Economic Lot-Sizing with Start-up Costs: The Convex Hull

A partial description of the convex hull of solutions to the economic lot-sizing problem with start-up costs (ELSS) has been derived recently. Here a larger class of valid inequalities is given and it is shown that these inequalities describe the convex hull of ELSS. This in turn proves that a plant location formulation as a linear program solves ELSS. Finally a separation algorithm is given

Notions of Connectivity in Overlay Networks

International audience" How well connected is the network? " This is one of the most fundamental questions one would ask when facing the challenge of designing a communication network. Three major notions of connectivity have been considered in the literature, but in the context of traditional (single-layer) networks, they turn out to be equivalent. This paper introduces a model for studying the three notions of connectivity in multi-layer networks. Using this model, it is easy to demonstrate that in multi-layer networks the three notions may differ dramatically. Unfortunately, in contrast to the single-layer case, where the values of the three connectivity notions can be computed efficiently, it has been recently shown in the context of WDM networks (results that can be easily translated to our model) that the values of two of these notions of connectivity are hard to compute or even approximate in multi-layer networks. The current paper shed some positive light into the multi-layer connectivity topic: we show that the value of the third connectivity notion can be computed in polynomial time and develop an approximation for the construction of well connected overlay networks

Geochemical bio-signatures in Martian analogue basaltic environments using laboratory experiments and thermochemical modelling

The identification of geochemical bio-signatures is important for assessing whether life existed on early Mars. In this paper, experimental microbiology and thermochemical modelling were combined to identify potential inorganic bio-signatures for life detection on early Mars. An analogue mixed microbial community from an analogue terrestrial fluvio-lacustrine environment similar to an ancient lacustrine system at Gale Crater was used to study microbial dissolution of a basalt regolith simulant and the formation of bio-signatures over a short time frame (1°month) at 14°C, 2 bar. Microbial growth influenced element dissolution (Mg, Fe, Mn, Ca and K) and the formation of morphologies and Fe-Si amorphous layers on mineral surfaces. Thermochemical models were performed at 14°C, 2 bar; the results were compared with experimental data to predict bio-signatures that would occur over geological timescales. The pH was varied to simulate abiotic and biotic experimental conditions. Model results suggest that, at water to rock ratios of 100 to 38, a less complex secondary mineral assemblage forms during biotic dissolution compared to abiotic weathering. Carbonates, quartz, pyrite and hydroxyapatite form under biotic conditions, whereas in the abiotic system magnetite and phyllosilicates would also precipitate. These results could be used to distinguish between abiotic and biotic basalt weathering processes, aiding the interpretation of data from Mars exploration missions

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

Tracking cells in Life Cell Imaging videos using topological alignments

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens