Vehicle Routing Problem with Stochastic Demand

Main Article Content

เกียรติกุลไชย จิตต์เอื้อ


Vehicle routing problem (VRP) is a combinatorial optimization problem and always is classified as an NP-hard problem that is difficult to be solved. The VRP is one of the most widely studied topics in the fields of Operations Research (OR) and logistics, and has received the greatest attention in the scientific literatures. The VRP is extensively studied because of its wide applicability and its importance in determining efficient strategies for reducing operational costs in distribution networks. This article aims to provide a basic knowledge of deterministic VRP and stochastic VRP with uncertain demand. Also, the stochastic models and its solution methods are reviewed and categorized in accordance to the relevant literature.

Article Details

How to Cite
จิตต์เอื้อ เ. (2018). Vehicle Routing Problem with Stochastic Demand. NKRAFA JOURNAL OF SCIENCE AND TECHNOLOGY, 13, 19–24. Retrieved from
Research Articles


[1] G. B. Dantzig and J.H.Ramser. The truck dispatching problem. Management Science, 6(1):80-91, 1959.

[2] L.Bodin et al. Routing and scheduling of vehicles and crews: The state of the art. Computers & Operations Research, 10(2): 69-211, 1983.

[3] A.Ak and AL. Erera. A paired-vehicle recurs strategy for the vehicle routing problem with stochastic demands. Transportation Science, 41(2): 222-237, 2007.

[4] G.Laporte et al. The vehicle routing problem with stochastic travel times. Transportation Science, 26(3): 161-170, 1992.

[5] M.Gendreau et al. Stochastic vehicle routing. European Journal of Operational Research, 88: 3-12, 1996.

[6] M.Reimann. Analyzing a vehicle routing problem with stochastic demand using ant colony optimization. Advanced OR and AI methods in Transportation. Poznan Technical University, Poznan: 764-769,2005.

[7] E. Berhan et al. Stochastic vehicle routing problem: a literature survey. Journal of Information & Knowledge Management: 1-12, 2014.

[8] M.Dror and T.Trudeau. Savings by split delivery routing. Transportation Science, 23: 141-145, 1989.

[9] G.Laporte et al. Models and exact solutions for a class of stochastic location routing problems. European Journal of Operational Research, 39: 71-78, 1989.

[10] D.Bertsimas. A vehicle routing problem with stochastic demand. Journal of Operations Research, 40(3): 554-585, 1991.

[11] P.Yong and Z.Hai-Ying. Research on vehicle routing problem with stochastic demand and PSO-DP algorithm with inver-over operator. SETP, 28(10): 76-81, 2008.

[12] W-H.Yang et al., Stochastic vehicle routing problem with restocking. Transportation Science, 34: 99-112, 2000.

[13] L.Smith et al. Dynamic vehicle routing with priority classes of stochastic demands. IAM Journal on Control and Optimization, 48(5): 3224-3245, 2010.

[14] N.Secomandi and F.Margot. Reoptimization approaches for the vehicle routing problem with stochastic demands. Journals of Operations Research, 57(1): 214-230, 2009.

[15] F.B.Moghaddam et al. Vehicle routing problem with uncertain demands: An advanced particle swarm algorithm. Computer and Industrial Engineering, 196: 306-317, 2012.

[16] M.Gendreau et al. An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transportation Science, 29: 143-155, 1995.

[17] S.A.Kenyon and P.D.Morton. Stochastic vehicle routing with random travel times. Journal of Transportation Science, 37(1): 69-82, 2003.

[18] Z.Guo. A heuristic algorithm for the stochastic vehicle routing problems with soft time windows. In Evolutionary Computation, Hong Kong University: 1449-1456, 2004.

[19] C.Cortes et al. Routing technicians under stochastic service times: A robust optimization approach. On the Sixth Triennial Symposium on Transportation Analysis, Phuket Island, 2007.

[20] M.A. Campbell and M.Gendreau. The orienteering problem with stochastic travel and service time. Annals of Operations Research, 186: 61-81, 2011.

[21] ทรงยศ กิจธรรมเกษร และคณะ. การจัดสรรงานของผู้ให้บริการโลจิสติกส์ด้วยต้นทุนต่ำภายใต้ความไม่แน่นอน. กรุงเทพมหานคร: จุฬาลงกรณ์ธุรกิจปริทัศน์, 2557.

[22] K.C.Tan et al. Solving multi-objective vehicle routing problem with stochastic demand via evolutionary computation. European Journal of Operational Research, 177 (2): 813-839, 2007.

[23] ไพโรจน์ แสนดี และคณะ. การศึกษาเส้นทางเดินรถในการเคลื่อนย้ายผู้ประสบอุทกภัยออกจากพื้นที่อันตรายเมื่อระดับน้ำสูง กรณีศึกษา: ตำบล ลาดสวาย อำเภอลำลูกกา จังหวัดปทุมธานี. วารสารวิชาการอุตสาหกรรมศึกษา, 2557.

[24] Braekers et al.The vehicle routing problem: state of the art classification and review. Computers & Industrial Engineering, 99: 300-313, 2016.