CN111709570A - Optimization method for network drop-and-drop transport scheduling - Google Patents

Abstract

The invention discloses an optimization method for network drop and pull transportation scheduling, and belongs to the technical field of drop and pull transportation. Aiming at the situation that the demands at two ends of operation are unbalanced and a plurality of throwing demands possibly exist in throwing and hanging transportation, the optimization method for network throwing and hanging transportation scheduling establishes a full network throwing and hanging scheduling optimization model by taking the minimum total transportation cost of a network and the minimum number of tractors as targets, designs a heuristic algorithm to solve the model, and verifies the effectiveness of the model by using an example. The invention fully considers the condition that the requirements of two ends are unbalanced and the requirement is possibly multiple in actual drop and pull transportation, provides the vehicle scheduling optimization in the whole network range in the highway and harbor network, can be close to the actual application scene, and is beneficial to the drop and pull transportation enterprises to improve the economic benefit.

Description

Optimization method for network drop-and-drop transport scheduling

[ technical field ] A method for producing a semiconductor device

The invention relates to the technical field of drop and pull transportation, in particular to an optimization method for network drop and pull transportation scheduling.

[ background of the invention ]

Drop and pull transportation is taken as a cargo transportation organization mode with economic benefit and social benefit, and is highly valued by governments and enterprises. The actual carrying rate can be obviously improved by the swing-hanging transportation, the economic benefit is improved, and the average oil consumption and the carbon emission are reduced through the trial of projects.

The development of swing-hanging transportation needs to rely on a freight station (depot), which is a starting point and a returning end point of a swing-hanging transportation vehicle. Highway ports have become the most common freight yard in china. The highway port is a comprehensive logistics center of a city, generally occupies a large area, and comprises the businesses of throwing and hanging trunk line transportation, city distribution, temporary storage and the like. In China, the world convergence road port is already arranged in more than 50 cities, nearly 100 road ports are owned, and a more perfect drop and pull transport network is formed. Therefore, how to optimize the swing vehicle scheduling in a centralized manner in the whole network becomes a real problem to be solved urgently.

In practical applications, drop and pull transportation is applied to a plurality of scenes, including the problem of goods delivery in grocery stores, the problem of collection and transportation of garbage, the problem of delivering goods to a plurality of stores in warehouses, and the like. It is generally assumed that a customer has a certain amount of demand, i.e., a dump vehicle needs to visit the customer only once to meet the demand for cargo delivery or garbage collection. However, in the haul trunk network for highway harbors, haul and haul operations are performed between highway harbors, which are both haul and haul operation sites and customer demand sites. Different from the requirements in the practical application of general drop and pull transportation, the drop and pull requirements of the highway ports take trailers as units, the required quantity can be a plurality of trailers, and the requirements of the two ends of the drop and pull can be unequal, namely, the situations that multiple drop and pull transportation exist between the two highway ports and the requirements of the two ends of the drop and pull are unbalanced, and the complexity of drop and pull transportation scheduling optimization is increased.

And the highway ports need to be connected into a net in a linear mode to fully exert the advantages of the highway ports. Depending on a rented or self-built highway port site, a certain enterprise carries out drop and pull transportation among a plurality of highway ports of a plurality of large and medium-sized cities, and at the moment, the highway port is not only a tractor and trailer yard, but also a drop and pull transportation demand point. As shown in fig. 1, every two road ports are connected by a channel, drop and pull transportation services among a plurality of road ports already form a network, but due to unbalanced drop and pull requirements and the condition that the requirements are larger than 1, numbers beside a trailer in fig. 1 represent drop and pull transportation requirements in a certain direction, so that drop and pull transportation is not a simple one-line two-point two-end or one-line multi-point drop and pull scheduling mode, but is scheduled in the whole network range according to requirements.

Generally, in order to ensure stability on a certain transportation line, a drop and pull transportation enterprise usually arranges some vehicles to be specially used for drop and pull transportation between two points, and arranges other vehicles to complete other drop and pull tasks, i.e. the network drop and pull transportation process can be divided into two stages.

Stage 1: two ends of a line are hung, as shown in fig. 2. Because the organization of the two ends of the one-line two-point swing-hanging mode is relatively simple, and the driver and the passengers can drive between the two points for a long time, the road condition can be familiar, and the accidents are reduced, therefore, every two points in the whole network can be regarded as independent. Because the phenomenon that the throwing and hanging requirements are unbalanced often exists between two points, the smaller quantity in the two directions is taken as the working quantity of throwing and hanging at the two ends of the line, and the requirement in a certain direction is met at the moment. If the demand in the other direction is not met, it is transferred to the next stage. For example, in fig. 1, the number beside the trailer represents the swing and hang demand, that is, 5 trailers need to be swung and hung from point 1 to point 2, 3 trailers need to be swung and hung from point 2 to point 1, the demand between point 1 and point 2 is unbalanced, and the smaller demand 3 between the two points is taken as the work load of the swing and hang at both ends of one line, so that the swing and hang demand from point 2 to point 1 is satisfied, and the remaining demands from point 1 to point 2 and 2 other trailers are not satisfied, and need to be dispatched in the whole network, and then the next stage is shifted.

And (2) stage: the whole network is circularly hung, as shown in figure 3. After the drop-hang scheduling in the stage 1, the phenomenon that the one-way requirement between two points is not met exists, and scheduling arrangement needs to be carried out in the whole network. As shown in fig. 3, 2, 1,2 trailers need to be transported between point 1 to point 2, point 1 to point 4, point 1 to point 5, point 2 to point 3, and point 2 to point 4, respectively. Due to the limited daily operation time of the tractor, a scheduling scheme which enables the lowest network scheduling cost and the least tractor purchase is needed at the stage.

