CN116187531A - Solution algorithm for scheduling optimization of finished oil secondary logistics distribution vehicle - Google Patents
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Abstract
The invention discloses a solution algorithm for scheduling optimization of a finished oil secondary logistics distribution vehicle, which comprises the following steps: inputting a basic logistics plan and logistics data of a secondary logistics distribution problem of the finished oil; aiming at the problem characteristics and solving targets of the secondary logistics distribution of the finished oil, constructing an objective function and a corresponding mathematical model; solving a secondary distribution problem of the product oil based on a constructed heuristic algorithm, so as to obtain an initial feasible solution; performing iterative optimization on an initial feasible solution obtained by a structural algorithm based on a tabu search algorithm, and storing an output history optimal solution; and exporting the historical optimal solution obtained based on the algorithm into an optimal vehicle scheduling scheme. The invention carries out iterative optimization on the initial solution based on an improved tabu search algorithm to obtain a vehicle scheduling scheme with higher quality, thereby meeting the goals of reducing logistics cost and improving customer satisfaction of enterprises and promoting the construction of modern logistics systems of the enterprises.
Description
Technical Field
The invention belongs to the technical field of vehicle dispatching, and particularly relates to a solving algorithm for dispatching optimization of a finished oil secondary logistics distribution vehicle.
Background
In recent years, along with rapid development of social economy and application and upgrading of the internet of things technology, modern logistics technology has changed and broken through on the basis of the traditional mode, so that intelligent logistics with development trend of automation, informatization and intelligence is increasingly recognized and accepted by enterprises such as transportation, storage, production, sales and the like.
The petrochemical industry, which is the traditional energy industry, is not only subject to great impact of fluctuation of crude oil and oil markets, but also faces double pressure of economy and energy structure adjustment. In this situation, there is an increasing need for optimizing the petroleum supply chain. The secondary distribution of the finished oil is used as a final link of a petroleum supply chain, and the purpose of the secondary distribution is to convey the finished oil in the oil depot to each filling station through the tank truck, so that the filling requirements of the filling stations are met. In the product oil logistics system, the cost of secondary distribution of the product oil accounts for 60% -70% of the total logistics cost, and the optimization potential is huge, so that more and more petroleum enterprises use the optimized logistics distribution mode of the product oil as an important break for reducing the operation cost and increasing the enterprise benefit.
The secondary distribution system of the finished oil mainly comprises elements such as an oil depot, a distribution vehicle, a gas station site and the like, and is uniformly managed by a distribution center. However, petroleum enterprises also have a number of short plates in the distribution of product oil streams, such as: the logistics informatization level is low, and the distribution center cannot quickly respond to site demands; the vehicle distribution scheme is mostly obtained based on manual experience, and the solving quality and the solving efficiency are low. The problem of secondary distribution of the finished oil belongs to a vehicle path problem (Vehicle Routing Problem) in classification, is a typical NP problem, and has high solving complexity. Therefore, a solution is needed to obtain a vehicle scheduling solution for secondary distribution of the product oil with higher quality in a shorter time.
Disclosure of Invention
In view of the above, the invention aims to provide a solving algorithm for scheduling and optimizing a finished oil secondary logistics distribution vehicle, and designs an improved tabu search algorithm to solve problems rapidly and efficiently on the basis of mathematical modeling of a finished oil secondary logistics distribution scene, so as to achieve the aims of assisting staff in decision making, reducing vehicle distribution cost and improving customer satisfaction.
The solving algorithm for the scheduling optimization of the finished oil secondary logistics distribution vehicle comprises the following steps.
Symbol definition
N= {0,1, …, |n| }: a node set; wherein {0} represents the oil depot, i.e., the start and end points of the route; n (N) ′ = {1, …, |n| } represents a filling station to be dispensed;
k= {1,2, …, |k| }: a distribution vehicle collection;
P i ＝{1,2,…,|P i | }: a demand order set of a gas station i;
M k ＝{1,2,…,|M k | }: a vehicle cabin set of the delivery vehicle k;
R k ＝{1,2,…,|R k | }: a travel set of the delivery vehicle k;
i, j: node number, i, j e N;
k: the number of the delivery vehicle, K epsilon K;
and p: order number, p.epsilon.P i ；
m: vehicle cabin number, M epsilon M k ；
r: vehicle journey number R e R k ；
Parameter definition
d ij : route distance (km) between node i and node j;
q ip : the demand (kiloliter) of order p for site i;
Q km : capacity (kiloliter) of cabin m of vehicle k;
lambda: maximum operating time (hours) of the vehicle;
v: vehicle travel speed (km/h);
s 1 : oil loading rate (kiloliter/min);
s 2 : oil unloading rate (kiloliter/min);
a: the lowest load ratio of the cabin;
beta: the lowest delivery rate of the order;
c 1 : vehicle fixed use cost (meta/vehicle);
c 2 : vehicle unit delivery cost (yuan/km);
c 3 : unit loss cost (yuan/kiloliter) for the undelivered portion of the order;
c 4 : unit loss cost (yuan/kiloliter) of undelivered orders;
variable definition
x ijkr : if vehicle k passes along route (i, j) from station i to station j, x ijkr =1, otherwise x ijkr ＝0；
y ikpmr : if order p for station i is loaded into cabin m of vehicle k and is dispensed on trip r, y ikpmr =1, otherwise y ikpmr ＝0；
z ikr : representing the order in which vehicle k accesses station i in course r;
u kr : if the vehicle k is delivered on the trip r, u kr =1, otherwise u kr ＝0；
Objective function
The problem of product oil secondary distribution can be described as: for a single oil depot and a plurality of oil stations, the oil tank truck completes loading of the required oil orders of the oil stations in the oil depot, then sequentially accesses the oil stations along a delivery route to complete the oil discharging task, and finally returns to the oil depot. However, due to limited vehicle resources and diversified oil orders, the distribution requirements of all the gas stations cannot be met. In this case, the vehicle scheduling scheme for the secondary distribution of the product oil needs to be designed in consideration of not only the overall distribution cost but also the satisfaction degree of the requirement of the gas station.
