Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC

Distributed Sensor Fusion for Wire Fault Location Using Sensor Clustering Strategy

International audienceFrom reflectometry methods, this work aims at locating accurately electrical faults in complex wiring networks. Increasing demand for online diagnosis has imposed serious challenges on interference mitigation. In particular, diagnosis has to be carried out while the target system is operating. The interference becomes more even critical in the case of complex networks where distributed sensors inject their signals simultaneously. The objective of this paper is to develop a new embedded diagnosis strategy in complex wired networks that would resolve interference problems and eliminate ambiguities related to fault location. To do so, OMTDR (Orthogonal Multi-tone Time Domain Reflectometry) method is used. For better coverage of the network, communication between sensors is integrated using the transmitted part of the OMTDR signal. It enables data control and transmission for fusion to facilitate fault location. In order to overcome degradation of diagnosis reliability and communication quality, we propose a new sensor clustering strategy based on network topology in terms of distance and number of junctions. Based on CAN bus network, we prove that data fusion using sensor clustering strategy permits to improve the diagnosis performance