Vehicle routing problem with stochastic demands in logistics management systems

In this paper, the Vehicle Routing Problem with Stochastic Demands (VRPSD) is considered where customer demands are normally distributed. A new function is proposed for computing the expected length of a given ?a priori? tour. Monte Carlo simulation is used to demonstrate the accuracy of the function on randomly generated test problems. Service policy used in the study is called as full delivery service policy and it requires that the customer demands are totally satisfied at one time. The function is re-designed for utility of the proposed function in heuristic methods and for accelerating the computation time and an alternative expected tour computation function is developed. On the other hand, in the study it is decided to try the preventive restocking policy for VRPSD and for this purpose three heuristic procedures are developed. Finally a special case is defined for VRPSD. In the special case, the demands of each customer are assumed to be normally distributed, and the mean and standard deviation of the stochastic demands are assumed to be same for each customer. We design a mathematical model for special case and propose a heuristic algorithm to solve large scale test problems.