Based on the above, the objective function of the problem of secondary distribution of the product oil is set as a comprehensive objective function, which mainly comprises two parts: vehicle distribution costs and order loss costs. The vehicle distribution cost reflects the cost generated in the transportation process of the vehicle, and the order loss cost reflects the loss cost generated when the requirement of the gas station is not satisfied.
The vehicle delivery costs can be further divided into a fixed delivery cost of the vehicle, which represents a fixed fee for the vehicle to be used, and a variable transportation cost of the vehicle, which is positively correlated with the transportation distance of the vehicle.
The expression of the vehicle stationary use cost is as shown in formula (1):
c 1 ∑ k∈K u k1 (1)
the expression of the vehicle variable transportation cost is shown in the formula (2):
the order loss costs can be further divided into an undelivered portion of the order loss costs, which represents the loss of the portion of the order that cannot be dispensed beyond the cabin capacity, and undelivered order loss costs, which represents the loss of the order that cannot be dispensed.
The expression of the order undelivered partial loss cost is shown in equation (3):
the expression of the undelivered order loss cost is shown in equation (4):
the expression of the comprehensive objective function is shown as the formula (5):
the design model solves the problem that the target is minimized in the comprehensive cost function, and not only considers the total transportation distance of the vehicle, but also considers the demand satisfaction degree of the gas station, so that the solution scheme is more fit with the reality of enterprises.
Model constraints
The problem of secondary delivery of the finished oil is essentially a vehicle path problem, but due to the specificity and complexity of the oil delivery scenario, besides the general features of the conventional VRP problem, such as multiple vehicles, multiple products, etc., the following oil delivery features are also provided:
(1) Vehicle multi-compartment: the finished oil delivery vehicles are mainly divided tank trucks, each tank truck is correspondingly loaded with an order, and the tank trucks can be loaded with various oil orders at a time and deliver for a plurality of gas stations.
(2) Cabin loading: because the finished oil belongs to inflammable and explosive dangerous goods, under the condition that the loading of the vehicle cabin is too low, vehicle accidents are easy to be caused by friction between the finished oil and the tank wall, and the shaking liquid is unfavorable for stable running of the vehicle, the loading constraint of the vehicle cabin needs to be met when the loading rate needs to be above the standard.
(3) Multi-trip delivery: due to the large order size, tank trucks are often required to perform multiple passes of delivery tasks to meet the current day delivery schedule, and the total delivery time for all trips of the tank truck cannot exceed its maximum working time.
Based on the characteristics of secondary distribution of the finished oil, the invention uses a mathematical expression to convert the characteristic into model constraint so as to carry out mathematical modeling.
For the delivery vehicle, each trip starts from the oil depot, and returns to the oil depot after delivery of the oil order is completed, so that delivery of the next trip is prepared. And the delivery vehicle can deliver the next course only after the delivery task of the previous course is completed. Furthermore, since the problem is defined on one connected graph, each node on the graph has a flow balancing constraint, i.e. the number of times a node is entered is equal to the number of times it starts from the node. To avoid creating sub-loops in the vehicle path scheme, the present invention adopts MTZ constraints to eliminate sub-loops. Thus, constraints as shown in the formulas (6) to (10) are obtained.
Equation (6) shows that any travel of any vehicle starts from the oil depot;
equation (7) shows that any travel of any vehicle is finished and returned to the oil reservoir;
equation (8) shows that for any vehicle, the following travel can only be started after the previous travel is completed;
equation (9) represents the inflow-outflow equilibrium constraint;
equation (10) represents the MTZ cancellation sub-loop constraint;
in order to solve the problem of secondary distribution of the finished oil, each oil order can only be loaded on one vehicle cabin at most, and each vehicle cabin can only be loaded with one order at most. In addition, the loading feasibility of the order on the vehicle cabin is related to the order capacity actually loaded on the vehicle cabin, the ratio of the actual loading capacity to the vehicle cabin capacity needs to be not lower than the lowest allocation rate of the vehicle cabin, and the ratio of the actual loading capacity to the order capacity needs to be not lower than the lowest allocation rate of the order. Thus, the present invention defines the constraint as in formula (11) -formula (14).
Equation (11) shows that for any cabin in any journey of any vehicle, it can only load one order at most; equation (12) represents any order for any site that can be loaded into at most one cabin;
equation (13) shows that the loading rate of the vehicle cabin cannot be lower than the lowest loading rate α if the order is loaded onto the vehicle cabin; equation (14) shows that the order part is allowed not to be delivered, but the actual delivery rate of the order cannot be lower than the minimum delivery rate β;
for any delivery vehicle, its total delivery time must not exceed the maximum operating time. The delivery time of a vehicle on a certain journey is mainly composed of three parts: loading time of the oil order, unloading time of the oil order, and vehicle transportation time. The total delivery time of the vehicle is the sum of all travel delivery times. Thus, the present invention defines the constraint as in equation (15).