Therefore, the invention establishes a full-network swing and hang scheduling optimization model aiming at the characteristics of the road port network swing and hang transportation and considering the complex condition that the customer has multiple swing and hang demands and the demands at two ends of the swing and hang are unbalanced in the actual swing and hang transportation, and can provide reference for the actual road port network swing and hang optimization (efficiency improvement).

[ summary of the invention ]

The invention provides an optimization method for network drop and pull transport scheduling, which fully considers the condition that the requirements at two ends are unbalanced and the requirements are possibly multiple in actual drop and pull transport, provides vehicle scheduling optimization in a whole network range in a highway and harbor network, can be close to an actual application scene, and is beneficial to drop and pull transport enterprises to improve economic benefits.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

an optimization method for network drop and pull transport scheduling is applied to network drop and pull transport of a highway port consisting of a tractor, a trailer and the highway port, and comprises the following steps:

(1) establishing a network throwing and hanging scheduling target optimization model;

(2) solving the target optimization model in the step (1) by using a two-stage heuristic algorithm:

firstly, the throwing and hanging requirements q between any two highway ports_ijDivided into two fractions q'_ijAnd q "_ij(ii) a If q is_ij≥q_jiThen q'_ij＝q_ji＝q'_ji，q”_ij＝q_ij-q_ji，q”_ji0; if q is_ij＜q_jiThen q'_ij＝q_ij＝q'_ji，q”_ij＝0，q”_ji＝q_ji-q_ij，q’_ijThe formed matrix is a symmetric matrix; wherein q is_ij: representing the drop and pull transportation requirements of the highway ports i to j by using the drop and pull transportation times; q. q.s_ji: representing the drop and pull transportation requirements of the highway ports j to i by using the drop and pull transportation times; since the requirements are not necessarily balanced, q_ijIs not necessarily equal to q_ji；

Stage 1: to q 'of demand'_ijAnd dispatching the throwing hanging requirement: scheduling the trailer in a throwing manner by adopting two ends of a line, namely selecting a highway port arbitrarily in the network, starting to assign a throwing and hanging task of the tractor, and throwing and hanging the tractor back and forth between the two highway ports with heavy load;

and (2) stage: for phase 1 modulationQ after degree "_ijAnd dispatching the throwing hanging requirement: and (3) adopting full-network circulation throwing and hanging vehicle scheduling, namely selecting the least line in the residual throwing and hanging requirements after scheduling in the 1 st stage, firstly throwing and hanging in the stage, and taking the starting point of singular requirements as the starting point of the tractor.

The invention also provides another optimization method for network drop-off and drop-off transportation scheduling, which is applied to network drop-off and drop-off transportation of a highway port consisting of a tractor, a trailer and the highway port, and comprises the following steps:

(1) establishing a network throwing and hanging scheduling target optimization model;

(2) solving the target optimization model in the step (1) by using a heuristic algorithm: the pure network circulation throwing and hanging requirements q between any two highway ports_ijAnd carrying out vehicle dispatching.

Preferably, the network drop-and-hang scheduling objective optimization models in step (1) of the two methods are both:

an objective function:

the network operation cost is composed of heavy-hanging running cost, empty running cost and fixed cost, and the heavy-hanging running cost

The empty running cost is as follows:

the fixed cost of using the vehicle on the same day is Z_{Fixing device}＝Kc；

The objective is that the network operation cost is expressed minimally as:

the constraint conditions are as follows:

get rid of and hang the demand and obtain satisfying:

tractor continuous operating time limit:

in the formula, i, j, l: the number of the road port, i, j, l belongs to N;

k: representing the set of tractors, K ═ {1,2, …, K }, and K also represents the total number of tractors required for the road network;

k: representing the number of the tractor, and K belongs to K;

d_ij: represents the distance between the road ports i, j, in units: km;

q_ij: representing the drop and pull transportation requirements of the highway ports i to j by using the drop and pull transportation times;

C_ij,c_ij: respectively represent the cost of towing heavy hanging and empty running of the tractor, unit: yuan/km;

c: the fixed cost of tractor use in unit time is shown, including vehicle depreciation, staff wage, unit: element;

t: the time of the continuous work of the tractors is represented, and the time of the continuous work of all the tractors every day is regulated to be equal;

v₁，v₂: respectively representing the speed of the tractor for towing heavy hanging and empty running, unit: km/h;

k₁，k₂respectively showing the states of heavy suspension and empty running of the tractor, K ∈ K;

the number of trips the tractor takes to travel from a highway port to a highway port for a heavy load and an empty ride, respectively.

Preferably, the stage 1 of the step (2) is performed as follows:

the first step is as follows: setting initial parameters, i is 1, K is 0, and Z_{Heavy load}＝0，Z_{Air conditioner}＝0，Z_{Fixing device}＝0；

The second step is that: selecting q'_ij> 0, and max (d)_ij) The corresponding highway port i, j is a throwing and hanging terminal of the first vehicle service; if q'_ij> 0 and d_ij≥v₁T, then K ═ K +2q'_ij,q'_ij＝0＝q'_ji，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}Kc; if q'_ij> 0 and d_ij＜v₁T, and if

Then K is K +1, Z_{Fixing device}＝Kc，q'_ij＝0＝q'_jiAnd if q "_ijIf the working time is more than 0, the departure distance of the highway port j is selected to be small (d)_jl) Is taken as the next hanging point until the working time is used up, wherein (d)_jl) Denotes the distance, q ″, from road harbor j to road harbor l "_ij＝q”_ij-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ijC_ij+d_jlC_jl+..; if q "_ijIf 0, then choose the departure distance of the highway harbor i to be the next smallest (d)_il) L is used as the next throwing point, until the vehicle working time is used up, corresponding q'_jl＝q'_jl-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ilC_il+..; if q'_ij> 0 and d_ij＜v₁T, and if

