Inventory routing problem with non-stationary stochastic demands

In this paper we solve Stochastic Periodic Inventory Routing Problem (SPIRP) when the accuracy of expected demand is changing among the periods. The variability of demands increases from period to period. This variability follows a certain rate of uncertainty. The uncertainty rate shows the change in accuracy level of demands during the planning horizon. To deal with the growing uncertainty, we apply a safety stock based SPIRP model with different levels of safety stock. To satisfy the service level in the whole planning horizon, the level of safety stock needs to be adjusted according to the demand's variability. In addition, the behavior of the solution model in long term planning horizons for retailers with different demand accuracy is taken into account. We develop the SPIRP model for one retailer with an average level of demand, and standard deviation for each period. The objective is to find an optimum level of safety stock to be allocated to the retailer, in order to achieve the expected level of service, and minimize the costs. We propose a model to deal with the uncertainty in demands, and evaluate the performance of the model based on the defined indicators and experimentally designed cases

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

A regret model applied to the facility location problem with limited capacity facilities

This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Facility Location Problem proposed by Balinski [27], an alternative perspective is added associating regret values to particular solutions.N/