Equation (15) indicates that the total vehicle delivery time cannot exceed the maximum operating time;
equation (16) -equation (19) is a definition of a variable.
Construction heuristic algorithm
The invention provides a construction heuristic algorithm based on improved nearest neighbor insertion to quickly obtain an initial feasible solution of the problem of secondary distribution of finished oil. The feasible solution comprises a delivery route scheme of each vehicle for accessing the gas station and a loading scheme of the oil product order on the vehicle cabin.
The primary goal of initial solution generation is to reconsider lower delivery costs while meeting as much as possible the delivery requirements of the oil orders at all sites. Based on the goal, the construction heuristic algorithm provided by the invention adopts the solving idea of grouping first and then routing, namely, firstly, the combination of gas stations to be distributed is determined, and then, the most suitable distribution vehicle is selected for distribution according to the station combination, so that a corresponding vehicle distribution scheme is generated.
In the case of determining the loading scheme of the vehicle, that is, the combination of stations to be visited by the vehicle is already known, it is very easy to solve the optimal route scheme of the vehicle at this time, and since the number of cabins of the vehicle is not more than 4 at most, the number of stations visited by the vehicle in the journey is not more than 4, and the route scheme for minimizing the journey distribution distance can be obtained quickly by traversing. However, the available loading schemes for vehicles may be varied for different combinations of stations, and the vehicle resources are limited, and the division of station combinations and the selection of loading schemes may have an impact on subsequent decisions, thereby affecting the quality of the overall distribution scheme. In order to obtain a better distribution scheme in the whole, the invention carries out site grouping and decision of order loading scheme selection by defining evaluation indexes such as order distribution urgency, site distribution priority, loading scheme distribution benefit and the like.
Symbol definition:
n= {0,1, …, |n| }: a node set; wherein {0} represents the oil depot, i.e., the start and end points of the route; n (N) ′ = {1, …, |n| } represents a filling station to be dispensed;
k= {1,2, …, |k| }: a distribution vehicle collection;
P i ＝{1,2,…,|P i | }: the to-be-distributed order set of the gas station i;
M k ＝{1,2,…,|M k | }: a vehicle cabin set of the delivery vehicle k;
R k ＝{1,2,…,|R k | }: a travel set of the delivery vehicle k;
l: the order corresponds to a loading scheme of the cabin;
d: a set of all possible loading schemes;
s: a vehicle distribution scheme set;
i, j: node number, i, j e N;
k: the number of the delivery vehicle, K epsilon K;
and p: order number, p.epsilon.P i ；
m: vehicle cabin number, M epsilon M k ；
r: vehicle journey number R e R k ；
d ij : route distance between node i and node j;
θ ipkmr : the amount of state of the cabin m of the vehicle k that the journey r can meet the order p load of the station i is measured,
if theta is ipkmr =1 means that the vehicle cabin can load and distribute orders, otherwise θ ipkmr ＝0；
w 1 ,w 2 ,w 3 ,w 4 ,w 5 : controlling parameters;
for any order p of any gas station i, it delivers urgency O ip The calculation formula of (2) is as follows:
the method comprises the steps that through statistics of the available distribution times of all vehicle cabins meeting the loading requirement of an order, the evaluation of available distribution resources of the order is obtained, if the distribution resources are fewer, the higher the distribution emergency degree of the order is indicated, and therefore the vehicle cabins are preferentially distributed to the order is considered;
distribution priority J for arbitrary gas station i i The calculation formula of (2) is as follows:
wherein d 0i Representing the route distance from the gas station i to the oil depot; the evaluation of delivery priority mainly takes into account two aspects: the distance from the station to the oil depot and the distribution urgency of the order to which the station belongs. The greater the distance from the station to the oil depot and the greater the sum of the distribution urgency of all orders for the station, the greater the distribution priority for the station.
For a viable order loading scheme L, the calculation formula of the delivery benefit is as follows:
f(L)＝w 4 C(L)+w 5 u (L) (22) wherein f (L) represents the delivery benefit of the loading scheme, C (L) represents the delivery cost of the loading scheme, and U (L) represents the total order delivery urgency in the loading scheme. The index indicates that the distribution benefit of a distribution scheme is higher if the distribution cost of the scheme is lower and the distribution urgency of the order the scheme is loading is higher.
