ADAPTED DYNAMIC PROGRAM TO FIND SHORTEST PATH IN A NETWORK HAVING NORMAL PROBABILITY DISTRIBUTION ARC LENGTH
Mohammad Hessam Olya1, Babak Shirazi1, Hamed Fazlollahtabar2
1Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran
2Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
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We adapt a dynamic program to find the shortest path in a network having normal probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two normal probability distributions being employed in the dynamic program. Generally, stochastic shortest path problems are treated using expected values of the arc probabilities, but in the proposed method using distributed observed past data as arc lengths, an integrated value is obtained as the shortest path length.
Shortest path, Dynamic program, Convolution, Normal distribution