 PS72 PS73 PS74 PS75 PS76 PS77 PS78 |

PD3 | PS10 PS11 PS21 PS22 PS23 PS24 PS25 PS26 PS27 PS28 PS45 PS46 PS60 PS61 PS62 PS79 PS80 PS81 PS82 |

PD4 | PS34 PS35 PS36 PS39 PS40 PS41 PS42 PS43 PS44 PS63 PS64 PS65 PS83 PS84 |

PD5 | PS12 PS13 PS37 PS38 PS47 PS48 PS49 PS50 PS51 PS52 PS53 PS54 PS55 PS56 PS85 PS86 |

As mentioned in the previous Section

TW demand of PS.

PS | Demand TW | PS | Demand TW | PS | Demand TW |
---|---|---|---|---|---|

PS1 | [10, 16] | PS30 | [7, 13] | PS59 | [19, 24] |

PS2 | [8, 14] | PS31 | [13, 18] | PS60 | [17, 23] |

PS3 | [11, 17] | PS32 | [10, 16] | PS61 | [12, 17] |

PS4 | [16, 22] | PS33 | [17, 23] | PS62 | [9, 14] |

PS5 | [7, 13] | PS34 | [8, 14] | PS63 | [14, 19] |

PS6 | [14, 20] | PS35 | [12, 17] | PS64 | [13, 18] |

PS7 | [12, 18] | PS36 | [15, 21] | PS65 | [10, 15] |

PS8 | [10, 15] | PS37 | [9, 14] | PS66 | [7, 12] |

PS9 | [6, 12] | PS38 | [16, 22] | PS67 | [18, 23] |

PS10 | [15, 21] | PS39 | [11, 17] | PS68 | [6, 11] |

PS11 | [17, 23] | PS40 | [14, 20] | PS69 | [11, 16] |

PS12 | [9, 15] | PS41 | [6, 11] | PS70 | [10, 15] |

PS13 | [12, 17] | PS42 | [18, 24] | PS71 | [16, 21] |

PS14 | [18, 24] | PS43 | [10, 16] | PS72 | [15, 20] |

PS15 | [8, 13] | PS44 | [8, 13] | PS73 | [8, 13] |

PS16 | [16, 21] | PS45 | [15, 21] | PS74 | [10, 16] |

PS17 | [10, 16] | PS46 | [12, 18] | PS75 | [12, 17] |

PS18 | [15, 20] | PS47 | [7, 12] | PS76 | [19, 24] |

PS19 | [11, 17] | PS48 | [19, 24] | PS77 | [14, 19] |

PS20 | [17, 23] | PS49 | [9, 15] | PS78 | [9, 15] |

PS21 | [7, 12] | PS50 | [14, 20] | PS79 | [11, 17] |

PS22 | [14, 19] | PS51 | [8, 14] | PS80 | [16, 22] |

PS23 | [9, 15] | PS52 | [18, 23] | PS81 | [13, 19] |

PS24 | [17, 22] | PS53 | [11, 17] | PS82 | [7, 13] |

PS25 | [15, 21] | PS54 | [17, 23] | PS83 | [15, 21] |

PS26 | [11, 16] | PS55 | [10, 16] | PS84 | [10, 16] |

PS27 | [13, 19] | PS56 | [12, 18] | PS85 | [8, 14] |

PS28 | [19, 24] | PS57 | [16, 21] | PS86 | [15, 20] |

PS29 | [18, 23] | PS58 | [7, 13] |

PS demand for different petrol types during a working period.