In summary, the steps of the structured heuristic algorithm provided by the invention are as follows:
step 1: initializing a station set N' to be distributed, a vehicle set K capable of being distributed and a vehicle distribution scheme set S;
step 2: if the current distribution site set N' is not empty, turning to step 3; otherwise, go to step 13;
step 3: updating the distribution emergency degree of all orders based on a formula (20), calculating the distribution priority degree of all stations to be distributed based on a formula (21), selecting a station with the highest distribution priority degree as a seed station i, and generating an initial station combination { i };
step 4: for the initial station combination, sequentially selecting vehicles from the distributable vehicle set K, and adding a feasible order loading scheme L to the loading scheme set D if the vehicles exist;
step 5: setting an optimal loading scheme L best Setting optimal distribution benefit f for empty best Is 0;
step 6: if the current loading scheme set D is empty, go to step 10; otherwise, go to step 7;
step 7: sequentially selecting loading schemes from the loading scheme set D for removal, and if the vehicle cabin is not allocated with a loading order in the selected loading schemes, turning to step 8; otherwise, go to step 9;
step 8: for the selected loading scheme L, according to the order information loaded by the loading scheme L, the site combination visited by the current vehicle is obtained, the optimal site insertion is selected based on the nearest neighbor insertion algorithm, and whether a feasible insertion loading scheme L' exists or not is judged according to the site combination after insertion. If so, adding the new loading scheme L' to the set D, and turning to the step 7; otherwise, go to step 9;
step 9: for the selected loading scheme L, calculate the delivery benefit of the loading scheme based on equation (22), if f (L)>f best Then update L best ＝L，f best =f (L), go to step 5;
step 10: if L best Empty, indicating that no viable delivery scheme exists for seed site i, go to step 11; otherwise, go to step 12;
step 11: removing a seed site i from the set of sites to be dispatched N'; turning to step 2;
step (a)12: according to the optimal loading scheme L best Solving the corresponding optimal distribution route scheme, storing the loading scheme and the route scheme into a vehicle distribution scheme set S, and updating a station set N' to be distributed and a distributable vehicle set K; turning to step 2;
step 13: the algorithm is terminated, and a final vehicle distribution scheme set S is output;
improved tabu search algorithm
Aiming at the characteristic of the problem of secondary distribution of the finished oil, the invention provides an improved tabu search algorithm, and the initial feasible solution obtained by the nearest neighbor inserted structural heuristic algorithm is subjected to iterative optimization, so that a high-quality vehicle scheduling scheme is obtained, and the aims of reducing logistics distribution cost and improving customer satisfaction are fulfilled.
The design of the tabu search algorithm provided by the invention is as follows.
Symbol definition:
S 0 : secondary distribution of finished oil is an initial vehicle distribution scheme;
n: the number of gas stations;
k: the number of the delivery vehicles;
S best : the current best vehicle delivery scheme;
f best : a current optimal objective function value;
l: tabu table length;
n: a candidate solution set;
m: maximum number of iterations;
form of solution:
the overall vehicle delivery scheme can be divided into three levels of "overall-vehicle-trip" and for a single-trip delivery scheme of a single vehicle, it needs to include both the order of vehicle visits at the current trip and the allocation of orders to the vehicle cabin, therefore, the invention defines the solution in the form of x= { ζ 1 ,ξ 2 ,…,ξ i ,…ξ m }, wherein ζ i Is regarded as a node of the distribution scheme and serves as a basic element of the solution.
ξ i Storage ofIs a pairing scheme of order and cabin, such as xi 1 ＝(O 1 ,M 1 ) Indicating order O 1 Loaded into the cabin M 1 Applying; in addition to storing pairing information for orders and cabins, ζ i The subscript i of (a) indicates the order in the delivery scheme, e.g., ζ, in which orders are delivered 1 ＝(O 1 ,M 1 )，ξ 1 The subscript of 1 indicates order O 1 Is the first order to be dispatched, thereby determining the access order of the gas stations.
Adaptive value function:
the invention sets the adaptive value function as the comprehensive cost function corresponding to the vehicle distribution scheme.
Neighborhood actions:
for a vehicle delivery scheme, its quality is determined by a vehicle path scheme and its feasibility is determined by an order loading scheme. In order to better explore the neighborhood space of the solution, three different neighborhood operators are defined to realize the neighborhood exploration in different directions.
(1) The nodes exchange swap: exchanging the positions of two nodes in the same route or different routes;
(2) Reassigning relocation: removing one node on a certain route and inserting the node into other positions;
(3) 2-opt: selecting two nodes on different routes, and exchanging travel segments after the selected nodes;
to improve the efficiency of neighborhood exploration, the invention assigns an assigned weight to each neighborhood operator, defines the probability of each operator being selected based on equation (23) in each iteration, and selects by adopting rules of roulette.
Wherein w is i Representing the weights of the operators i.
Tabu object and tabu table:
from the definition of the solution form, node ζ i Is the basic element of the travel scheme, the neighborhoodThe transformation of actions, i.e. the transformation of nodes, thus selects the movement of the nodes as a tabu object, which is essentially the removal and insertion of orders.
In order to enable the algorithm to search for as many neighborhood solutions as possible in the early stage, the algorithm is fully searched for the better solutions in the later stage. Therefore, the present invention sets the length of the tabu list to be dynamic, and the length of the tabu list is gradually increased with the increase of the iteration number, which is obtained by the formula (24).
Wherein L is 0 For the initial tabu step length of the short tabu table, i is the number of iterations, rand is a random number in the interval (0, 1), and τ is based on parameters set by the scale of the problem, so as to ensure that the variation of the tabu step length is not excessive.
In addition, in order to avoid the algorithm from falling into repeated and invalid iterations, after a certain number of iterations, if the optimal solution is not improved, the tabu list can be reset or the length of the tabu list can be reduced so as to perform more neighborhood operations. Or after iterating for a certain number of times, if the optimal solution is not improved, setting the current optimal solution or the better solution as the initial solution for re-iterating, and resetting the tabu table.
Centralization and diversification strategies:
the candidate solution is a solution generated by the initial solution through the neighborhood action, and in order to balance the local searching capability and the global searching capability, different candidate solutions can be generated based on different strategies and then stored in a candidate solution set. The centralized strategy is used for enhancing the more complete exploration of the neighborhood of the currently searched good solution in order to find the globally optimal solution. The diversified strategies are used for widening the search area, particularly the unknown area, and particularly when the search area is in the local optimum, the search direction based on the diversified strategies can be changed, and the local optimum is jumped out, so that the global optimization is realized.