Then between the harbors i, jOther vehicles need to be arranged for transportation, and the number of the vehicles is required to be

The vehicle with remaining capability can still complete other haul-off tasks, then q'_ij＝0＝q'_ji，

Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}＝Kc；

Third step of applying to all i ∈ N, i ═ i +1, if q'_ijIf the value is more than 0, the calculation is returned to the second step; if all q'_ijWhen it is 0, the calculation is stopped, Z₁'＝Z_{Heavy load}+Z_{Fixing device}。

Preferably, the phase 2 in the two-phase heuristic algorithm of the step (2) is performed as follows:

the first step is as follows: optionally i ∈ N;

the second step is that: q is selected "_ijThe highway port i, j greater than 0 is a throwing and hanging scheduling demand point; if d is_ij≥v₁T, then K ═ K + q "_ij,q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Fixing device}Kc; if d is_ij＜v₁T, there are two strategies at this time:

strategy 1 is that a vehicle k travels back and forth between highway ports i and j, and only one way of loading goods is needed, and the highway ports j to i are empty; if vehicle k can complete q within time T "_ijThe hanging amount is K +1, q "_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji，Z_{Fixing device}If the remaining working time is not enough, the departure q of the highway harbor j can be selected "_jlTaking the port more than 0 as the next hanging point; if vehicle k cannot complete q within time T "_ijAnd if the load is thrown and hung, other vehicles are required to be dispatched to throw and hang, and the number of the vehicles required for completing the throwing and hanging task between the highway ports i and j is equal to that of the vehicles

If the vehicle with the residual capacity can still finish other throwing and hanging tasks

q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji，Z_{Fixing device}＝Kc；

The strategy 2 is that the vehicle k completes the throwing and hanging task in the highway port network, at the moment, heavy load and no load exist in the whole network, the vehicle k completes one-time throwing and hanging transportation from the highway ports i to j, and q'_ij＝q”_ij-1, selecting a highway harbor j departure q "_jlL harbor > 0 is used as the next hanging point, q "_jl＝q”_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jl+. cndot; if all q's are started from the highway harbor j "_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···，Z_{Fixing device}＝Kc；

In the third step, all i ∈ N, i +1, if q "_ijIf the value is more than 0, the calculation is returned to the second step; if all q "_ijWhen it is 0, the calculation is stopped, Z₁”＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}；

Therefore, the total cost of the network drop scheduling is as follows: z₁＝Z'₁+Z₁”。

Preferably, the pure network circular throwing and hanging is adopted in the step (2) to throw and hang the demand q between any two highway ports_ijThe vehicle dispatching is carried out according to the following steps:

the first step is as follows: optionally i ∈ N;

the second step is that: select q_ijThe highway port i, j greater than 0 is a throwing and hanging scheduling demand point; if d is_ij≥v₁T, then K ═ K + q_ij,q_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q_ijd_ijC_ij，Z_{Fixing device}Kc; if d is_ij＜v₁T, completing a throwing and hanging task by the vehicle k in the highway port network, wherein at the moment, heavy load and no load exist in the whole network, completing one-time throwing and hanging transportation from the highway ports i to j by the vehicle k, and q_ij＝q_ij-1, selecting the departure q of the highway harbor j_jlL port more than 0 is used as the next hanging point, q_jl＝q_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jl+. cndot; if all q start from the port j of the highway_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···，Z_{Fixing device}＝Kc；

In the third step, all i ∈ N, i ═ i +1, if q_ijIf the value is more than 0, the calculation is returned to the second step; if all q are_ijWhen it is 0, the calculation is stopped, Z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

Therefore, the net network drop scheduling total cost is: z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

By adopting the technical scheme, the invention has the beneficial effects that:

according to the invention, by establishing the whole network swing-hanging scheduling optimization model, designing a heuristic algorithm to solve the model, and verifying the effectiveness of the model by using the example, the swing-hanging transportation optimization in the network can reduce the use number of traction vehicles, and the overall transportation cost is reduced. And in the network drop and hang transportation, scheduling optimization is carried out in a pure network range, so that the use number of traction vehicles can be more effectively reduced, and the transportation cost can be reduced. The invention fully considers the condition that the requirements of two ends are unbalanced and the requirement is possibly multiple in actual drop and pull transportation, provides the vehicle scheduling optimization in the whole network range in the highway and harbor network, can be close to the actual application scene, and is beneficial to the drop and pull transportation enterprises to improve the economic benefit.

[ description of the drawings ]

FIG. 1 is a schematic diagram of a network drop-and-drop transport in a highway and harbor network in the prior art;

FIG. 2 is a schematic diagram of a two-point end-to-end swing at stage 1 in the prior art;

FIG. 3 is a schematic diagram of a full-network cyclic swing and hang of stage 2 in the prior art;

[ detailed description ] embodiments

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The method mainly comprises the steps of model hypothesis, model establishment, model solving by utilizing a two-stage heuristic algorithm and the like.

First, the model assumes:

according to the characteristics of the network drop and drop transportation of the highway harbor, the following assumptions are made:

(1) all tractors and trailers in the network belong to standard models, and the models are consistent;

(2) enough trailers are arranged in each highway port in the network, and the assumption can be achieved by integrating social resources of highway port drop-and-pull transportation enterprises;

(3) the operation time of the trailer throwing and hanging of the tractor is not considered, the number of the trailers is enough, and the tractor is not required to wait for the trailer loading and unloading operation;

(4) the distance and time of the back-and-forth driving between the two highway ports are the same;

(5) the throwing and hanging demands are generated in the network every day, the daily demands fluctuate, and the enterprise can schedule according to the daily actual demands. Because some nodes are far away from each other, drop and hang transportation can not be completed in one day, and therefore it is assumed that the drop and hang tasks which are not completed in the previous day do not influence subsequent scheduling.

