CN110689307B - Method and system for optimizing article delivery time - Google Patents
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Abstract
The invention provides a method and a system for optimizing article delivery time. The method comprises the following steps: acquiring parameters related to article delivery time in a mode of direct acquisition or probability statistics from a database, wherein the parameters comprise article information, delivery vehicle information and customer information; establishing an article delivery time optimization model by using the parameters; and obtaining a delivery path of the delivery vehicle according to the item delivery time optimization model, wherein the delivery path enables the sum of the total transportation time and the total assembly time to be minimum. According to the invention, parameters are acquired in a mode of direct acquisition or probability statistics from the database, and a solution for distribution and assembly is obtained according to the goods distribution time optimization model, so that the goods distribution time is saved.
Description
Technical Field
The invention relates to an article distribution time optimization method and system.
Background
With the adjustment of urban industrial layout, the continuous upgrade of modern consumption modes, the wide application of electronic commerce technology and the increasing diversification of urban industrial and commercial development modes, the demands of small-batch, multi-frequency, highly-efficient direct distribution, residential distribution and 'door-to-door' distribution are increasing day by day. How to shorten the total time of goods distribution is the key to improve the logistics service efficiency. For how the article delivery time is shortened, the existing research can refer to the article delivery Problem, and also refer to the Vehicle path Problem (VRP) with time window limitation or uncertain assembly time. Past research has often focused on customer order distribution, route optimization and distribution center location under certain conditions.
In recent years, network retail industry has emerged, and many e-commerce enterprises provide customers with high-quality urban logistics service, so that some researchers start to shift to new research directions. For example, non-patent document "Vehicle routing with routing delivery location" by Reyes in 2017 mentions VRP for mobile delivery locations; trentini and Malhn referred to integration of public transportation networks in non-patent publication Toward a shared urban transport system sensors & goods 2010; and unmanned aerial vehicles vigorously developed in the state are applied to article distribution. There have also been many studies to solve the problem of item delivery time through modeling and algorithms, for example, erico expressed the problem as a set partitioning model in 2018, which has a probability constraint on the global success probability of the routing plan, and proposed a branch price reduction algorithm combining the column generation process and the dynamic planning method; lee applied robust optimization in 2012 to the problem of VRP with uncertain transportation and demand, and customer demand deadlines.
However, in the delivery time optimization algorithm in the prior art, due to the fact that the order quantity of the customers is too large, the personalized requirements of the customers are more, the assembly time is greatly changed, uncertainty and random factors are too much, and therefore a solution is difficult to find, the delivery path of a delivery vehicle is not ideal, and the delivery time can not be saved.
Disclosure of Invention
Technical problem to be solved
The problem that a solution is difficult to find due to the fact that the customer order quantity is too large and the personalized requirements of customers are more, the assembly time is greatly changed, and uncertain and random factors are too much is solved, so that the delivery path of a delivery vehicle is not ideal, and the delivery time can not be saved.
(II) technical scheme
One aspect of the present invention provides a method for optimizing an article delivery time, including: acquiring parameters related to article delivery time in a mode of direct acquisition or probability statistics from a database, wherein the parameters comprise article information, delivery vehicle information and customer information; establishing an article delivery time optimization model by using the parameters; and obtaining a delivery path of the delivery vehicle according to the item delivery time optimization model, wherein the delivery path enables the sum of the total transportation time and the total assembly time to be minimum.
In another aspect of the present invention, there is provided an article delivery time optimization system, including: the system comprises a parameter acquisition module, a data base and a data processing module, wherein the parameter acquisition module is used for acquiring parameters related to article distribution time in a direct acquisition or probability statistics mode from the data base, and the parameters comprise article information, distribution vehicle information and customer information; the model building module is used for building an article delivery time optimization model by using the parameters; and the delivery path determining module is used for obtaining the delivery path of the delivery vehicle according to the article delivery time optimization model, and the sum of the total transportation time and the total assembly time is enabled to be the minimum value by the delivery path.
(III) advantageous effects
The conveying paths of the distribution vehicles are reasonably arranged, and compared with the prior art, the distribution time is saved.