The invention is based on the idea that the candidate solution set is divided into two parts, and the first half part element is called a centralized element and is used for centralized searching; the latter half of the elements is called diversity elements, which are used for diversity searching. For concentrated elements, the main quality is high, so that the concentrated elements can be generated by an insertion method; for the diversity element, the random method is used because the area which is never explored before is explored as much as possible.
Scofflaw:
in an iterative process, a solution may be obtained that is better than the solution in all the already accessed solution spaces, which is not justified. According to the invention, an scofflaw based on an adaptation value is adopted, if a tabu solution exists in the candidate solution set and is better than a known optimal solution, the solution is forbidden to serve as an initial solution of the next iteration, and the optimal solution is updated. Otherwise, selecting the current local optimal solution which is not tabulated from the candidate solution set as an initial solution of the next iteration;
algorithm termination criteria:
for the tabu search algorithm, the convergence condition in the strict sense, that is, the state space traversal is realized under the condition that the tabu length is sufficiently large, which is obviously impractical, so that the actual algorithm is generally designed by adopting an approximate convergence criterion. The invention sets the maximum iteration number as M.
The main steps of the tabu search algorithm are as follows:
step 1: initializing an algorithm, and setting parameters including a tabu table length, a candidate set length and a maximum iteration step number;
step 2: generating an initial feasible solution based on the constructed heuristic as a starting point for iterative search;
step 3: respectively applying a centralized strategy and a diversified strategy to generate a candidate solution set;
step 4: judging whether a solution meeting a scofflaw exists in the current candidate solution set according to the evaluation function, and if so, selecting the solution as an initial solution of the next iteration; otherwise, selecting the current local optimal solution which is not tabulated from the candidate solution set as an initial solution of the next iteration;
step 5: updating a tabu table;
step 6: judging whether the algorithm meets the termination condition, if so, outputting an optimal solution appearing in iteration, and terminating the algorithm; if not, the currently selected solution is taken as the starting point of the next iteration and the process goes to step 3.
The invention has the beneficial effects that: based on the characteristics of the problem of secondary distribution of the finished oil, the invention constructs a vehicle scheduling model with the lowest comprehensive cost as an objective function, rapidly obtains a feasible vehicle scheduling scheme as an initial feasible solution of subsequent iteration by designing a structural heuristic algorithm based on nearest neighbor insertion, and further carries out iterative optimization on the initial solution based on an improved tabu search algorithm to obtain a vehicle scheduling scheme with higher quality, thereby meeting the aims of reducing logistics cost and improving customer satisfaction of enterprises and promoting the construction of modern logistics systems of the enterprises.
Drawings
FIG. 1 is a flow chart of a secondary logistics distribution of finished oil;
FIG. 2 is a flow chart of a solution for a structured heuristic;
FIG. 3 is a diagram showing a solution to the problem of secondary distribution of product oil;
fig. 4 is a flow chart of a tabu search algorithm.
Detailed Description
The invention will be further described with reference to examples and drawings, to which reference is made by way of illustration, but not limitation, for the understanding of those skilled in the art.
A solving algorithm for scheduling optimization of a finished oil secondary logistics distribution vehicle comprises the following modeling process: symbol definition
N= {0,1, …, |n| }: a node set; wherein {0} represents the oil depot, i.e., the start and end points of the route; n (N) ′ = {1, …, |n| } represents a filling station to be dispensed;
k= {1,2, …, |k| }: a distribution vehicle collection;
P i ＝{1,2,…,|P i | }: a demand order set of a gas station i;
M k ＝{1,2,…,|M k | }: a vehicle cabin set of the delivery vehicle k;
R k ＝{1,2,…,|R k | }: a travel set of the delivery vehicle k;
i, j: node number, i, j e N;
k: the number of the delivery vehicle, K epsilon K;
and p: order number, p.epsilon.P i ；
m: vehicle cabin number, M epsilon M k ；
r: vehicle journey number R e R k ；
Parameter definition
d ij : route distance (km) between node i and node j;
q ip : the demand (kiloliter) of order p for site i;
Q km : capacity (kiloliter) of cabin m of vehicle k;
lambda: maximum operating time (hours) of the vehicle;
v: vehicle travel speed (km/h);
s 1 : oil loading rate (kiloliter/min);
s 2 : oil unloading rate (kiloliter/min);
alpha: the lowest load ratio of the cabin;
beta: the lowest delivery rate of the order;
c 1 : vehicle fixed use cost (meta/vehicle);
c 2 : vehicle unit delivery cost (yuan/km);
c 3 : unit loss cost (yuan/kiloliter) for the undelivered portion of the order;
c 4 : unit loss cost (yuan/kiloliter) of undelivered orders;
variable definition
x ijkr : if vehicle k passes along route (i, j) from station i to station j, x ijkr =1, otherwise x ijkr ＝0；
y ikpmr : if order p for station i is loaded into cabin n of vehicle k and is dispensed on trip r, y ikomr =1, otherwise y ikpmr ＝0；
z ikr : representing the order in which vehicle k accesses station i in course r;
u kr : if the vehicle k is delivered on the trip r, u kr =1, otherwise u kr ＝0；
The problem of product oil secondary distribution can be described as: for a single oil depot and a plurality of oil stations, the oil tank truck completes loading of the required oil orders of the oil stations in the oil depot, then sequentially accesses the oil stations along a delivery route to complete the oil discharging task, and finally returns to the oil depot. The flow chart of the logistics distribution is shown in figure 1.
