A shortest path problem in a stochastic network with exponential travel time. (28th August 2021)

• Record Type: Journal Article
• Authors: Peer, S.K.; Sharma, Dinesh K.; Chakraborty, B.; Jana, R.K.
• Is Part Of: International journal of applied management science. Volume 13:Number 3(2021)
• Page Start: 179
• Page End: 199
• Publication Date: 2021-08-28
• Subjects: chance constrained programming -- separable convex programming -- upper bound technique -- stochastic network; Management science -- Periodicals; 658
• Languages: English
• ISSNs: 1755-8913

Abstract

A shortest path problem in a stochastic network is studied in this paper. Assuming travel times between the nodes in the network as exponential random variables, a chance constrained programming formulation of the problem is obtained. Then the deterministic separable convex programming formulation of the problem is derived by using a proposed upper bound technique. The expected length and probability of the shortest path are obtained by solving the converted problem. Finally, the results obtained from the proposed approach are compared with Kulkarni's (1986) method as well as Peer and Sharma's (2007) method for a network of a practical application under consideration with exponential random variables.