Secondly, establishing a model:

according to the actual operation of the highway port network, the drop and pull transport enterprises pursue the minimum overall network operation cost, and the minimum number of tractors thrown into the drop and pull transport enterprises while meeting the requirements is used as a target to establish a model.

(1) Target 1: the network operation cost is composed of a heavy-hanging running cost, an empty running cost and a fixed cost, wherein the heavy-hanging running cost is

The empty running cost is as follows:

the fixed cost of using the vehicle on the same day is as follows: z_{Fixing device}Kc; the objective is that the network operation cost is expressed minimally as:

(2) target 2: the minimum number of tractors invested is expressed as:

min Z₂＝K

(3) constraint conditions are as follows:

get rid of and hang the demand and obtain satisfying:

tractor continuous operating time limit:

the problem of network throwing and hanging scheduling with unbalanced demands is a double-target problem. The goal 1 is to minimize the network operation cost, and the magnitude of the empty driving cost and the fixed cost of the tractor is mainly balanced under the goal that the throwing and hanging requirements are met. Tractor attachmentThe cost Kc is in direct proportion to the investment number K of the tractors, and if the idle running cost of the tractors is larger than the fixed cost, the investment of the tractors is increased to reduce the overall operation cost, which is contradictory to the target 2; if the tractor idle cost is less than the fixed cost, the tractor idle is scheduled without increasing the number of tractor drops, consistent with target 2. At this time, only the non-inferior solution satisfying the target 1 and the target 2 can be obtained, and the drop and hang requirement of the whole network is

If each hanging-off demand is arranged to be dragged by one tractor, obviously

I.e. one constraint that object 2 can become object 1.

From the above, the network drop-hang scheduling model with unbalanced demand finally changes into:

constraint s.t.:

wherein, the symbolic description is as follows:

i, j, l: the number of the road port, i, j, l belongs to N;

k: representing the set of tractors, K ═ {1,2, …, K }, and K also represents the total number of tractors required for the road network;

k: representing the number of the tractor, and K belongs to K;

d_ij: represents the distance between the road ports i, j, in units:km；

q_ij: representing the drop and pull transportation requirements of the highway ports i to j by using the drop and pull transportation times;

C_ij,c_ij: respectively representing the cost of towing heavy hanging and empty running of tractors of highway ports i to j, unit: yuan/km;

c: the fixed cost of tractor use in unit time is shown, including vehicle depreciation, staff wage, unit: element;

t: the time of the continuous work of the tractors is represented, and the time of the continuous work of all the tractors every day is regulated to be equal;

v₁，v₂: respectively representing the speed of the tractor for towing heavy hanging and empty running, unit: km/h;

k₁，k₂respectively showing the states of heavy suspension and empty running of the tractor, K ∈ K;

the number of trips the tractor takes to travel from a highway port to a highway port for a heavy load and an empty ride, respectively.

And finally, solving the model by using a two-stage heuristic algorithm, wherein the method comprises the specific steps of an algorithm thought and an algorithm.

The algorithm idea is as follows:

the problem of demand-unbalanced road port network drop-off and hang-off scheduling is essentially the problem of vehicle scheduling in a multi-yard, but each road port can be a yard and can also be regarded as a client, so the problem is also a special scheduling problem of coincidence of the yard and a demand point. Since the vehicle cannot determine the starting point and the ending point, starting from any one highway harbor, various paths can be selected, and the solving difficulty is increased. Can be in the whole network rangeScheduling in the enclosure, and also according to the conventional method, the throwing and hanging requirements q between any two highway ports_ijDivided into two fractions q'_ijAnd q "_ij(pure network dropping does not take separation into account). If q is_ij≥q_jiThen q'_ij＝q_ji＝q'_ji,q”_ij＝q_ij-q_ji,q”_ji0; if q is_ij＜q_jiThen q'_ij＝q_ij＝q'_ji,q”_ij＝0,q”_ji＝q_ji-q_ij，q'_ijThe constructed matrix is a symmetric matrix. To demand q'_ijAnd q "_ijAnd correspondingly designing a two-stage heuristic algorithm for solving.

Stage 1: and (4) throwing the vehicle to dispatch at two ends of the first line. Only pair q 'is required for this stage'_ijAnd carrying out scheduling. And (3) randomly selecting one highway port in the network, starting to assign a throwing and hanging task of the tractor, throwing and hanging the tractor back and forth between the two highway ports under heavy load, and fully utilizing power. If the distance d between ports i and j of the road_ijLarger, tractors can only complete the transport of 1 trip during the working time of day T (according to the assumption that even 1 trip is not complete, calculated as 1 trip), then 2q 'is required between road ports i and j'_ijThe vehicle tractor carries out traction; if the distance d between ports i and j of the road_ijThe small size is that the k-th tractor can finish the transportation of a plurality of times within the working time T of one day, so that the working time is fully utilized, and the traction times which can be finished within the time T are

(

Denotes rounded up), if a'_ijk＞2q'_ij＝q'_ij+q'_jiAnd the kth vehicle can finish all tasks between the highway ports i and j, and can also carry out throwing and hanging from the point i to other points which have throwing and hanging requirements and have the next largest distance. If a'_ijk≤2q'_ijThen the kth vehicle can not complete the busAll tasks between the ports i and j need to be completed together by selecting other vehicles, and the needs to be dispatched to fulfill the throwing and hanging requirements between the ports i and j

The vehicle tractor, the vehicle that has the residual capacity still can accomplish other and get rid of the task of hanging.