Mathematical model
The mathematical model of the secondary logistics distribution of the finished oil is as follows:
equation 1 is an objective function that minimizes the comprehensive distribution cost;
equation 2 shows that any travel of any vehicle starts from the oil depot;
equation 3 shows that the end of any journey of any vehicle is returned to the oil depot;
equation 4 shows that for any vehicle, the following travel can only be started after the previous travel is completed;
equation 5 represents the inflow and outflow equilibrium constraint;
equation 6 represents the MTZ cancellation sub-loop constraint;
equation 7 shows that for any cabin in any journey of any vehicle, it can only load one order at most;
equation 8 represents any order for any site that can be loaded to at most one cabin;
equation 9 shows that if an order is loaded onto a cabin, the loading rate of the cabin cannot be lower than the lowest loading rate α;
equation 10 shows that the order part is allowed not to be delivered, but the actual delivery rate of the order cannot be lower than the minimum delivery rate β; equation 11 shows that the total vehicle delivery time cannot exceed the maximum operating time;
equation 12-equation 15 are definitions of variables.
Construction heuristic algorithm
The algorithm flow of the construction heuristic is shown in fig. 2:
step 1: initializing a station set N' to be distributed, a vehicle set K capable of being distributed and a vehicle distribution scheme set S;
step 2: if the current distribution site set N' is not empty, turning to step 3; otherwise, go to step 13;
step 3: updating the distribution emergency degree of all orders based on a formula (16), calculating the distribution priority degree of all stations to be distributed based on a formula (17), selecting a station with the highest distribution priority degree as a seed station i, and generating an initial station combination { i };
step 4: for the initial station combination, sequentially selecting vehicles from the distributable vehicle set K, and adding a feasible order loading scheme L to the loading scheme set D if the vehicles exist;
step 5: setting an optimal loading scheme L best Setting optimal distribution benefit f for empty best Is 0;
step 6: if the current loading scheme set D is empty, go to step 10; otherwise, go to step 7;
step 7: sequentially selecting loading schemes from the loading scheme set D for removal, and if the vehicle cabin is not allocated with a loading order in the selected loading schemes, turning to step 8; otherwise, go to step 9;
step 8: for the selected loading scheme L, according to order information loaded by the loading scheme L, acquiring a site combination visited by the current vehicle, selecting the optimal site insertion based on the nearest neighbor insertion algorithm, judging whether a feasible insertion loading scheme L ' exists for the inserted site combination, adding a new loading scheme L ' into the set D if the feasible insertion loading scheme L ' exists, and turning to the step 7; otherwise, go to step 9;
step 9: for the selected loading scheme L, calculating the delivery benefit of the loading scheme based on equation (18), if f (L)>f best Then update L best ＝L，f best =f (L), go to step 5;
step 10: if L best Empty, indicating that no viable delivery scheme exists for seed site i, go to step 11; otherwise, go to step 12;
step 11: removing a seed site i from the set of sites to be dispatched N'; turning to step 2;
step 12: according to the optimal loading scheme L best Solving the corresponding optimal distribution route scheme, storing the loading scheme and the route scheme into a vehicle distribution scheme set S, and updating a station set N' to be distributed and a distributable vehicle set K; turning to step 2;
step 13: the algorithm is terminated, and a final vehicle distribution scheme set S is output;
symbol definition:
n= {0,1, …, |n| }: a node set; wherein {0} represents the oil depot, i.e., the start and end points of the route; n (N) ′ = {1, …, |n| } represents a filling station to be dispensed;
k= {1,2, …, |k| }: a distribution vehicle collection;
P i ＝{1,2,…,|P i | }: the to-be-distributed order set of the gas station i;
M k ＝{1,2,…,|M k | }: a vehicle cabin set of the delivery vehicle k;
R k ＝{1,2,...,|R k | }: a travel set of the delivery vehicle k;
l: the order corresponds to a loading scheme of the cabin;
d: a set of all possible loading schemes;
s: a vehicle distribution scheme set;
i, j: node number, i, j e N;
k: the number of the delivery vehicle, K epsilon K;
and p: order number, p.epsilon.P i ；
m: vehicle cabin number, M epsilon M k ；
r: vehicle journey number R e R k ；
d ij : route distance between node i and node j;
θ ipkmr : the amount of state of the cabin m of the vehicle k that the journey r can meet the order p load of the station i is measured,
if theta is ipkmr =1 means that the vehicle cabin can load and distribute orders, otherwise θ ipkmr ＝0；
w 1 ,w 2 ,w 3 ,w 4 ,w 5 : controlling parameters;
for any order p of any gas station i, it delivers urgency O ip The calculation formula of (2) is as follows:
distribution priority J for arbitrary gas station i i The calculation formula of (2) is as follows:
for a viable order loading scheme L, the calculation formula of the delivery benefit is as follows:
f(L)＝w 4 C(L)+w 5 U(L) (18)
improved tabu search algorithm
A flow chart of the tabu search algorithm is shown in fig. 4.
