Most studied attri- butes are stochastic customer demand, capacitated vehicle, geographically dispersed cities or customers Laporte et al. The 1. Dantzig and Ramser ; Chenghua and Xiaofeng, and others. Berhan et al. The former assumes static or deterministic of arcs. In some context, Cij ever, considers stochastic parameters. When C is symmetrical, it is the solution is implemented. According to the survey route starts and ends at the depot, each customer is visited made by Eksioglu et al.
With all theses assump- exponentialy with 6. Variants of VRP the readers and identify future research directions. For instance, the most commonly studied variant is research methodology, Sec. It is future research directions. Literature Review interval wherein the customer has to be supplied Balak- rishnan, ; Taillard et al.
Vehicle routing problem Stefan and Natalia, ; Xiangyong et al. VRP is represented in a graph theory. Multiple Depot VRP 2. The ran- In addition to the above variants, more additional side dom parameters may be the presence of customers, the constraints are also added in the problem structures that nature of customer demand at a given location, the time lead to have more variants of VRP. Some of them are such as service time, or travel time or windows time multiple depots Bertsimas and Van Ryzin, , a Reimann, Novoa et al.
Trudeau, and stochastic service time Laporte, However, the classical VRP model usually does not SVRP also addresses other areas such as unknown capture an important aspect of real life transportation and knowledge of the road conditions, passengers shift and distribution-logistic problems.
This is due to the fact that working hours, heterogenous vehicles, split customer de- several of the problem parameters such as demand, time, mand, number and size of vehicle, and others. Brief summary of literatures related to SVRP. The number of articles and year of istics and special factors considered under each category. VRP review has been done by Bodin , Desrochers et al. Identifying domains and attributes , Parragh et al. They are introduced by considering 3.
Research Methodology the main domains and attributes shown as headings and In order to conduct the meta-analysis, this research used a sub-headings. Finally based on the meta-anal- veloped by Eksioglu et al. Categorising and classifying articles journal were used as a source to search VRP literatures.
The phrase s. These include journal articles, book chapters, levelling is from abstraction to the details in order to technical reports, and articles from various conference provide clear view to the reader. But for this research, the term article is used The meta-analysis was used to classify each articles and it means any one of them. All of them were kept for based on the domains and attributes developed in Sec. For each domain, more detailed attributes as sub- categories were also derived so as to help to classify SVRP 3.
Screening related literatures literatures. Table 2. Years and numbers of publication. Means the number of articles in each year. Attribute that has only one marked cell is maximisa- tion objective function 7. The other attribute that has two cells marked is 1. Attribute that has only 1. In 4 Data 8 Applied Models 4. To solve SVRP models, the solution 4.
However, the use of meta-heuristics 5 Number of Vehicle 8. As explained in the literatures, most VRP models are 4. Results and Discussions represented in a graph. Accordingly, from those that Based on the meta-analysis, articles that represent rather represented their model in a graph, symmetric graph 3.
The remaining presentation 3. With regard to the nature columns represent the domains and their corresponding of data used, most SVRP are studied using synthesis data attributes. While classifying, some column cells may re- 4. The synthesis data in the main vacant. This means that, the article does not data attribute is dominant because most SVRP address or involve that cell's attribute.
But, if the article researchers either used instances from previous research or addresses the attribute in the domain corresponding to hypothetical data to test their model.
The full shaded columns represent the point of SVRP articles, the dominant one is multiple vehicle 5. This representation is designed followed by single vehicle 5. However, out of 38 articles that involved either the domain or attribute they belong to.
As shown in single or multiple vehicles 37 of them were studied with Table 4, the articles appear to be uniformly distributed in capacitated vehicles consideration 6. Figure 1, shows the relative With respect to objective function, the survey showed proportion of each domain and attributes.
But variation that cost minimisation 7. Therefore, function as compared to other attributes in the mini- a closer look at each domain and attribute is very im- misation domain. Whereas maximisation objective func- portant.