And (2) stage: full network round robin swing trailer scheduling (if no demand q will be swung_ijDivided into two fractions q'_ijAnd q "_ijI.e. directly taking into account the demand q_ijThe pure network throwing and hanging vehicle dispatching algorithm can be designed according to the idea of the stage). This stage is to q "_ijScheduling is performed, and at this time, the tractor may run empty. In the dispatching of the tractor, the ideal state is that after the tractor finishes heavy load throwing and hanging of one line, the tractor can continue to throw and hang the heavy load of the next line, so that the least line in the residual throwing and hanging requirements is selected to firstly throw and hang in the stage, and the singular requirement starting point i is used as the starting point of the tractor. If the distance d between ports i and j of the road_ijLarger, tractors can only finish 1 transportation within a working time T of a day, and then road ports i to j need q "_ijThe vehicle tractor carries out traction; if the distance d between ports i and j of the road_ijSmaller, T_kA plurality of traction passes can be completed in time, and only the throwing and hanging requirements q from i to j exist between i and j in the stage "_ijAnd q "_jiIf j is selected from the highway port j to the other point l which has the throwing and hanging requirements and has the largest distance, if j is selected from the highway port j, the distance is the largest, and if j is selected from the highway port j, the distance is the largest

The tractor k can also continue to pull the next path; if it is

The paths j to l cannot be hung by k, and j needs to be selected to other points which have hanging requirements and have the next largest distance for judgment.

The algorithm comprises the following specific steps:

will get rid of and hang demand q_ijDivided into two fractions q'_ijAnd q "_ij。

Stage 1: to q 'of demand'_ijAnd dispatching the throwing hanging requirement.

The first step is as follows: setting initial parameters, i is 1, K is 0, and Z_{Heavy load}＝0，Z_{Air conditioner}＝0，Z_{Fixing device}＝0。

The second step is that: selecting q'_ij> 0, and max (d)_ij) And the corresponding road port i, j is a throwing and hanging terminal point served by the first vehicle. If q'_ij> 0 and d_ij≥v₁T, then K ═ K +2q'_ij,q'_ij＝0＝q'_ji，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}Kc. If q'_ij> 0 and d_ij＜v₁T, and if

Then K is K +1, Z_{Fixing device}＝Kc，q'_ij＝0＝q'_jiAnd if q "_ijIf the working time is more than 0, the departure distance of the highway port j is selected to be small (d)_jl) Is taken as the next hanging point until the working time is used up, wherein (d)_jl) Denotes the distance, q ″, from road harbor j to road harbor l "_ij＝q”_ij-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ijC_ij+d_jlC_jl+..; if q "_ijIf 0, then choose the departure distance of the highway harbor i to be the next smallest (d)_il) Is taken as the next drop-and-hang point until the vehicle working time is exhausted, wherein (d)_il) Represents the distance from road port i to road port l, corresponding to q'_jl＝q'_jl-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ilC_il+.... If q'_ij> 0 and d_ij＜v₁T, and if

Other vehicles need to be arranged between the highway ports i, j for transportation, and the number of the vehicles is required to be equal to

The vehicle with remaining capability can still complete other haul-off tasks, then q'_ij＝0＝q'_ji，

Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}＝Kc。

Third step of applying to all i ∈ N, i ═ i +1, if q'_ijIf the value is more than 0, the calculation is returned to the second step; if all q'_ijWhen it is 0, the calculation is stopped, Z₁'＝Z_{Heavy load}+Z_{Fixing device}。

And (2) stage: for q after phase 1 scheduling "_ijAnd dispatching the throwing hanging requirement.

The first step is as follows: optionally i ∈ N;

the second step is that: q is selected "_ijAnd the road port i, j more than 0 is a throwing and hanging scheduling demand point. If d is_ij≥v₁T, then K ═ K + q "_ij,q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Fixing device}Kc. If d is_ij＜v₁T, there are two strategies at this time. Strategy 1 is that vehicle k travels to and from highway harbors i, j, where only a single trip is available to load the cargo and highway harbors j to i are empty. If vehicle k can complete q within time T "_ijThe hanging amount is K +1, q "_ij＝0Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij,Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji,Z_{Fixing device}If the remaining working time is not enough, the departure q of the highway harbor j can be selected "_jlThe port l > 0 is used as the next hanging point. If vehicle k cannot complete q within time T "_ijThe amount of hanging and throwing is also requiredDispatching other vehicles for throwing and hanging, and completing the throwing and hanging tasks between the highway ports i, j requires the number of the vehicles to be equal to

If the vehicle with the residual capacity can still finish other throwing and hanging tasks

q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji，Z_{Fixing device}Kc. The strategy 2 is that the vehicle k completes the throwing and hanging task in the highway port network, at the moment, heavy load and no load exist in the whole network, the vehicle k completes one-time throwing and hanging transportation from the highway ports i to j, and q'_ij＝q”_ij-1, selecting a highway harbor j departure q "_jlL harbor > 0 is used as the next hanging point, q "_jl＝q”_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jlC.. The is a reaction product of +. The reaction product. If all q's are started from the highway harbor j "_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···。

In the third step, all i ∈ N, i +1, if q "_ijIf the value is more than 0, the calculation is returned to the second step; if all q "_ijWhen it is 0, the calculation is stopped, Z₁”＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

Therefore, the total cost of the network drop scheduling is as follows: z₁＝Z'₁+Z₁”。