Step 1: initializing an algorithm, and setting parameters including a tabu table length, a candidate set length and a maximum iteration step number;
step 2: generating an initial feasible solution based on the constructed heuristic as a starting point for iterative search;
step 3: respectively applying a centralized strategy and a diversified strategy to generate a candidate solution set;
step 4: judging whether a solution meeting a scofflaw exists in the current candidate solution set according to the evaluation function, and if so, selecting the solution as an initial solution of the next iteration; otherwise, selecting the current local optimal solution which is not tabulated from the candidate solution set as an initial solution of the next iteration;
step 5: updating a tabu table;
step 6: judging whether the algorithm meets the termination condition, if so, outputting an optimal solution appearing in iteration, and terminating the algorithm; if not, the currently selected solution is taken as the starting point of the next iteration and the process goes to step 3.
Symbol definition:
S 0 : secondary distribution of finished oil is an initial vehicle distribution scheme;
n: the number of gas stations;
k: the number of the delivery vehicles;
S best : the current best vehicle delivery scheme;
f best : a current optimal objective function value;
l: tabu table length;
n: a candidate solution set;
m: maximum number of iterations;
form of solution:
the overall vehicle distribution scheme may be divided into three levels of "overall-vehicle-trip" as shown in fig. 3.
X＝{ξ 1 ,ξ 2 ,…,ξ i ,…ξ m } (19)
Selection of a neighborhood operator:
length of the tabu table:
Claims (5)
1. a solution algorithm for scheduling optimization of a product oil secondary logistics distribution vehicle, comprising the steps of:
1) Inputting a basic logistics plan and logistics data of a secondary logistics distribution problem of the finished oil;
2) Aiming at the problem characteristics and solving targets of the secondary logistics distribution of the finished oil, constructing an objective function and a corresponding mathematical model;
3) Solving a secondary distribution problem of the product oil based on a constructed heuristic algorithm, so as to obtain an initial feasible solution;
4) Performing iterative optimization on an initial feasible solution obtained by a structural algorithm based on a tabu search algorithm, and storing an output history optimal solution;
5) And exporting the historical optimal solution obtained based on the algorithm into an optimal vehicle scheduling scheme.
2. The solution algorithm of claim 1, wherein the objective function of step 2) is constructed as follows: setting the objective function of the secondary distribution problem of the finished oil as a comprehensive objective function, wherein the comprehensive objective function mainly comprises two parts of vehicle distribution cost and order loss cost, the vehicle distribution cost is divided into vehicle fixed distribution cost and vehicle variable transportation cost, the order loss cost is divided into order undelivered part loss cost and undelivered order loss cost,
the expression of the vehicle fixed use cost is shown as (1)
c 1 ∑ k∈K u k1 (1)
c 1 : vehicle fixed use cost (meta/vehicle); k: the number of the vehicle to be delivered is given,k∈K；u kr : if the vehicle k is delivered on the trip r, u kr =1, otherwise u kr ＝0；
The expression of the variable transportation cost of the vehicle is shown as (2)
c 2 : vehicle unit delivery cost (yuan/km); i, j: node number, i, j e N; r: vehicle journey number R e R k ；d ij : route distance (km) between node i and node j; x is x ijkr : if vehicle k passes along route (i, j) from station i to station j, x ijkr =1, otherwise x ijkr ＝0；
The expression of the loss cost of the undelivered part of the order is shown as (3)
c 3 : unit loss cost (yuan/kiloliter) for the undelivered portion of the order; and p: order number, p.epsilon.P i The method comprises the steps of carrying out a first treatment on the surface of the m: vehicle cabin number, M epsilon M k ；y ikpmr : if order p for station i is loaded into cabin m of vehicle k and is dispensed on trip r, y ikpmr =1, otherwise y ikpmr ＝0；q ip : the demand (kiloliter) of order p for site i; q (Q) km : capacity (kiloliter) of cabin m of vehicle k;
the expression of the undelivered order loss cost is shown as (4)
c 4 : unit loss cost (yuan/kiloliter) of undelivered orders;
the expression of the comprehensive objective function is shown as the formula (5):
3. the solution algorithm of claim 2, wherein step 2) is essentially a vehicle path problem based on the product oil secondary delivery problem, but because of the specificity and complexity of the oil delivery scenario, the model needs to be constrained to perform mathematical modeling, and for the delivery vehicle, each trip starts from the reservoir, and returns to the reservoir after delivery of the oil order is completed, in preparation for delivery of the next trip. And the delivery vehicle can deliver the next journey only after completing the delivery task of the previous journey, in order to avoid generating sub-loops in the vehicle path scheme, MTZ constraint is adopted to eliminate the sub-loops, and constraint as shown in the formulas (6) - (10) is obtained
Equation (6) shows that any travel of any vehicle starts from the oil depot;
equation (7) shows that any travel of any vehicle is finished and returned to the oil reservoir;
equation (8) shows that for any vehicle, the following travel can only be started after the previous travel is completed;
equation (9) represents the inflow-outflow equilibrium constraint;
equation (10) represents the MTZ cancellation sub-loop constraint; z ikr : representing the order in which vehicle k accesses station i in course r;
aiming at the problem of secondary distribution of the finished oil, each oil order can only be loaded on one vehicle cabin at most, each vehicle cabin can only be loaded with one order at most, the loading feasibility of the order on the vehicle cabin is related to the actual loading capacity of the vehicle cabin, the ratio of the actual loading capacity to the vehicle cabin capacity is not lower than the lowest loading rate of the vehicle cabin, the ratio of the actual loading capacity to the order capacity is not lower than the lowest distribution rate of the order, the constraint as shown in the formula (11) -the formula (14) is defined,
equation (11) shows that for any cabin in any journey of any vehicle, it can only load one order at most;
equation (12) represents any order for any site that can be loaded into at most one cabin;
equation (13) shows that the loading rate of the vehicle cabin cannot be lower than the lowest loading rate α if the order is loaded onto the vehicle cabin;
equation (14) shows that the order part is allowed not to be delivered, but the actual delivery rate of the order cannot be lower than the minimum delivery rate β;
for any delivery vehicle, the total delivery time cannot exceed the maximum working time, and the delivery time of the vehicle on a certain journey mainly consists of three parts: loading time of the oil product order, unloading time of the oil product order and vehicle transportation time, total delivery time of the vehicle is the sum of all travel delivery time, constraint as shown in formula (15) is defined,
equation (15) indicates that the total vehicle delivery time cannot exceed the maximum operating time; s is(s) 1 : oil loading rate (kiloliter/min);
s 2 : oil unloading rate (kiloliter/min); lambda: maximum operating time (hours) of the vehicle; v: vehicle travel speed (km/h);
equation (16) -equation (19) is a definition of a variable.