Except the column that branches the domain, tion 7. However, there domain of objective function. However, the other types of are very few columns that have one, two and three objective function 7. The distribution of articles based on attributes. In this ; Dror, ; Dror et al. It is indi- the tools and techniques that are used in solution ap- cated as others 8. However, all the remaining SVRP literatures are summarised well. However, the tated vehicles 6.
As shown in here. SVRP problems are used to model urban public bus Fig. Sumalee et al. Moreover, stochastic customer 1. Conclusion function with time minimisation 7.
The and Markov-chain applied model 8. A paired-vehicle recurs through time. Transportation Science, 41 2 , — Balakrishnan, N Journal of tomer demand, and synthesis data are the most domi- Operations Research Society, 44 3 , — Exact solution of vehicles and cost minimisation objective functions. The stochastic vehicle routing problem revisited. European Journal of Oper- were conducted using exact heuristic solution techniques.
Solving stochastic vehicle routing problem with literatures. In Innovations in Bio-Inspired Computing the stochastic consideration is not limited to customer, and Applications, Advances in Intelligent Systems and demand, and time; rather includes also other side con- Computing, Vol. Switzerland: straints such as road weather conditions, workers' shift, Springer International Publishing.
A vehicle routing problem with study that tried to classify and categorise SVRP studies stochastic demand. Journal of Operations Research, except for some survey in a very few areas of focus.
Furthermore, based on the systematic review of the Bertsimas, D A vehicle routing problem with stochastic demand. Operations Research, 40, — Stochastic and minimisation and capacitated vehicles with synthesis dynamic vehicle routing with general demand and interarrival time distributions. Advances in Applied data. Multiple vehicle istics techniques. However, SVRP which maximises routing with time and capacity constraints using ge- vehicle utilisation, number of customer to be serviced, netic algorithms, in Proceedings of the Fifth Interna- revenue earned, and others remain most untouched tional Conference on Generic Algorithms ICGA , areas in the SVRP literatures.
A taxonomy structure for vehicle routing real world stochastic parameters considered in its and scheduling problems.
Computers and Urban Society, study to solve problems using real world data. They tested using Vehicle routing problems with soft time windows: An synthesis data or previously generated instance or optimization based approach.
Journal of Monografas del Seminario Matemtico Garca de Galdeano, 31, — using mathematical proof of lemma, theorem, and The orien- 3 Due to the dynamic nature of side constraints in VRP teering problem with stochastic travel and service or SVRP, except some open source instances devel- times. Ann Oper Res, , 61— This highly hinders tional Journal of Advancements in Computing Tech- the strategy to improve the solution methods.
The vehicle routing problem with stochastic demands using the routing problem: A taxonomic review. Computers and cross-entropy method. Annals of Operations Research, Industrial Engineering, 57 4 , — A dynamic scheme for Christopher, GJ Solutions methedologies for VRP stochastic vehicle routing.
Report, Georgia Institute of with stochastic demand, Dessertation, Iowa. Clarke, G and J Wright The numerous variants of the problem that have been studied in the literature are described and categorized.
Keywords Most of the work was completed while the author was at Molde University College. This is a preview of subscription content, log in to check access. References Adulyasak Y, Jaillet P Models and algorithms for stochastic and robust vehicle routing with deadlines. Lecture Notes in Computer Science, volA survey on and exact solutions for a class of stochastic location- pickup and delivery problems. For each domain, more detailed attributes as sub- categories were also derived so as to help to classify. Kallehauge, B Categorising and classifying articles journal were used Dror et al. Intelligent 2- In this ; Dror, ; as a source to search VRP literatures. essay about typhoon yolanda in philippines
Report, Georgia Institute of with stochastic demand, Dessertation, Iowa. Screening related literatures literatures. Computer Operations Research 12 7 , — An ant based simulation problems with time windows and stochastic travel and optimization for vehicle problem with stochastic service times: Models and algorithm.
European Journal of Operational —