Military transport path selection directly affects the transport speed, efficiency, and safety. To a certain degree, the results of the path selection determine success or failure of the war situation. The purpose of this paper is to propose a model based on DEA (data envelopment analysis) and multiobjective fuzzy decisionmaking for path selection. The path decision set is established according to a search algorithm based on overlapping section punishment. Considering the influence of various fuzzy factors, the model of optimal path is constructed based on DEA and multitarget fuzzy decisionmaking theory, where travel time, transport risk, quick response capability, and transport cost constitute the evaluation target set. A reasonable path set can be calculated and sorted according to the comprehensive scores of the paths. The numerical results show that the model and the related algorithms are effective for path selection of military transport.
During the hitech local war, the mission of the military supplies support is very heavy, so the status of the military transport has become increasingly prominent [
With the increasing uncertainty in occurrence and the quick decision of modern war, military transport needs more reliability and higher speed, so path optimization has become an important part of the military transport system. A good path selection plays an important role in completing the whole transport task on time, improving the efficiency of the transport, and enhancing logistic support capability.
There are many successful applications about routing optimization and selection in literatures [
Path must be feasible and better controlled traffic roads are required to be chosen in the first place to ensure that troops and supplies can reach the destination on time and safely.
Try to select the path with short travel time, high safety, high economic benefit, and the least number of transfers as much as possible.
The emergency transport plans are required to deal with various potential damage states to ensure that alternate routes may be selected flexibly after the enemy fire.
In view of the peculiarity of military highway transport in war, various factors should be comprehensively considered in path selection, such as the mileage of the path, speed, travel time, reliability, security, fuel consumption, transport loss, and supporting capability [
For military transport path selection, sections that do not conform to the requirements of the transport task should be removed from the existing road network. After that, considering the particularity of military transportation, we also want to choose paths with high dissimilarity so as to equally distribute the risk as much as possible [
To meet needs of warfare, transport task needs to be accomplished within the prescribed period of time. So in this paper, dissimilar paths [
Given a graph
The problem of searching the dissimilar path set
Using the dissimilar path algorithm based on overlapping punishment, the dissimilar path set
Consider
Using the Dijkstra algorithm [
If
If
Update
Using this algorithm, path decision set is obtained and arranged in order to increase travel time on each path:
In the path selection of military transport, considering the influence of various fuzzy factors, multiobjective fuzzy decisionmaking method is an effective way [
In wartime path selection, the decisionmaker often considers simultaneously multiple conflicting objectives [
The purpose of transport time evaluation is only to compare the relative length of travel time on different routes. Therefore, the difference between travel time on each route and the shortest travel time is used as the evaluation criteria. Consider
According to the experience of military transport, in general, for
The common forms of membership functions include triangle, trapezoid, Gaussian, and clock form. Here, triangular fuzzy function is used to determine the membership degree of travel time. Then, membership functions of travel time difference
So membership vector of travel time difference
The three factors are of great fuzziness and difficult to quantify, and their membership functions are difficult to be defined directly. In this paper, comprehensive weighted statistics method is used to establish these membership functions.
The weight of each type of personnel for transport risks assessment is
The weight of each type of personnel for rapid response capability assessment is
The weight of each type of personnel for transport costs assessment is
Then, membership degree of each objective factor is as follows:
Then, the evaluation vector of route
Then, the evaluation matrix of route set
DEA method [
(1) Using path from path decision set as decisionmaking unit and using membership degree as input and output indicators, for each path, the score value of each remark grade on each objective factor is calculated.
In this paper,
The weight vectors of input and output are given as the variable vectors as follows:
For route
By choosing appropriate weight vector
This model is fractional program and can be converted into linear program to solve by using the CharnesCooper transformation.
Taking membership degree of route
(2) Using path from path decision set as decisionmaking unit and using
To meet the demand of the combat replenishment, a batch of military supplies need to be moved from node 1 to node 7 in time. Figure
Road section travel time.
Section  12  13  14  23  25  26  34  46  56  57  67 
Travel time (h)  1  2  1  1  5  6  3  5  4  4  5 
The road networks.
Path decision set is
The weight of each type of personnel for transport risk assessment is
The weight of each type of personnel for rapid response capability is
The weight of each type of personnel for transport cost is
The evaluation results for path decision set by the evaluation personnel are shown in Table
Evaluation results by evaluation personnel.
Path 




 

Transportrisk  Excellent 





Good 






Medium 






Poor 






Rapid responsecapability  Excellent 





Good 






Medium 






Poor 






Transport costs  Excellent 





Good 






Medium 






Poor 





The difference between travel time on each route and the shortest travel time is shown in Table
Travel time difference of each route.
Path 





Travel time difference  0  1  2  2  4 
Membership degree is calculated in Table
Membership degree.
Route 




 

Travel time  Excellent  1  0.667  0  0  0 
Good  0  0.333  0.75  0.75  0  
Medium  0  0  0.25  0.25  0.917  
Poor  0  0  0  0  0.083  
Transportrisk  Excellent  0.123  0.262  0.448  0.587  0.503 
Good  0.352  0.387  0.387  0.352  0.400  
Medium  0.387  0.303  0.165  0.061  0.097  
Poor  0.138  0.048  0.0  0.0  0.0  
Rapid response capability  Excellent  0.348  0.384  0.304  0.400  0.268 
Good  0.384  0.217  0.435  0.332  0.517  
Medium  0.200  0.348  0.165  0.200  0.182  
Poor  0.068  0.051  0.096  0.068  0.033  
Transportcosts  Excellent  0.503  0.433  0.360  0.430  0.263 
Good  0.367  0.337  0.367  0.404  0.234  
Medium  0.130  0.197  0.210  0.133  0.303  
Poor  0.0  0.033  0.063  0.033  0.200 
Score value of each route on each remark grade.
Remark grade 






Excellent  0.551  0.462  0.245  0.313  0.232 
Good  0.238  0.324  0.519  0.498  0.250 
Medium  0.163  0.185  0.204  0.169  0.442 
Poor  0.048  0.029  0.032  0.020  0.076 
Using
Final score of each path.
Route 





Final score  0.393  0.371  0.312  0.340  0.250 
So, the calculation results are sorted in a descending order:
In this paper, path selection problem considering the influence of various fuzzy factors in military transport is investigated. Based on overlapping section punishment search algorithm, the path decision set is established. Then, a path selection decision model is presented based on DEA and multiobjective fuzzy decisionmaking method, where the evaluation target set consists of travel time, transport risk, quick response capability, and transport cost. For factors of great fuzziness and difficult to quantify, comprehensive weighted statistics method is used to establish the membership functions. Using path as decisionmaking unit, the comprehensive evaluation by DEA model can sort the path set, where the path with the higher comprehensive score indicates the much better one. Finally, the calculation results show the validity and effectiveness of the proposed method.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is partly supported by Science and Technology Program of Beijing, China (Grant no. Z121100000312101).