Unlike its deterministic counterpart, static and stochastic vehicle routing problems (SSVRP) aim at modeling and solving real-life operational problems by considering uncertainty on data. We consider the SS-VRPTW-CR introduced in Saint-Guillain et al. (2017). Like the SS-VRP introduced by Bertsimas (1992), we search for optimal first stage routes for a fleet of vehicles to handle a set of stoch...

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly all existing exact methods for the VRP with stoch...

In any supply chain, distribution planning of products is of great importance to managers. With effective and flexible distribution planning, mangers can increase the efficiency of time, place, and delivery utility of whole supply chain. In this paper, inventory routing problem (IRP) is applied to distribution planning of perishable products in a supply chain. The studied supply chain is compos...

In this paper we address the long-standing problem of finding computationally efficient and provably good inventory control policies in supply chains with correlated and nonstationary (time-dependent) stochastic demands. This problem arises in many domains and has many practical applications such as dynamic forecast updates (for some applications see Erkip et al. 1990 and Lee et al. 1999). We c...

We study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs. We show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem (EVP), in which random variables are replaced by their expectations. In the case of uncertain independe...

This study presents a multimodal hub location problem which has the capability to split commodities by limited-capacity hubs and transportation systems, based on the assumption that demands are stochastic for multi-commodity network flows. In the real world cases, demands are random over the planning horizon and those which are partially fulfilled, are lost. Thus, the present study handles dema...

In today’s world, logistics problems are crucial for the supply chain management. The vehicle routing one of most studied combinatorial optimization in literature. real life applications, all parameters problem may not be known. this paper, we considered capacitated with stochastic demands. Uniform and normal distributions were analyzed on customer demands to observe nature problem. These metho...