The invention obtains uncertain parameters in the prior art from a database by means of direct acquisition or probability statistics, for example, the assembly time of each commodity is uncertain in general and is influenced by various practical conditions.
On the basis of the method in the prior art, a time sliding mechanism is added, so that the actual situation that the total time of distribution service is influenced by the change of the assembly time is better met, and a better solution is possibly found while the total time is optimized;
the data in the real article distribution database is adopted, namely the data acquisition comes from a real enterprise database and the like, so that the management inspiration of the article distribution problem can be provided for enterprises.
Drawings
FIG. 1 is a flow chart of a method for optimizing the delivery time of an article according to an embodiment of the present invention;
FIG. 2 is a graph of the time it takes for different vehicles to deliver their cargo according to their routes, according to one embodiment of the present invention;
fig. 3 is a block diagram of an item delivery time optimization system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
The invention provides a method for optimizing article delivery time, which comprises the following steps:
and 101, acquiring parameters related to article delivery time by means of direct acquisition or probability statistics from a database, wherein the parameters comprise article information, delivery vehicle information and customer information.
Wherein the delivery vehicle information includes a mean and variance of the assembly time of each commodity, a vehicle speed, a number of vehicles, a total number of vehicles at the delivery point, and a maximum load capacity of the vehicle. The customer information includes the latest starting service time allowed by each customer, the earliest starting service time allowed by each customer, the distance between the customers, the total number of the customers, and the r < th > number i The number of p-th products purchased by each customer. The item information includes the total amount of the kinds of commodities, the volume of the commodity p, and the commodity amount of each customer. It will be understood by those skilled in the art that the various parameters herein are virtually all parameters required in the item delivery time optimization model and its first constraints。
The mean and variance of the assembly time for each commodity is calculated by probabilistic statistics from data already available in the database, which as used herein may include real data statistically derived from enterprise databases. In addition, all parameters required by the model can be obtained from a database, such as assembly time, volume of the commodity and the like.
It should be noted that, in the present invention, the vehicle speed is set as a known quantity, the maximum load of the vehicle, and the maximum load of all vehicles in the model is uniform.
And 102, establishing an article distribution time optimization model by using the parameters.
The item delivery time optimization model is represented by the following formula:
wherein, minF EDP (x, y) to minimize the sum of the transit time, the expected total assembly time, and the expected additional wait time; d ij Distance from client i to client j; v, vehicle speed; t is t p Assembly time for each commodity; o is ip Number of items p for customer i; x is the number of ijk A binary variable having a value of 1 if vehicle k passes customer i from customer j, and a value of 0 if vehicle k passes customer i, with x being equal to (x) ijk )；y ik Is a binary variable, with a value of 1 if vehicle k serves customer i, otherwise a value of 0, let y equal (y) ik )；
Is a set of the categories of the goods,
p is the total amount of commodity types; v, a set of vehicle numbers, V ═ 1, 2. K is the total number of vehicles at the distribution point; and C, collecting the number of the clients.
The item delivery time optimization model includes first constraints including:
wherein x is i0k Returning to the warehouse from customer i for vehicle k; x is a radical of a fluorine atom 0jk Run from the warehouse to the location of customer j for vehicle k; x is the number of jik If the vehicle k passes through the client j from the client i, the value is 1, otherwise the value is 0;
is a set of the categories of the goods,
p, total amount of commodity types; v, a set of vehicle numbers, V ═ 1, 2, a. K is the total number of vehicles at the distribution point; c, a customer number set; n is the total number of customers; a is i The start time of actual acceptance of delivery and assembly for customer i; a is j Actual access time for jth client; m is a given, very large positive number, preferably a positive number equal to or greater than 24; v p Volume of commodity p; q, the maximum loading capacity of the vehicle; x is the number of ijk Is a binary variable having a value of 1 if vehicle k passes customer i from customer j, otherwise 0, let x ═ x (x ijk )；y ik Is a binary variable, with a value of 1 if vehicle k serves customer i, otherwise a value of 0, let y equal (y) ik )；y ik A binary 0-1 variable, meaning that if vehicle k serves customer j, the value is 1, otherwise the value is 0, let y be (y) jk )；
Phi is a normalized dynamic distribution function, phi -1 Is the inverse function of phi; mu.s p The mean value of the assembly time of the commodity p;
is the assembly time variance of the commodity P;
is the r th i The number of p-th products purchased by each customer;
the distance from client i to client i + 1; l, is the latest delivery activity end time;
for a customer n k Allowed latest starting service time;
for a customer n k Allowed earliest starting service time; epsilon 1 The maximum deviation probability of the punctuality of the time service window for the client takes a positive number close to zero; epsilon 2 The maximum deviation probability of the punctuality of the operation service is a positive number close to zero.