The pure network circulation throwing and hanging requirements q between any two highway ports_ijThe vehicle dispatching is carried out according to the following steps:

the first step is as follows: optionally i ∈ N;

the second step is that: select q_ijThe highway port i, j greater than 0 is a throwing and hanging scheduling demand point; if d is_ij≥v₁T, then K ═ K + q_ij,q_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q_ijd_ijC_ij，Z_{Fixing device}Kc; if d is_ij＜v₁T, completing a throwing and hanging task by the vehicle k in the highway port network, wherein at the moment, heavy load and no load exist in the whole network, completing one-time throwing and hanging transportation from the highway ports i to j by the vehicle k, and q_ij＝q_ij-1, selecting the departure q of the highway harbor j_jlL port more than 0 is used as the next hanging point, q_jl＝q_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jl+. cndot; if all q start from the port j of the highway_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···，Z_{Fixing device}＝Kc；

In the third step, all i ∈ N, i ═ i +1, if q_ijIf the value is more than 0, the calculation is returned to the second step; if all q are_ijWhen it is 0, the calculation is stopped, Z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

Therefore, the net network drop scheduling total cost is: z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

In this application, the parameters with the subscript jl each refer to the parameters from road port j to road port l, such as (d)_jl) Denotes the distance, q, from road port j to road port l_jlIndicating the haul-off demand from highway port j to highway port l. C_jlAnd c_jlThe cost of towing a heavy-duty trailer and an empty-drive for a tractor from highway port j to highway port l is shown, respectively. Since the equivalent letters (parameters) have the same meaning, and the differences in subscripts only indicate different ports, which is common knowledge in the art, the description thereof is not repeated here. The subscript is the parameter il.

Examples

Depending on the heaven and earth converging highway harbors, the logistics enterprise L has drop and hang transportation points in 10 cities, and how to arrange vehicle scheduling in a drop and hang network ensures that the cost of the whole network is the lowest, which is a technical problem that enterprise managers want to solve.

Assuming that the cost of heavy-hanging and no-load running of the tractor is C_ij0.8 yuan/km,. c_ij0.4 yuan/km, the speed of the tractor for heavy hanging and empty running is v₁＝50km/h,v₂70km/h, fixed cost c 500 yuan per day, continuous working time T16 hours per day, d_ijValues were mapped according to Google as shown in table 1. q. q.s_ijThe values are measured using randint function in Matlab 2010a software at [0, 10%]And (3) generating drop-and-hang transportation tasks among 10 customer points, wherein all the drop-and-hang transportation tasks are integers, as shown in a table 2.

According to the two-stage heuristic algorithm, the MATLAB 2010a is applied to perform programming calculation, and the obtained result is shown in Table 3. Wherein the conventional method is to send a truck to transport each transportation task (generally not used, here for comparison); pure network transportation means that two stages are not divided, a transportation task is assigned in the whole network, when a certain vehicle has the remaining transportation time, the next task can be transported, and solution can be carried out according to the idea of the strategy 2 in the stage 2 in the heuristic algorithm.

TABLE 1 distance between road and harbor Meter (Unit, km)

Serial number	A	B	C	D	E	F	G	H	I	J
											A	0	1218	680	120	290	1080	600	690	945	1010
B	1218	0	540	1200	1500	2300	1710	1800	2000	2120
											C	680	540	0	660	960	1760	1170	1260	1170	1590
D	120	1200	660	0	314	1108	525	609	818	930
											E	290	1500	960	314	0	816	402	586	846	964
F	1080	2300	1760	1108	816	0	661	832	1131	1128
											G	600	1710	1170	525	402	661	0	274	594	600
H	690	1800	1260	609	586	832	274	0	323	356
											I	945	2000	1170	818	846	1131	594	323	0	276
J	1010	2120	1590	930	964	1128	600	356	276	0

TABLE 2 get rid of and hang the demand table (Unit: vehicle) between the harbors of the highway

Serial number	A	B	C	D	E	F	G	H	I	J
											A	0	7	8	0	1	4	6	2	0	1
B	9	0	2	0	10	0	3	3	2	7
											C	1	3	0	5	0	9	8	5	8	5
D	10	0	7	0	8	10	2	2	0	8
											E	6	1	9	10	0	5	7	9	10	7
F	1	9	10	1	9	0	2	2	8	9
											G	3	7	6	6	0	3	0	2	5	9
H	6	3	1	5	4	9	6	0	6	3
											I	10	10	1	0	2	4	8	2	0	7
J	10	0	2	3	8	1	0	4	5	0

TABLE 3 comparison of the calculated results

It can be seen from table 3 that the two-stage network swing and hang mode and the pure network swing and hang mode both use less tractors and have lower cost than the traditional mode. Compared with the traditional throwing and hanging traction vehicle, the two-stage network throwing and hanging strategy 1, strategy 2 and pure network throwing and hanging are respectively reduced by 7%, 10.4% and 27.1%, and the cost is saved by 0.8%, 0.7% and 8.6%. Compared with the traditional mode, in the two-stage network throwing and hanging and the pure network throwing and hanging, the tractor is allowed to pull a plurality of trailer tasks under possible conditions, and therefore the number of the used tractors is necessarily reduced. And when the cost increased by the empty running of the tractors is less than the fixed cost saved due to the reduction of the number of the tractors, the drop-off and hanging transportation cost of the two networks is presented.

The pure network swing-hang transportation has better performance than two-stage network swing-hang on the number and cost of the tractors. Compared with the two-stage network throwing and hanging strategy 1 and the two-stage network throwing and hanging strategy 2, the number of pure network throwing and hanging traction vehicles is reduced by 21.6 percent and 18.6 percent, and the cost is saved by 7.8 percent and 7.9 percent. The scheduling optimization is carried out in the whole network, so that the purchase of tractor vehicles and the overall cost reduction can be effectively reduced. The throwing and hanging enterprise operator changes the original mode of carrying out network throwing and hanging according to two stages, and better operation performance can be realized by adopting full network scheduling optimization, so that the cost is reduced, and the profit is improved.