4. A solving algorithm according to claim 3, characterized in that for any order p of any filling station i, it delivers the degree of urgency O ip The calculation formula of (2) is as follows:
the method comprises the steps that through statistics of the available distribution times of all vehicle cabins meeting the loading requirement of an order, the evaluation of available distribution resources of the order is obtained, if the distribution resources are fewer, the higher the distribution emergency degree of the order is indicated, and therefore the vehicle cabins are preferentially distributed to the order is considered;
distribution priority J for arbitrary gas station i i The calculation formula of (2) is as follows:
wherein d 0i Representing the route distance from the gas station i to the oil depot; the evaluation of delivery priority mainly takes into account two aspects: the distance from the station to the oil depot and the distribution urgency of the order to which the station belongs,
for a viable order loading scheme L, the calculation formula of the delivery benefit is as follows:
f(L)＝w 4 C(L)+w 5 U(L) (22)
wherein f (L) represents the delivery benefit of the loading scheme, C (L) represents the delivery cost of the loading scheme, U (L) represents the total order delivery urgency in the loading scheme, and w 1 ，w 2 ，w 3 ，w 4 ，w 5 : controlling parameters;
the specific operation mode of the step 3) comprises the following steps:
step 1: initializing a station set N' to be distributed, a vehicle set K capable of being distributed and a vehicle distribution scheme set S;
step 2: if the current distribution site set N' is not empty, turning to step 3; otherwise, go to step 13;
step 3: updating the distribution emergency degree of all orders based on a formula (20), calculating the distribution priority degree of all stations to be distributed based on a formula (21), selecting a station with the highest distribution priority degree as a seed station i, and generating an initial station combination { i };
step 4: for the initial station combination, sequentially selecting vehicles from the distributable vehicle set K, and adding a feasible order loading scheme L to the loading scheme set D if the vehicles exist;
step 5: setting an optimal loading scheme L best Setting optimal distribution benefit f for empty best Is 0;
step 6: if the current loading scheme set D is empty, go to step 10; otherwise, go to step 7;
step 7: sequentially selecting loading schemes from the loading scheme set D for removal, and if the vehicle cabin is not allocated with a loading order in the selected loading schemes, turning to step 8; otherwise, go to step 9;
step 8: for the selected loading scheme L, according to order information loaded by the loading scheme L, acquiring a site combination visited by the current vehicle, selecting the optimal site insertion based on the nearest neighbor insertion algorithm, judging whether a feasible insertion loading scheme L ' exists for the inserted site combination, adding a new loading scheme L ' into the set D if the feasible insertion loading scheme L ' exists, and turning to the step 7; otherwise, go to step 9;
step 9: for the selected loading scheme L, calculate the delivery benefit of the loading scheme based on equation (22), if f (L)>f best Then update L best ＝L，f best =f (L), go to step 5;
step 10: if L best If the seed station i is empty, the step 11 is switched to, and if the seed station i is empty, a feasible distribution scheme does not exist for the seed station i, otherwise, the step 12 is switched to;
step 11: removing a seed site i from the site set N' to be distributed, and turning to step 2;
step 12: according to the optimal loading scheme L best Solving the corresponding optimal distribution route scheme, and combining the loading scheme and the routeThe online scheme is stored in a vehicle distribution scheme set S, and a station set N' to be distributed and a vehicle set K capable of being distributed are updated; turning to step 2;
step 13: the algorithm terminates and the final vehicle distribution scenario set S is output.
5. The solution algorithm of claim 4, wherein the main steps of the tabu search algorithm of step 4) are as follows:
step 1: initializing an algorithm, and setting parameters including a tabu table length, a candidate set length and a maximum iteration step number;
step 2: generating an initial feasible solution based on the constructed heuristic as a starting point for iterative search;
step 3: respectively applying a centralized strategy and a diversified strategy to generate a candidate solution set;
step 4: judging whether a solution meeting a scofflaw exists in the current candidate solution set according to the evaluation function, and if so, selecting the solution as an initial solution of the next iteration; otherwise, selecting the current local optimal solution which is not tabulated from the candidate solution set as an initial solution of the next iteration;
step 5: updating a tabu table;
step 6: judging whether the algorithm meets the termination condition, if so, outputting an optimal solution appearing in iteration, and terminating the algorithm; if not, the currently selected solution is taken as the starting point of the next iteration and the process goes to step 3.
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