The article distribution time optimization model established in the steps is obtained by converting a random optimization model and an opportunity constraint optimization model.
In particular, the invention uses probabilistic constraints to express these uncertainties, and the stochastic optimization model is represented by the following sub-equations:
wherein, E.]To find the mathematical expectation value, o i Set of order quantities for customer i, o ═ o (o) 1 ，...，o N ) T ＝(o ip ) NiP 。
The second constraint of the stochastic optimization model comprises the following conditions:
wherein e is i Allowed for client iThe earliest starting service time of l i The latest starting service time allowed for client i, so [ e ] i ，l i ]The time window is served to the customer. E, the earliest delivery activity starting time; l, is the latest delivery campaign end time, so [ E, L]The boundaries are scheduled for scheduling.
The objective function in the stochastic optimization model, equation (24), represents minimizing the sum of the transit time, the expected total assembly time, and the expected additional wait time; the constraint (2) ensures that each customer is delivered by exactly one vehicle at a time; constraints (3) - (5) describe the flow on the travel path of vehicle k, i.e. vehicle k must leave and return to the distribution point and the transit node; the constraint (6) ensures that the service start time of the next customer is not earlier than the sum of the start time of the previous customer, the assembly time and the transit time between the two customers; constraint (7) is the time window of the client; the constraint (8) indicates the possibility of forming arrangements subject to load limitations; the constraints (9) (10) are combined constraints connecting the decision variables x and y; constraints (11) ensure that all customers will be serviced; the constraint condition (12) ensures that the working time of each vehicle does not exceed the latest ending time of the total delivery task; the constraint (13) indicates that the variable class is binary. An opportunity constraint optimization model is recombined on the basis of the random optimization model, and the method is an effective method for simulating the random optimization problem.
The opportunistic constraint optimization model is subject to the constraints (2) - (6), (8) - (11), (13) above and the following conditions:
here, the constraint (14) ensures that the client's time window is at the interval [ e ] i ，l i ]And the probability guarantees 1-epsilon 1 The situation will decrease; the constraint (15) ensures that 1-epsilon is guaranteed at probability 2 The operating time of each vehicle will not exceed the latest total delivery task time.
Pro {.. } is the probability of occurrence of a probabilistic event {. L is the latest delivery activity end time; epsilon 1 The maximum deviation probability of the punctuality of the time service window for the client takes a positive number close to zero; epsilon 2 The maximum deviation probability of the punctuality of the operation service is a positive number close to zero.
The present invention takes a commodity P as an example to illustrate the statistics of the assembly time probability distribution parameters. Let the mean value of the assembly time of the product P be mu p Variance of
Xi rule 1 ，ξ 2 ，...ξ n A series of observations of the assembly time of the item P in the data set. By using the dynamic difference estimation method, the method can obtain,
applying a convex combination averaging method to historical data of the assembly time of the goods, assuming
Is the average assembly time of the commodity P on the working day T, and rho (T) (T epsilon {1, …, T }) is a time proportion coefficient vector and meets the following three conditions:
ρ (t) > 0 and is an increasing function of t; Δ ρ (t) ═ ρ (t) - ρ (t-1) < ε; ε is a small positive constant and represents the lower limit of precision;
based on the above three conditions, we can derive:
these can be put into our Equivalent delivery time optimization model, which is an deterministic model (EDP), it is easy to prove that the above two equations are also an unbiased estimate of the total mean and variance of the time of shipment.
Order to
The kth Path for CCP model conclusion, where 0 represents warehouse, R k Indicating the path of the kth vehicle.