Compared with two strategies of two-stage network throwing and hanging, as the stage 2 of the strategy 2 is optimized in the whole network, and the stage 2 of the strategy 1 is optimized between two end points and then is optimized in the network, the quantity of tractors can be reduced by the whole network vehicle scheduling. Although strategy 2 has a slightly smaller number of tractors than strategy 1, strategy 1 is slightly better in cost performance than strategy 2 because strategy 2 increases the idle cost by 44% over strategy 1.

Compared with the traditional transportation mode, the swing and hanging transportation optimization in the network can reduce the use number of traction vehicles and reduce the overall transportation cost. And in the network drop and hang transportation, scheduling optimization is carried out in the whole network range, so that the use number of traction vehicles can be more effectively reduced, and the transportation cost can be reduced. The invention fully considers the condition that the requirements of two ends are unbalanced and the requirement is possibly multiple in actual drop and pull transportation, provides the vehicle scheduling optimization in the whole network range in the highway and harbor network, can be close to the actual application scene, and is beneficial to the drop and pull transportation enterprises to improve the economic benefit.

The above description is intended to describe in detail the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the claims of the present invention, and all equivalent changes and modifications made within the technical spirit of the present invention should fall within the scope of the claims of the present invention.

Claims (6)

1. A network drop and pull transport scheduling optimization method is characterized by being applied to network drop and pull transport of a highway port consisting of a tractor, a trailer and the highway port, and comprising the following steps of:

(1) establishing a network throwing and hanging scheduling target optimization model;

(2) solving the target optimization model in the step (1) by using a two-stage heuristic algorithm:

firstly, the throwing and hanging requirements q between any two highway ports_ijIs divided into two partsQ's of'_ijAnd q "_ij(ii) a If q is_ij≥q_jiThen q'_ij＝q_ji＝q'_ji，q”_ij＝q_ij-q_ji，q”_ji0; if q is_ij＜q_jiThen q'_ij＝q_ij＝q'_ji，q”_ij＝0，q”_ji＝q_ji-q_ij，q’_ijThe formed matrix is a symmetric matrix; wherein q is_ij: representing the drop and pull transportation requirements of the highway ports i to j by using the drop and pull transportation times; q. q.s_ji: representing the drop and pull transportation requirements of the highway ports j to i by using the drop and pull transportation times; since the requirements are not necessarily balanced, q_ijIs not necessarily equal to q_ji；

Stage 1: to q 'of demand'_ijAnd dispatching the throwing hanging requirement: scheduling the trailer in a throwing manner by adopting two ends of a line, namely selecting a highway port arbitrarily in the network, starting to assign a throwing and hanging task of the tractor, and throwing and hanging the tractor back and forth between the two highway ports with heavy load;

and (2) stage: for q after phase 1 scheduling "_ijAnd dispatching the throwing hanging requirement: and (3) adopting full-network circulation throwing and hanging vehicle scheduling, namely selecting the least line in the residual throwing and hanging requirements after scheduling in the 1 st stage, firstly throwing and hanging in the stage, and taking the starting point of singular requirements as the starting point of the tractor.

2. A network drop and pull transport scheduling optimization method is characterized by being applied to network drop and pull transport of a highway port consisting of a tractor, a trailer and the highway port, and comprising the following steps of:

(1) establishing a network throwing and hanging scheduling target optimization model;

(2) solving the target optimization model in the step (1) by using a heuristic algorithm: the pure network circulation throwing and hanging requirements q between any two highway ports_ijAnd carrying out vehicle dispatching.

3. The optimization method of network drop-off transport scheduling according to claim 1 or 2, wherein the optimization model of the network drop-off scheduling objective in the step (1) is:

an objective function:

the network operation cost is composed of heavy-hanging running cost, empty running cost and fixed cost, and the heavy-hanging running cost

The empty running cost is as follows:

the fixed cost of using the vehicle on the same day is Z_{Fixing device}＝Kc；

The objective is that the network operation cost is expressed minimally as:

the constraint conditions are as follows:

get rid of and hang the demand and obtain satisfying:

tractor continuous operating time limit:

in the formula, i, j, l: the number of the road port, i, j, l belongs to N;

k: representing the set of tractors, K ═ {1,2, …, K }, and K also represents the total number of tractors required for the road network;

k: representing the number of the tractor, and K belongs to K;

d_ij: represents the distance between the road ports i, j, in units: km;

q_ij: the drop and pull transportation requirements of the highway ports i to j are shown, and the drop and pull transportation times are used for showingShown in the specification;

C_ij,c_ij: respectively representing the cost of towing heavy hanging and empty running of tractors from i to j of highway ports, unit: yuan/km;

c: the fixed cost of tractor use in unit time is shown, including vehicle depreciation, staff wage, unit: element;

t: the time of the continuous work of the tractors is represented, and the time of the continuous work of all the tractors every day is regulated to be equal;

v₁，v₂: respectively representing the speed of the tractor for towing heavy hanging and empty running, unit: km/h;

k₁，k₂respectively showing the states of heavy suspension and empty running of the tractor, K ∈ K;

the number of trips the tractor takes to travel from a highway port to a highway port for a heavy load and an empty ride, respectively.

