The two-echelon vehicle routing problem (2E-VRP) consists in making deliveries to a set of customers using two distinct fleets of vehicles. First-level vehicles pick up requests at a distribution center and bring them to intermediate sites. At these locations, the requests are transferred to second-level vehicles, which deliver them. This paper addresses a variant of the 2E-VRP that integrates ...

The delivery of freight from its origin to its destination is often managed through one or more intermediate facilities where storing, merging and consolidation activities are performed. This type of distribution systems is commonly called multi-echelon, where each echelon refers to one level of the distribution network. Multi-echelon distribution systems are often considered by public administ...

In Multi-Echelon Vehicle Routing Problems the delivery from one or more depots to the customers is managed by routing and consolidating the freight through intermediate depots, called satellites. This family of problems differs from Multi-Echelon Distribution Systems present in the literature. In the latter the attention is focused on the flow assignment among the levels only, while we also con...

In this paper, a supplier-retailer transportation system is investigated as a two-echelon environment. There is a single location in each echelon; the unique supplier at the first echelon has to replenish the retailer's warehouse at the second echelon. By the way, the shortage situation should be avoided. For this situation, a model is provided based on the traditional EOQ model. The inventory ...

Driven by the new laws and regulations concerning emission of greenhouse gases, it is becoming more popular for enterprises to adopt cleaner energy. This research proposes a novel two-echelon vehicle routing problem consisting mixed vehicles considering battery swapping stations, which includes one depot, multiple satellites with unilateral time windows, customers given demands. The fossil fuel...

This paper studies a two-echelon supply chain with stochastic and discrete consumer demand, batch order quantities, periodic inventory review, and deterministic transportation times. Reorder point policies manage inventories at every location. Average inventory, backorders and fill rates are evaluated exactly for each location. Safety stock is evaluated exactly at the lower echelon and a good a...

in this paper, a supplier-retailer transportation system is investigated as a two-echelon environment. there is a single location in each echelon; the unique supplier at the first echelon has to replenish the retailer's warehouse at the second echelon. by the way, the shortage situation should be avoided. for this situation, a model is provided based on the traditional eoq model. the inven...

In this paper, the cost function for a three-echelon inventory system with two warehouses is derived. Transportation times are constant and retailers face independent Poisson demand. Replenishments are one-for-one. The lead time of a retailer is determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. We co...

In this paper, we establish the convexity of important cost functions in a general class of multi-echelon inventory models. In particular, we first study an assembly system with a single finished product managed using an echelon order-up-to policy. We show that the shortage penalty cost over any horizon is jointly convex with respect to the base-stock levels and capacity levels. Our second resu...

Nasopharyngeal carcinoma (NPC) is most commonly an undifferentiated carcinoma with a strong association with the Epstein Barr virus (EBV) and familial tendency. MRI is the modality of choice for NPC staging of the primary tumour and nodal metastases. The primary tumour spreads to the nasal cavity and infrequently to the oropharynx (T1); parapharyngeal space, medial and lateral pterygoid, and pr...