PS | Petrol demand (gallons) | ||
---|---|---|---|

92 | 95 | 98 | |

PS1 | 1309 | 691 | — |

PS2 | 2781 | 933 | 422 |

PS3 | 857 | 334 | 182 |

PS4 | 1289 | — | 157 |

PS5 | 2387 | 491 | 806 |

PS6 | 2576 | 327 | 969 |

PS7 | 2891 | 383 | 262 |

PS8 | 1989 | — | — |

PS9 | 1467 | 1028 | 946 |

PS10 | 1510 | 1351 | 721 |

PS11 | 1016 | 1258 | 730 |

PS12 | 1010 | 879 | 376 |

PS13 | 1696 | 411 | 607 |

PS14 | 1557 | 1066 | 312 |

PS15 | 2335 | 1194 | 690 |

PS16 | 632 | 1137 | 691 |

PS17 | 1635 | 816 | 228 |

PS18 | 2372 | 288 | 993 |

PS19 | 694 | 658 | 949 |

PS20 | 2481 | 452 | — |

PS21 | 1570 | 1064 | 829 |

PS22 | 1736 | 752 | — |

PS23 | 1949 | 925 | 577 |

PS24 | 2774 | 1298 | 182 |

PS25 | 1783 | 1126 | 277 |

PS26 | 2935 | 907 | 667 |

PS27 | 2830 | — | 971 |

PS28 | 875 | 1383 | 214 |

PS29 | 1791 | — | 597 |

PS30 | 1967 | 794 | 154 |

PS31 | 2058 | 520 | 930 |

PS32 | 2024 | 346 | — |

PS33 | 770 | 297 | 225 |

PS34 | 927 | 322 | 651 |

PS35 | 2955 | 1060 | 727 |

PS36 | 515 | 1246 | 924 |

PS37 | 1684 | 941 | 474 |

PS38 | 1326 | 539 | 972 |

PS39 | 1672 | 839 | 694 |

PS40 | 574 | 959 | 686 |

PS41 | 680 | — | 493 |

PS42 | 982 | 478 | — |

PS43 | 1485 | 1345 | 261 |

PS44 | 1609 | 282 | 237 |

PS45 | 1931 | 1387 | 690 |

PS46 | 1887 | 1223 | 221 |

PS47 | 2260 | 1082 | 348 |

PS48 | 528 | 456 | 194 |

PS49 | 1753 | 354 | — |

PS50 | 2558 | 410 | 549 |

PS51 | 2782 | 1264 | 1000 |

PS52 | 507 | 1096 | 953 |

PS53 | 2366 | 1117 | 533 |

PS54 | 885 | — | 845 |

PS55 | 639 | 292 | — |

PS56 | 513 | — | 656 |

PS57 | 667 | — | 678 |

PS58 | 2700 | 507 | 456 |

PS59 | 919 | 1330 | — |

PS60 | 962 | 1372 | 645 |

PS61 | 1105 | 830 | — |

PS62 | 997 | 1199 | 468 |

PS63 | 2431 | 874 | 967 |

PS64 | 646 | 787 | 663 |

PS65 | 2449 | — | 439 |

PS66 | 732 | 1186 | 865 |

PS67 | 2892 | 1191 | 386 |

PS68 | 2473 | 711 | 783 |

PS69 | 1801 | 740 | 464 |

PS70 | 2396 | — | 871 |

PS71 | 2428 | 879 | 223 |

PS72 | 1852 | 631 | 685 |

PS73 | 1917 | 1357 | 436 |

PS74 | 756 | 970 | 334 |

PS75 | 2244 | 926 | 674 |

PS76 | 1300 | 361 | — |

PS77 | 1028 | 717 | 942 |

PS78 | 577 | 563 | — |

PS79 | 791 | 1209 | 547 |

PS80 | 2832 | 266 | 892 |

PS81 | 640 | 1301 | 912 |

PS82 | 2084 | 683 | 387 |

PS83 | 522 | — | 619 |

PS84 | 1108 | 1202 | 430 |

PS85 | 833 | 837 | 919 |

PS86 | 2447 | 915 | 273 |

In this study, a working period can be regarded as a working day. Based on the participation of different cooperation subjects, five PDs can have

Comparison between initial and optimized network over one working period (unit: USD).

