Approximation Algorithms for VRP with Stochastic Demands

• 成果类型: Article
• 署名作者: Gupta, Anupam; Nagarajan, Viswanath; Ravi, R.
• 署名单位: Carnegie Mellon University; International Business Machines (IBM); IBM USA; Carnegie Mellon University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1110.0967
• 发表日期: 2012
• 页码: 123-127
• 关键词: delivery problems; vehicle; heuristics; bounds

摘要

We consider the vehicle routing problem with stochastic demands (VRPSD). We give randomized approximation algorithms achieving approximation guarantees of 1 + alpha for split-delivery VRPSD, and 2 + alpha for unsplit-delivery VRPSD; here alpha is the best approximation guarantee for the traveling salesman problem. These bounds match the best known for even the respective deterministic problems [Altinkemer, K., B. Gavish. 1987. Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper Res. Lett. 6(4) 149-158; Altinkemer, K., B. Gavish. 1990. Heuristics for delivery problems with constant error guarantees. Transportation Res. 24(4) 294-297] We also show that the cyclic heuristic for split-delivery VRPSD achieves a constant approximation ratio, as conjectured in Bertsimas [Bertsimas, D. J. 1992. A vehicle routing problem with stochastic demand. Oper Res. 40(3) 574-585].