Optimal paths in multi-stage stochastic decision networks - Mina Roohnavazfar; Daniele Manerba; Juan Carlos De Martin; Roberto Tadei (Operations Research Perspectives, 2019)
This paper deals with the search of optimal paths in a multi-stage stochastic decision network as a first application of the deterministic approximation approach proposed by Tadei et~al. [48]. In the network, the involved utilities are stage-dependent and contain random oscillations with an unknown probability distribution. The problem is modeled as a sequential choice of nodes in a graph layered into stages, in order to find the optimal path value in a recursive fashion. It is also shown that an optimal path solution can be derived by using a Nested Multinomial Logit model, which represents the choice probability at the different stages. The accuracy and efficiency of the proposed method are experimentally proved on a large set of randomly generated instances. Moreover, insights on the calibration of a critical parameter of the deterministic approximation are also provided.
Keywords: 330; Asymptotic approximation; Multi-stage; Nested Multinomial Logit; Optimal paths; Stochastic decision process