Is a path R k The set of customers. If the assembly time t of each commodity p Including normally distributed random variables, t can be derived based on (18) and (19), respectively p Mean and variance of, then client
The chance constraint (14) of (a) can be equivalently converted into the following equation:
Φ is the normalized dynamic distribution function. Let the mean time of assembly of the product P be mu p Variance is
The constraint (14) ensures that the client's time window is at the interval [ e ] i ，l i ]And the probability guarantees 1-epsilon 1 Will reduce under the circumstances
For the path R k Of any customer in (1), his/her actual delivery time may be deduced as
By means of a recursive algorithm, it is possible to,
then can obtain
By further combining (14), it is possible to obtain:
order to
Due to all t p (P ∈ P) is an independent random variable that follows a normal distribution, and the random variable θ is also normally distributed, i.e.
By using the additivity of the normal distribution, the mean value and the variance of θ are derived as follows:
therefore, we can normalize the constraint (21) to be:
if epsilon in the constraint (14) 1 Being a positive number small enough to mean that all vehicles can arrive within the respective customer-specified time window, we can therefore translate the constraint (15) into:
let the mean time of assembly of the product P be mu p Variance is
The constraint (15) ensures that 1-epsilon is guaranteed at probability 2 The operating time of each vehicle will not exceed the latest total delivery task time.
Phi is a standard normal distribution, phi -1 Is the inverse function of phi. L is the latest delivery campaign end time. Order the k-th vehicle path
The total working hours eta of the kth vehicle path is
The constraint (22) may be converted into
Due to all t p Are normally distributed random variables, so η is also a normally distributed random variable, and the mean and variance of η can be derived as:
equation (22) can then be simplified to
From the inverse function of the above inequality
From the above results, we can obtain
With the above results, we can transform the opportunity constrained optimization model into an equivalent delivery time optimization model, i.e., the delivery time optimization model described above is a transformation of the deterministic capacity constrained vehicle routing problem, which minimizes not only transit time for all delivery vehicles, but also assembly and waiting time for all goods.
And 103, obtaining a delivery path of the delivery vehicle according to the article delivery time optimization model, wherein the sum of the total transportation time and the total assembly time is the minimum value through the delivery path.
The step of obtaining the delivery path of the delivery vehicle according to the article delivery time optimization model comprises the step of calculating the delivery time optimization model through a first algorithm based on a time sliding mechanism and a saving algorithm and a variable neighborhood search algorithm to obtain the delivery path.
Wherein the first algorithm based on the time-sliding mechanism and the saving algorithm comprises: the route with the most time saving is obtained through a time saving algorithm, the time of the earliest arrival of all customers is sequenced by using a time sliding mechanism, and then the route is assigned to each vehicle.
Specifically, the present invention needs to calculate the delivery Time optimization model, and the calculation of the model includes two sub-algorithms, wherein one of the sub-algorithms is a first algorithm based on a Time sliding mechanism and a saving algorithm, that is, a Time sliding and saving algorithm-based heuristic (TSSA), and the other is a Variable neighbor Search algorithm (VNS) that has been applied to various VRPs. The calculation comprises the following steps:
initializing all distribution time optimization model parameters;
sort in descending order of time according to the client time window and then prioritize the clients that were dispatched earlier, i.e., the time-sliding mechanism. Then a feasible solution is found by utilizing a first algorithm;
finding a better feasible scheme from the generated feasible schemes by using a variable neighborhood searching algorithm;
if the preset condition is satisfied, outputting an optimal solution, otherwise, returning to the previous step.
Namely: initial recipe x, record function value as F EDP (x) Let the optimal solution x * Current solution x ═ x cs ＝x；
Circulation of
Let gamma shaking 1 and γ local ＝1；
Circulation of
From
In using x cs Randomly generating a solution x'
From
Finding the best neighbor x 'with x';
if F EDP (x”)＜F EDP (x') then
Let x * ＝x”；
End judgment
If F EDP (x”)＜F EDP (x) Then
Let x be x ";
end judgment
Let gamma shaking ＝γ shaking +1 and gamma local ＝γ local mod 3+1；
If the termination condition is satisfied;
output best solution x * .