Alliance | Initial cost | Optimized cost | Cost saving |
---|---|---|---|

{PD1} | 7558 | 4489 | 3069 |

{PD2} | 7413 | 4785 | 2628 |

{PD3} | 8437 | 5312 | 3125 |

{PD4} | 6725 | 4153 | 2572 |

{PD5} | 7264 | 4547 | 2717 |

{PD1 PD2} | 14,475 | 7528 | 6947 |

{PD1 PD3} | 14,993 | 8536 | 6457 |

{PD1 PD4} | 13,135 | 6171 | 6964 |

{PD1 PD5} | 13,587 | 7612 | 5975 |

{PD2 PD3} | 14,486 | 8083 | 6403 |

{PD2 PD4} | 13,270 | 7345 | 5925 |

{PD2 PD5} | 13,964 | 7956 | 6008 |

{PD3 PD4} | 13,440 | 6692 | 6748 |

{PD3 PD5} | 14,175 | 7953 | 6222 |

{PD4 PD5} | 12,766 | 6975 | 5791 |

{PD1 PD2 PD3} | 21,405 | 9567 | 11,838 |

{PD1 PD2 PD4} | 19,313 | 7646 | 11,667 |

{PD1 PD2 PD5} | 20,725 | 8734 | 11,991 |

{PD1 PD3 PD4} | 19,694 | 7508 | 12,186 |

{PD1 PD3 PD5} | 20,216 | 8407 | 11,809 |

{PD1 PD4 PD5} | 20,583 | 8505 | 12,078 |

{PD2 PD3 PD4} | 19,997 | 8156 | 11,841 |

{PD2 PD3 PD5} | 21,034 | 9445 | 11,589 |

{PD2 PD4 PD5} | 19,172 | 7105 | 12,067 |

{PD3 PD4 PD5} | 20,895 | 9057 | 11,838 |

{PD1 PD2 PD3 PD4} | 26,763 | 11,302 | 15,461 |

{PD1 PD2 PD3 PD5} | 27,442 | 10,608 | 16,834 |

{PD1 PD2 PD4 PD5} | 27,136 | 10,715 | 16,421 |

{PD1 PD3 PD4 PD5} | 25,724 | 9556 | 16,168 |

{PD2 PD3 PD4 PD5} | 26,625 | 10,234 | 16,391 |

{PD1 PD2 PD3 PD4 PD5} | 33,176 | 11,415 | 21,761 |

Comparison between initial and optimized networks cost solutions.

Figure

Table

Comparison between initial delivery time and optimized delivery time (unit: minutes).

Alliance | Initial delivery time | Optimized delivery time | Time saving |
---|---|---|---|

{PD1} | 1148 | 1148 | — |

{PD2} | 1176 | 1176 | — |

{PD3} | 1134 | 1134 | — |

{PD4} | 952 | 952 | — |

{PD5} | 1079 | 1079 | — |

{PD1 PD2} | 2,324 | 1157 | 1167 |

{PD1 PD3} | 2,282 | 1136 | 1146 |

{PD1 PD4} | 2,100 | 1043 | 1057 |

{PD1 PD5} | 2,227 | 1105 | 1122 |

{PD2 PD3} | 2,310 | 1134 | 1176 |

{PD2 PD4} | 2,128 | 1032 | 1096 |

{PD2 PD5} | 2,255 | 1116 | 1139 |

{PD3 PD4} | 2,086 | 1025 | 1061 |

{PD3 PD5} | 2,213 | 1084 | 1129 |

{PD4 PD5} | 2,031 | 1007 | 1024 |

{PD1 PD2 PD3} | 3,472 | 1528 | 1,944 |

{PD1 PD2 PD4} | 3,276 | 1473 | 1,803 |

{PD1 PD2 PD5} | 3,403 | 1495 | 1,908 |

{PD1 PD3 PD4} | 3,234 | 1466 | 1,768 |

{PD1 PD3 PD5} | 3,361 | 1484 | 1,877 |

{PD1 PD4 PD5} | 3,179 | 1452 | 1,727 |

{PD2 PD3 PD4} | 3,262 | 1479 | 1,783 |

{PD2 PD3 PD5} | 3,389 | 1495 | 1,894 |

{PD2 PD4 PD5} | 3,207 | 1449 | 1,758 |

{PD3 PD4 PD5} | 3,165 | 1446 | 1,719 |

{PD1 PD2 PD3 PD4} | 4,410 | 2,113 | 2,297 |

{PD1 PD2 PD3 PD5} | 4,551 | 2,167 | 2,384 |

{PD1 PD2 PD4 PD5} | 4,355 | 2,108 | 2,247 |

{PD1 PD3 PD4 PD5} | 4,313 | 2094 | 2,219 |

{PD2 PD3 PD4 PD5} | 4,341 | 2,010 | 2,331 |

{PD1 PD2 PD3 PD4 PD5} | 5,503 | 2,389 | 3,114 |

Comparison between initial and optimized network delivery time solutions.

