A simple dual ascent algorithm for the multilevel facility location problem

We present a simple dual ascent method for the multilevel facility location problem which finds a solution within $6$ times the optimum for the uncapacitated case and within $12$ times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual technique. \u

An approximation algorithm for a facility location problem with stochastic demands

In this article we propose, for any $\epsilon>0$, a $2(1+\epsilon)$-approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs). \u

C-diagrams, shifts and solidarity values

In the theory of cooperative games so called dividends of a coalition $S$ are considered, which are defined as $\frac{c_S}{|S|}$. The costs $c_S$ form a c-diagram. On these c-diagrams several types of shifts are defined and analysed. Different solution concepts and their properties are related to shifts. We introduce reward games and fine games as components of a cooperative game. Some solution concepts for applications are analysed in terms of c-diagrams, as well as the solidarity concept. \u

World trends in fertilizer use and projections to 2020

Fertilizers have played an important role in increased crop production, especially in cereal yields, and will continue to be a cornerstone of the science-based agriculture required to feed the expanding world population. Fertilizers replenish the nutrients removed from soils by harvested crops, encourage adoption of high-yielding varieties, and increase biomass in the nutrient-poor soils of the tropics. Bumb and Baanante trace fertilizer use until the 1990s as well as production and price trends. Finally they propose projected trends in use, requirements, and production. The authors conclude that, overall, a conducive and stable policy environment, including macroeconomic stability, price incentives, credit availability, efficient organizational arrangements, research and extension support, regulatory frameworks, and environmental monitoring, will be essential to promote environmentally friendly growth in fertilizer use and supply to 2020.Fertilizers. ,Crops Economic aspects. ,Cereal crops. ,Environmental protection. ,

A combinatorial approximation algorithm for CDMA downlink rate allocation

This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of utility functions of the users, is maximized

A multiple-choice knapsack based algorithm for CDMA downlink rate differentiation under uplink coverage restrictions

This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of downlink rates, is maximized. \u

CHALLENGES FOR BANKS IN ROMANIA IN THE INTERNATIONAL ECONOMIC CRISIS

In this paper we are analyzing the current state of the Romanian banking system which is facing different challenges due to the economic crisis. Identifying the main channels of crisis transmission, we can notice that the banking system has played a major role due to its structure, and the change of the banking behavior on the Romanian market. Analyzing the main indicators reflecting the health of the banking system, hence of the economy, generally speaking, the paper is trying to identify the measures which should have been taken and we still believe should be taken in order to obtain the economic recovery, the premise of a healthy economic growth.financial crisis, channel of transmission, Romanian banking system

The standard set game of a cooperative game

We show that for every cooperative game a corresponding set game can be defined, called the standard set game. Values for set games can be applied to this standard game and determine allocations for the cooperative game. On the other hand, notions for cooperative games, like the Shapley value, the $\tau-$value or the core can be considered in the context of the standard set games. \u

Policy options for improving regional fertilizer markets in West Africa:

A primary motivation for this study is to identify a key set of policy options for improving fertilizer markets in West Africa (among Economic Community of West African States member countries) in ways that ultimately will help improve the efficiency of regional markets and lower the transaction costs and fiscal burdens of increasing fertilizer use in the region. Guided by the 2008 fertilizer crisis, many governments are tempted to impose fertilizer subsidies to reduce fertilizer prices. Yet, in an environment riddled with inefficiencies that contribute to the high costs of using fertilizers, the introduction of subsidies only adds more fiscal burden.To carry out the study, we undertook four country case studies to review the key constraints and bottlenecks along the fertilizer supply chain. The countries were Ghana, Mali, Nigeria, and Senegal, and the research included field visits in 2009 and 2010. The current paper is based on the country case study results, complemented by a literature review and analysis of secondary data sources.common fertilizer market, fertilizer use and supply, harmonization of products and regulations, improved technology, policy environment, regional market integration, structure and performance of markets, supply chain,