In this algorithm, the stopping criterion is set as follows: if the solution quality for a given number of iterations does not improve, or a preset number of iterations is performed, the search process will stop.
The invention is further illustrated in the following by a specific example:
the warehouse management system database of the enterprise A is used for acquiring the order quantity, the detailed address of the client, the expected time window of the client, the commodity information, the vehicle information and the like. From the viewpoint of cost saving, companies currently use only one truck and have a total of 14 trucks.
The company needs to distribute 64 products to customers and collect their data over 30 working days. First, we used the assembly times of the first 29 working days to study and estimate distribution parameters for each cargo, including the mean and variance of the assembly times for representative commodities (10 commodities) (see below)
Table 1), and probability distribution parameters, i.e., mean and variance, corresponding to the ten product assembly times.
TABLE 1 Assembly time mean and variance table for representative articles
Then, we substitute the distribution parameters of the cargo assembly time (including the estimated average assembly time and variance of all products to be delivered) into the distribution time optimization model (EDP model) to obtain the distribution and assembly solution, see fig. 2, fig. 2 is the time taken by 14 vehicles to distribute cargo according to their routes, see table 2, table 2 is the result obtained by the method provided according to the embodiment of the present invention, and 14 vehicles are respectively assigned with routes, and the total assembly time of the 14 vehicles is 97.8 hours.
Table 2 table of results obtained by the algorithm provided in the embodiment of the present invention
In addition, the embodiment of the invention compares the calculated result of the invention with two selection meta-heuristics widely applied to practice and the current algorithm of enterprise a, see table 3, and it can be seen that the calculated result of the invention has better performance, which saves 8.79% of the total time of the scheme of the Genetic Algorithm (GA), 12.35% of the total time of the scheme of the simulated annealing algorithm (SA), and 19.62% of the total time of the scheme currently used by the enterprise, compared with the results obtained by the Genetic Algorithm (GA), the simulated annealing algorithm (SA), and the current method of enterprise a.
TABLE 3 comparison table of algorithm provided by the present invention and conventional algorithm
| Completion time (h) | Performance improvement (%) | Run time (h) | |
| The method provided by the invention | 97.8 | 128 | |
| Genetic algorithm | 107.22 | 8.79 | 371 |
| Simulated annealing algorithm | 111.58 | 12.35 | 433 |
| Enterprise A Current approach | 121.67 | 19.62 |
In another aspect of the present invention, there is provided an article delivery time optimization system, where the system 300 includes:
a parameter obtaining module 301, configured to obtain parameters related to article delivery time through direct collection from a database or a probability statistics manner, where the parameters include article information, delivery vehicle information, and customer information; a model building module 302 for building an item delivery time optimization model using the parameters; a delivery path determining module 303, configured to obtain a delivery path of the delivery vehicle according to the item delivery time optimization model, where the delivery path minimizes a sum of a total transportation time and a total assembly time.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only examples of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A method for optimizing delivery time of an item, the method comprising:
acquiring parameters related to article delivery time in a mode of direct acquisition or probability statistics from a database, wherein the parameters comprise article information, delivery vehicle information and customer information;
establishing an article delivery time optimization model by using the parameters;
obtaining a delivery path of a delivery vehicle according to the item delivery time optimization model, comprising: calculating the distribution time optimization model through a first algorithm based on a time sliding mechanism and a saving algorithm and a variable neighborhood search algorithm to obtain the conveying path;
wherein the first algorithm based on the time-sliding mechanism and the saving algorithm comprises: obtaining a route which saves most time through a saving algorithm, sequencing the earliest arriving time of all customers by using a time sliding mechanism, and designating a conveying route for each vehicle according to the sequencing;
the transport path minimizes the sum of total transport time and total assembly time.
2. The method of claim 1, wherein the delivery vehicle information includes a mean and a variance of an assembly time of each commodity.
3. The method of claim 1, wherein the customer information comprises a latest starting service time allowed for each customer, an earliest starting service time allowed for each customer, and a distance between customers.