Table

Comparison of truck usage between initial and optimized networks (trucks/time).

Alliance | Initial truck usage | Truck usage after optimization | ||||
---|---|---|---|---|---|---|

{PD1} | 6 | 8 | 6 | 6 | 8 | 6 |

{PD2} | 6 | 8 | 5 | 6 | 8 | 5 |

{PD3} | 6 | 7 | 7 | 6 | 7 | 7 |

{PD4} | 5 | 6 | 4 | 5 | 6 | 4 |

{PD5} | 5 | 7 | 5 | 5 | 7 | 5 |

{PD1 PD2} | 12 | 16 | 11 | 2 | 8 | 15 |

{PD1 PD3} | 12 | 15 | 13 | 2 | 8 | 16 |

{PD1 PD4} | 11 | 14 | 10 | 3 | 7 | 12 |

{PD1 PD5} | 11 | 15 | 11 | 2 | 8 | 14 |

{PD2 PD3} | 12 | 15 | 12 | 2 | 8 | 15 |

{PD2 PD4} | 10 | 14 | 9 | 3 | 7 | 11 |

{PD2 PD5} | 11 | 15 | 10 | 2 | 8 | 13 |

{PD3 PD4} | 11 | 13 | 11 | 3 | 6 | 12 |

{PD3 PD5} | 11 | 14 | 12 | 2 | 8 | 15 |

{PD4 PD5} | 10 | 13 | 9 | 3 | 7 | 12 |

{PD1 PD2 PD3} | 18 | 23 | 18 | 3 | 12 | 24 |

{PD1 PD2 PD4} | 16 | 22 | 15 | 2 | 11 | 21 |

{PD1 PD2 PD5} | 17 | 23 | 16 | 3 | 12 | 22 |

{PD1 PD3 PD4} | 17 | 21 | 17 | 2 | 11 | 23 |

{PD1 PD3 PD5} | 17 | 22 | 18 | 4 | 12 | 24 |

{PD1 PD4 PD5} | 16 | 21 | 15 | 3 | 11 | 21 |

{PD2 PD3 PD4} | 17 | 21 | 16 | 2 | 11 | 22 |

{PD2 PD3 PD5} | 17 | 22 | 17 | 3 | 12 | 23 |

{PD2 PD4 PD5} | 15 | 21 | 14 | 3 | 10 | 20 |

{PD3 PD4 PD5} | 16 | 20 | 16 | 2 | 11 | 21 |

{PD1 PD2 PD3 PD4} | 22 | 29 | 22 | 4 | 14 | 28 |

{PD1 PD2 PD3 PD5} | 23 | 30 | 23 | 5 | 16 | 30 |

{PD1 PD2 PD4 PD5} | 16 | 29 | 20 | 4 | 14 | 26 |

{PD1 PD3 PD4 PD5} | 22 | 28 | 22 | 5 | 15 | 29 |

{PD2 PD3 PD4 PD5} | 21 | 28 | 21 | 5 | 14 | 28 |

{PD1 PD2 PD3 PD4 PD5} | 27 | 36 | 27 | 6 | 17 | 35 |

Figures

Comparison between initial and optimized networks

Comparison between initial and optimized networks

Figure

Comparison between initial and optimized networks

A large petrol distribution network consisting of five PDs and 86 PSs is relatively complex. Therefore, for the optimized truck distribution routes, the distribution truck route network formed by PD3 is taken as an example, as shown in Table

Distribution truck route arrangements of PD3 after optimization.

