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...

in this paper, the capacitated location-routing problem with fuzzy demands (clrp-fd) is considered. the clrp-fd is composed of two well-known problems: facility location problem and vehicle routing problem. the problem has many real-life applications of which some have been addressed in the literature such as management of hazardous wastes and food and drink distribution. in clrp-fd, a set of c...

This paper addresses a new version of the exible ow line prob- lem, i.e., the budget constrained one, in order to determine the required num- ber of processors at each station along with the selection of the most eco- nomical process routes for products. Since a number of parameters, such as due dates, the amount of available budgets and the cost of opting particular routes, are imprecise (fuzz...

By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events and then constructs a general framework of fuzzy random chance-constrained programming (CCP). We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random progra...

In this paper, a model of an optimal control problem with chance constraints is introduced. The parametersof the constraints are fuzzy, random or fuzzy random variables. Todefuzzify the constraints, we consider possibility levels.  Bychance-constrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical op...