4. The method of claim 1, wherein the item delivery time optimization model is represented by the following equation:
wherein, min F EDP (x, y) is the minimization of the sum of the total delivery time and the total assembly time of the delivery vehicle; d ij Distance from client i to client j; v is vehicle speed; t is t p Assembly time for each article; o ip The number of items p for customer i; x is the number of ijk Is a binary variable, the value is 1 if the vehicle k passes from customer j to customer i, otherwise the value is 0; let x be (x) ijk )；y ik Is a binary variable having a value of 1 if vehicle k serves customer i, and otherwise a value of 0, let y equal (y) ik ) (ii) a P is a commodity type set, P is {1, 2, …, P }, and P is a total quantity of commodity types; v is the set of vehicle numbers, V ═ {1, 2, …, k }; k is the total number of vehicles at the distribution point; and C is a customer number set.
5. The method of claim 4, wherein the item delivery time optimization model comprises first constraints, the first constraints comprising:
wherein x is i0k For vehicle k from customer i Returned to the warehouse, x 0jk Run from warehouse to customer j's location for vehicle k; x is the number of jik Is a binary variable, the value is 1 if the vehicle k passes the customer j from the customer i, otherwise the value is 0; p is a commodity type set, and P ═ {1, 2, …, P } P is a total quantity of commodity types; v is the set of vehicle numbers, V ═ 1, 2, …, k }; k is the total number of vehicles at the distribution point; c is a customer number set; n is the total number of customers; b is a mixture of i The start time of the actual acceptance of the delivery and assembly for customer i; a is j Actual access time for the jth client; m is a positive number of 24 or more; v. of p Is the volume of the commodity p; q is the maximum load capacity of the vehicle; x is the number of ijk Is a binary variable having a value of 1 if vehicle k passes customer i from customer j, otherwise 0, let x ═ x (x) ijk )；y ik Is a binary variable, which has a value of 1 if vehicle k serves customer i, and otherwise takes a value of 0, let y be (y) ik )；
Phi is a standardized dynamic distribution function, phi -1 Is the inverse function of phi; μ p is the mean assembly time of article p;
is the assembly time variance of the commodity p;
is the r i The number of p-th products purchased by each customer;
for the customer i Distance to customer i + 1; l is the latest delivery activity end time;
for a customer n k Allowed latest starting service time;
for a customer n k Allowed earliest starting service time; epsilon 1 Maximum deviation probability of the punctuality of the service window for the time of the client; epsilon 2 The maximum deviation probability of the punctuality of the operation service is served.
6. The method of claim 5, wherein the item delivery time optimization model is transformed from a stochastic optimization model and an opportunity constrained optimization model.
7. The method of claim 6, wherein the stochastic optimization model is represented by the following equation:
wherein E [ … ] is a mathematical expectation;
the stochastic optimization model includes second constraints, the second constraints including (2) - (6), (8) - (11), (13) of the first constraints, and the following conditions:
wherein e is i For the customer i Allowed earliest starting service time,/ i The latest starting service time allowed for client i;
the opportunity constraint optimization model further comprises the following conditions on the basis of the second constraint condition:
pro {.. } is the probability of occurrence of a probabilistic event {. L is the latest delivery activity end time; epsilon 1 Maximum deviation probability of the punctuality of the service window for the time of the client; epsilon 2 The maximum deviation probability of the punctuality of the operation service.
8. An item delivery time optimization system, comprising:
the system comprises a parameter acquisition module, a data processing module and a data processing module, wherein the parameter acquisition module is used for acquiring parameters related to article distribution time in a mode of direct acquisition or probability statistics from a database formed by historical operation data, and the parameters comprise article information, distribution vehicle information and customer information;
the model building module is used for building an article delivery time optimization model by using the parameters;
a delivery path determination module for obtaining a delivery path of a delivery vehicle according to the item delivery time optimization model, comprising: obtaining the delivery path through a first algorithm based on a time sliding mechanism and a saving algorithm, calculating a distribution time optimization model through a variable neighborhood search algorithm, and obtaining the delivery path;
wherein the first algorithm based on the time-sliding mechanism and the saving algorithm comprises: obtaining a route which saves most time through a saving algorithm, sequencing the earliest arriving time of all customers by using a time sliding mechanism, and designating a conveying route for each vehicle according to the sequencing;
the transport path minimizes the sum of total transport time and total assembly time.
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