PD | The distribution truck route network |
---|---|

PD3 | PD3 ⟶ PS21 ⟶ PS22 ⟶ PS31 ⟶ PD3; |

In the above example, the applications of several commonly used heuristic algorithms are compared to verify the effectiveness of the proposed IMOPSO algorithm. Table

Comparison of algorithm performances.

Sequence | IMOPSO | ACO | NSGA-II | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Cost (USD) | Trucks (trucks/time) | Distribution time (minutes) | Cost (USD) | Trucks (trucks/time) | Distribution time (minutes) | Cost (USD) | Trucks (trucks/time) | Distribution time (minutes) | |||||||

1 | 11,415 | 6 | 17 | 35 | 1980 | 13,248 | 8 | 20 | 33 | 2170 | 12,532 | 7 | 19 | 34 | 2060 |

2 | 15,324 | 6 | 15 | 37 | 1550 | 15,023 | 8 | 18 | 31 | 1380 | 14,473 | 6 | 18 | 32 | 1610 |

3 | 11,122 | 6 | 18 | 33 | 980 | 19,108 | 9 | 18 | 34 | 2220 | 12,914 | 7 | 17 | 32 | 2010 |

4 | 11,184 | 6 | 16 | 35 | 1690 | 18,197 | 8 | 21 | 32 | 1450 | 11,403 | 8 | 19 | 33 | 1650 |

5 | 10,707 | 6 | 16 | 36 | 1760 | 14,280 | 8 | 20 | 31 | 2130 | 14,627 | 8 | 17 | 34 | 2420 |

6 | 12,750 | 6 | 17 | 36 | 1980 | 12,556 | 9 | 19 | 34 | 2230 | 18,158 | 7 | 18 | 33 | 1980 |

7 | 12,566 | 8 | 15 | 32 | 2250 | 14,320 | 9 | 20 | 32 | 2180 | 16,232 | 8 | 17 | 33 | 2120 |

8 | 17,355 | 5 | 15 | 38 | 1760 | 16,886 | 7 | 20 | 32 | 1430 | 14,654 | 6 | 18 | 33 | 2410 |

9 | 12,229 | 6 | 18 | 35 | 1970 | 19,672 | 8 | 18 | 31 | 1300 | 12,434 | 6 | 18 | 34 | 1940 |

10 | 13,338 | 8 | 16 | 34 | 1820 | 12,780 | 9 | 20 | 33 | 2410 | 12,516 | 6 | 19 | 33 | 1630 |

11 | 14,820 | 8 | 15 | 34 | 1730 | 16,830 | 7 | 20 | 31 | 930 | 12,721 | 8 | 17 | 34 | 2310 |

12 | 14,842 | 8 | 17 | 32 | 2230 | 14,019 | 8 | 19 | 33 | 1690 | 17,029 | 7 | 17 | 34 | 1970 |

13 | 15,520 | 7 | 15 | 34 | 2270 | 14,210 | 9 | 19 | 34 | 2190 | 14,591 | 7 | 17 | 33 | 2090 |

14 | 14,670 | 5 | 18 | 33 | 1900 | 18,683 | 9 | 21 | 34 | 860 | 13,717 | 8 | 17 | 32 | 900 |

15 | 16,051 | 6 | 17 | 34 | 1950 | 17,252 | 8 | 19 | 32 | 2310 | 12,716 | 8 | 19 | 32 | 2010 |

16 | 15,862 | 7 | 18 | 36 | 860 | 17,760 | 8 | 19 | 32 | 2340 | 12,336 | 7 | 17 | 34 | 1680 |

17 | 12,312 | 6 | 17 | 36 | 1830 | 12,856 | 7 | 18 | 34 | 1570 | 15,641 | 8 | 18 | 34 | 1980 |

18 | 12,322 | 8 | 16 | 37 | 2060 | 17,903 | 8 | 19 | 34 | 880 | 17,947 | 7 | 19 | 33 | 2410 |

19 | 13,454 | 8 | 16 | 33 | 1610 | 15,404 | 7 | 20 | 31 | 2610 | 18,621 | 6 | 17 | 33 | 2530 |