4. The optimization method for network drop-off transport scheduling according to claim 1, wherein the stage 1 of the step (2) is performed according to the following steps:

the first step is as follows: setting initial parameters, i is 1, K is 0, and Z_{Heavy load}＝0，Z_{Air conditioner}＝0，Z_{Fixing device}＝0；

The second step is that: selecting q'_ij> 0, and max (d)_ij) The corresponding highway port i, j is a throwing and hanging terminal of the first vehicle service; if q'_ij> 0 and d_ij≥v₁T, then K ═ K +2q'_ij,q'_ij＝0＝q'_ji，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}Kc; if q'_ij> 0 and d_ij＜v₁T, and if the T time can complete the traction pass is

Then K is K +1, Z_{Fixing device}＝Kc，q'_ij＝0＝q'_jiAnd if q "_ijIf the working time is more than 0, the departure distance of the highway port j is selected to be small (d)_jl) Is taken as the next hanging point until the working time is used up, wherein (d)_jl) Represents the distance from road port j to road port l; corresponding q "_ij＝q”_ij-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ijC_ij+d_jlC_jl+..; if q "_ijIf 0, then choose the departure distance of the highway harbor i to be the next smallest (d)_il) Is taken as the next drop-and-hang point until the vehicle working time is exhausted, wherein (d)_il) Represents the distance from road port i to road port l, corresponding to q'_jl＝q'_jl-1，Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij+d_ilC_il+..; if q'_ij> 0 and d_ij＜v₁T, and if

Other vehicles need to be arranged between the highway ports i, j for transportation, and the number of the vehicles is required to be equal to

The vehicle with remaining capability can still complete other haul-off tasks, then q'_ij＝0＝q'_ji，

Z_{Heavy load}＝Z_{Heavy load}+2q'_ijd_ijC_ij，Z_{Fixing device}＝Kc；

Third step of applying to all i ∈ N, i ═ i +1, if q'_ijIf the value is more than 0, the calculation is returned to the second step; if all q'_ijWhen it is 0, the calculation is stopped, Z₁'＝Z_{Heavy load}+Z_{Fixing device}。

5. The optimization method for network drop-off transport scheduling according to claim 1, wherein the stage 2 of the step (2) is performed according to the following steps:

the first step is as follows: optionally i ∈ N;

the second step is that: q is selected "_ijThe highway port i, j greater than 0 is a throwing and hanging scheduling demand point; if d is_ij≥v₁T, then K ═ K + q "_ij,q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Fixing device}＝Kc；

If d is_ij＜v₁T, there are two strategies at this time:

strategy 1 is that a vehicle k travels back and forth between highway ports i and j, and only one way of loading goods is needed, and the highway ports j to i are empty; if vehicle k can complete q within time T "_ijThe hanging amount is K +1, q "_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji，Z_{Fixing device}If the remaining working time is not enough, the departure q of the highway harbor j can be selected "_jlTaking the port more than 0 as the next hanging point; if vehicle k cannot complete q within time T "_ijAnd if the load is thrown and hung, other vehicles are required to be dispatched to throw and hang, and the number of the vehicles required for completing the throwing and hanging task between the highway ports i and j is equal to that of the vehicles

If the vehicle with the residual capacity can still finish other throwing and hanging tasks

q”_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q”_ijd_ijC_ij，Z_{Air conditioner}＝Z_{Air conditioner}+(q”_ij-1)d_jic_ji，Z_{Fixing device}＝Kc；

The strategy 2 is that the vehicle k completes the throwing and hanging task in the highway port network, at the moment, heavy load and no load exist in the whole network, the vehicle k completes one-time throwing and hanging transportation from the highway ports i to j, and q'_ij＝q”_ij-1, selecting a highway harbor j departure q "_jlL harbor > 0 is used as the next hanging point, q "_jl＝q”_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jl+. cndot; if all q's are started from the highway harbor j "_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···，Z_{Fixing device}＝Kc；

In the third step, all i ∈ N, i +1, if q "_ijIf the value is more than 0, the calculation is returned to the second step; if all q "_ijWhen it is 0, the calculation is stopped, Z₁”＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}；

Therefore, the total cost of the network drop scheduling is as follows: z₁＝Z'₁+Z₁”。

6. The method for optimizing network drop-off transport scheduling as claimed in claim 2, wherein the step (2) of using pure network loop drop-off for drop-off demand q between any two highway ports_ijThe vehicle dispatching is carried out according to the following steps:

the first step is as follows: optionally i ∈ N;

the second step is that: select q_ijThe highway port i, j greater than 0 is a throwing and hanging scheduling demand point; if d is_ij≥v₁T, then K ═ K + q_ij,q_ij＝0，Z_{Heavy load}＝Z_{Heavy load}+q_ijd_ijC_ij，Z_{Fixing device}Kc; if d is_ij＜v₁T, completing a throwing and hanging task by the vehicle k in the highway port network, wherein at the moment, heavy load and no load exist in the whole network, completing one-time throwing and hanging transportation from the highway ports i to j by the vehicle k, and q_ij＝q_ij-1, selecting the departure q of the highway harbor j_jlL port more than 0 is used as the next hanging point, q_jl＝q_jl-1, until no working time remains, K ═ K +1, Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+d_jlC_jl+. cndot; if all q start from the port j of the highway_jlAnd (5) idling to a port I, selecting a road port with a throwing and hanging task from the port I for throwing and hanging until the working time is not left, wherein K is K +1, and Z_{Heavy load}＝Z_{Heavy load}+d_ijC_ij+···，Z_{Air conditioner}＝Z_{Air conditioner}+d_jlc_jl+···，Z_{Fixing device}＝Kc；

In the third step, all i ∈ N, i ═ i +1, if q_ijIf the value is more than 0, the calculation is returned to the second step; if all q are_ijWhen it is 0, the calculation is stopped, Z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

Therefore, the net network drop scheduling total cost is: z₁＝Z_{Heavy load}+Z_{Air conditioner}+Z_{Fixing device}。

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