A nonlinear model for a capacitated stochastic transportation network using multiple linear regression. Issue 4 (1st October 2016) - Shiripour, Saber; Mahdavi, Iraj; Mahdavi-Amiri, Nezam
Abstract: Here, a capacitated location-multi-allocation-routing problem with intelligent stochastic travel times is considered. In our study, the concept of intelligent stochastic travel times incurs two issues: (1) consideration of some random factors in computing the travel times and (2) impact of the traveling population on these random factors simultaneously. Here, a deterministic factor of road length and two random factors of the time spent in traffic and the number of accidents are considered. It is assumed that the time spent in traffic is distributed based on an exponential distribution function and the other factor is distributed based on a Poisson distribution function. Also, the capacities of server nodes and arcs for accepting the population are assumed to be limited. Using multiple linear regression, we formulate the problem as a mixed-integer nonlinear programming model. The objective is to find appropriate locations as server locations among the candidate locations, allocate the existing population in each demand node to server locations and determine the movement path of each member to reach its corresponding server with respect to the simultaneous change of the stochastic travel times so that the expected total transportation time is minimized. Also, to investigate the validation and behavior of the proposed probabilistic model, a network example is provided and computational results are analyzed.