20 | 13,254 | 6 | 15 | 33 | 2110 | 14,422 | 8 | 20 | 31 | 950 | 15,297 | 8 | 17 | 32 | 2420 |

Average | 13,555 | 7 | 16 | 35 | 1810 | 15,770 | 8 | 19 | 32 | 1760 | 14,528 | 7 | 18 | 33 | 2010 |

The optimization of coordinated PS replenishment vehicle route based on regional partitioning and reasonable resource sharing promotes the sustainable development of petrol distribution and emergency energy supply system. Through the optimization of CMPDVRPE, the petrol distribution service area is reasonably divided, long-distance and cross-traffic are reduced, and the distribution time is shortened. Thus, costs are minimized and additional benefits are provided to each PD. Effective vehicle routing arrangement and sharing matching strategy between vehicles and PSs are the important characteristics of this network. These improvements greatly enhance energy and social resources, cost savings, and emergency response capabilities for PD operators and transportation management.

Cooperation among logistics facilities plays an important role in optimizing the distribution in cases of emergency [

This study proposes an effective method to solve the CMPDVRPE optimization, which improves the cooperation of PDs and the efficient distribution vehicle routing optimization in emergencies. Through the cooperation between PDs, regional petrol joint distribution, optimization of distribution, and resource sharing can be formed. In the optimization, PS clustering mechanism, road blocking, and TS mechanism are considered. Comparison of the data before and after the cooperation shows that the total operating cost, total delivery time, and the total number of delivery vehicles are significantly decreased.

The optimization model considers customer clustering, multicompartment TS, roadblocks, and TWC, thereby reducing the overall transport distance and the number of trucks used. Taking the regional petrol distribution network in Chongqing as an example, the application of the model and method is evaluated. A heuristic algorithm IMOPSO is proposed, and a case study of different scales of petrol distribution networks was carried out. The operating cost, delivery time, and the number of different types of trucks are compared before and after optimization.

In summary, the optimization of petrol emergency distribution vehicle routing is consistent with reality. The proposed optimization method is superior to the existing research in this field. On the basis of the analysis, the following conclusions are drawn. (1) Through customer clustering, multicompartment TS, vehicle routing optimization, and TWC, the regional petrol distribution network can considerably reduce the delivery time, number of distribution trucks required, and the total operating cost of the petrol distribution network. (2) Optimizing the PSs for each PD and sharing trucks when the TW demand allows can reduce traffic pressure in urban areas and its negative impact on the energy supply system and contribute to the sustainable development of urban traffic. (3) Timely and efficient supply of petrol is guaranteed through optimization of vehicle routing of petrol emergency distribution.

The results of this study point to interesting research directions for the future. The following views can be considered. (1) This study only examines the cooperation between PD and PS in the secondary distribution of petrol. Thus, the cooperation between the two sides can extend to the transport energy supply chain. (2) Consistent with most existing joint distribution literature, this study assumes a constant transportation speed of petrol distribution trucks. Future research can consider real-time urban traffic speed analysis to obtain more realistic results. (3) From the perspective of vehicle-road interaction, the influence of road geometry on the selection of multicompartment vehicle types can be considered in the future. (4) In the future, a dynamic CMPDVRPE model can be established by considering the spatiotemporal change of roadblocks or congestion.

The service time window and demand quantity data used to support the findings of this study are available from the corresponding companies and administrative departments.

The authors declare that they have no conflicts of interest.

This research was supported by the Social Science Foundation of Chongqing of China (Grant nos. 2020BS62, 2020TBWT-ZD02, 2019YBGL049, and 2020YBGL85), the Special Project of Technology Foresight and System Innovation of Chongqing of China (Grant no. cstc2020jsyj-zdxwtB0003), the National Natural Science Foundation of China (Grant no. 71871035), Humanity and Social Science Foundation of Ministry of Education of China (Grant nos. 18YJC630189 and 17YJA630079), and Humanity and Social Sciences Research Project of Chongqing Education Commission (Grant no. 20SKGH232).