Stochastic location aided routing model : a two stage stochastic second-order cone programming formulation

We study the semidefinite stochastic location-aided routing (SLAR) model described in Ariyawansa and Zhu (2006) [2], and formulate it as a two-stage stochastic secondorder cone programming (SSOCP), see Alizadeh, D. Goldfarb (2003) [1] for second-order cone programming, where the main first-stage decision variables are the position of the destination node and its distance from the sender node. The random movements of the destination node are represented by ellipsoid scenarios randomly generated by a uniform distribution in a neighborhood of the starting position of the destination node. The MOSEK solver (under GAMS environment) allows to solve problems with a large number of scenarios (say 4040) versus the ten scenarios of MINOS solver. Stability results for the optimal first-stage solutions and the optimal function value are obtained.