This paper discusses a notion of approximate abstraction for linear stochastic hybrid automata (LSHA). The idea is based on the construction of the so called stochastic bisimulation function. Such function can be used to quantify the distance between a system and its approximate abstraction. The work in this paper generalizes our earlier work for jump linear stochastic systems (JLSS). In this p...

in this paper, a stochastic multi-depot multi-objective vehicle routing problem (vrp) is studied. based on observations in real-world problems, we develop an aspect of the problem, such as stochastic availability of routes. to solve the problem in this situation, a two-objective mathematical model is developed, in which the related objective functions are: (1) minimizing transportation costs an...

stochastic approach to vehicle routing problem: development and theories abstract in this article, a chance constrained (ccp) formulation of the vehicle routing problem (vrp) is proposed. the reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. knowing that reliable computer software for lar...

design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. this paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. first, an efficient complex mixed-integer linear programming (milp) model by considering some real-world assumptions is developed for the inte...

We introduce the stochastic linear programming (SLP) model classes, which will be considered in this paper, on the basis of a small-scale linear programming problem. The solutions for the various problem formulations are discussed in a comparative fashion. We point out the need for model and solution analysis. Subsequently, we outline the basic ideas of selected major algorithms for two classes...