Dynamic Facility Location via Exponential Clocks

The \emph{dynamic facility location problem} is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: there is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities, and connect every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use \emph{no clustering} and we allow clients to connect through paths of \emph{arbitrary lengths}. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem

Facility Location in Evolving Metrics

Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, or urban planning. During the past decade, data has been collected on such networks but has yet to be fully analyzed. We propose to use information on the dynamics of the data to find stable partitions of the network into groups. For that purpose, we introduce a time-dependent, dynamic version of the facility location problem, that includes a switching cost when a client's assignment changes from one facility to another. This might provide a better representation of an evolving network, emphasizing the abrupt change of relationships between subjects rather than the continuous evolution of the underlying network. We show that in realistic examples this model yields indeed better fitting solutions than optimizing every snapshot independently. We present an $O(\log nT)$-approximation algorithm and a matching hardness result, where $n$ is the number of clients and $T$ the number of time steps. We also give an other algorithms with approximation ratio $O(\log nT)$ for the variant where one pays at each time step (leasing) for each open facility

Changing Bases: Multistage Optimization for Matroids and Matchings

This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems, without creating too much churn in the solution itself. We model this as a multistage combinatorial optimization problem where the input is a sequence of cost functions (one for each time step); while we can change the solution from step to step, we incur an additional cost for every such change. We study the multistage matroid maintenance problem, where we need to maintain a base of a matroid in each time step under the changing cost functions and acquisition costs for adding new elements. The online version of this problem generalizes online paging. E.g., given a graph, we need to maintain a spanning tree $T_t$ at each step: we pay $c_t(T_t)$ for the cost of the tree at time $t$, and also $| T_t\setminus T_{t-1} |$ for the number of edges changed at this step. Our main result is an $O(\log m \log r)$-approximation, where $m$ is the number of elements/edges and $r$ is the rank of the matroid. We also give an $O(\log m)$ approximation for the offline version of the problem. These bounds hold when the acquisition costs are non-uniform, in which caseboth these results are the best possible unless P=NP. We also study the perfect matching version of the problem, where we must maintain a perfect matching at each step under changing cost functions and costs for adding new elements. Surprisingly, the hardness drastically increases: for any constant $\epsilon>0$, there is no $O(n^{1-\epsilon})$-approximation to the multistage matching maintenance problem, even in the offline case

Online Multistage Subset Maximization Problems

Numerous combinatorial optimization problems (knapsack, maximum-weight matching, etc.) can be expressed as subset maximization problems: One is given a ground set N={1,...,n}, a collection F subseteq 2^N of subsets thereof such that the empty set is in F, and an objective (profit) function p: F -> R_+. The task is to choose a set S in F that maximizes p(S). We consider the multistage version (Eisenstat et al., Gupta et al., both ICALP 2014) of such problems: The profit function p_t (and possibly the set of feasible solutions F_t) may change over time. Since in many applications changing the solution is costly, the task becomes to find a sequence of solutions that optimizes the trade-off between good per-time solutions and stable solutions taking into account an additional similarity bonus. As similarity measure for two consecutive solutions, we consider either the size of the intersection of the two solutions or the difference of n and the Hamming distance between the two characteristic vectors. We study multistage subset maximization problems in the online setting, that is, p_t (along with possibly F_t) only arrive one by one and, upon such an arrival, the online algorithm has to output the corresponding solution without knowledge of the future. We develop general techniques for online multistage subset maximization and thereby characterize those models (given by the type of data evolution and the type of similarity measure) that admit a constant-competitive online algorithm. When no constant competitive ratio is possible, we employ lookahead to circumvent this issue. When a constant competitive ratio is possible, we provide almost matching lower and upper bounds on the best achievable one

On the Unique Features and Benefits of On-Demand Distribution Models

To close the gap between current distribution operations and today’s customer expectations, firms need to think differently about how resources are acquired, managed and allocated to fulfill customer requests. Rather than optimize planned resource capacity acquired through ownership or long- term partnerships, this work focuses on a specific supply-side innovation – on-demand distribution platforms. On-demand distribution systems move, store, and fulfill goods by matching autonomous suppliers\u27 resources (warehouse space, fulfillment capacity, truck space, delivery services) to requests on-demand. On-demand warehousing systems can provide resource elasticity by allowing capacity decisions to be made at a finer granularity (at the pallet-level) and commitment (monthly versus yearly), than construct or lease options. However, such systems are inherently more complex than traditional systems, as well as have varying costs and operational structures (e.g., higher variable costs, but little or no fixed costs). New decision- supporting models are needed to capture these trade-offs

Study Of The Challenges That Hinder MSME Development In Montenegro : Country Report for the British Council and Swedish Institute

In addition to this Study, a further six studies were produced. One for each of the countries, under investigation (Albania, Bosnia Herzegovina, FYR Macedonia, Kosovo & Serbia) and a Main Report, which was published in May 2018.The European Commission’s Enlargement Package Report (2015), concluded that Montenegro continued to make progress as regards the political and economic criteria, and improved its ability to take on the obligations of EU membership. Good progress was made in improving the legislative framework for the independence of the judiciary and the fight against corruption (rule of law chapters, 23 and 24). However, Montenegro was tasked to make further progress in strengthening the institutional framework and in establishing a solid track record in the fight against corruption and organised crime. In December 2015, Montenegro received an invitation to join NATO, which was a major achievement; it became a member in 2017.  With a gross domestic product (GDP) of US 4.1 billion (constant 2010 value), Montenegro is the smallest economy in the Western Balkans and growth has been variable in recent years. However, Montenegro continues to play a constructive role in regional cooperation, ratifying its border agreements with both, Bosnia & Herzegovina and Kosovo. It terms of economic criteria, Montenegro has made progress in developing a functioning market economy (e.g. investments in infrastructure and tourism support economic activity). It has also strengthened the administration of its financial and labour markets, as well as on improving the business environment.. However, rapidly rising public debt and high fiscal deficits, together with high external imbalances and high unemployment are of concern. The combined effects of large-scale public infrastructure investments and several new expensive social expenditure programmes challenge fiscal sustainability. Montenegro is moderately prepared in its capacity to cope with competitive pressure and market forces within the Union. Some progress was achieved in improving the quality of infrastructure, the energy market and the digitalisation of the economy. SMEs support is modest but developing gradually. Unemployment in Montenegro is high, approaching 18% of the working population. However, this is average for the region, and only Serbia and Albania have lower rates. Montenegro is, however, a major importer of short-term labour to service the needs of the tourism, construction and agricultural sectors, which are the main pillars of its economy. However, substantial efforts are still required to develop human capital and a competitive export-oriented industry. In common with many of its Western Balkan neighbours, Montenegro has a skills shortage, although not to the extent of other countries. This shortage mainly translates into a need to import seasonal workers for the tourist, construction and agricultural sectors. Montenegro has a well-developed and competitive ICT sector compared with other countries in the region, but development remains in its infancy and there is a lot of potential for improvement. Despite this, business faces internal constraints and barriers, linked to skills, competences, finance and human resources. They also had problems with lack of information about foreign markets and how to access them. To contribute to the process of internationalisation, businesses need a better introduction to foreign markets, including information and facilitating access through contacts, legal and technical assistance or promotion. Total inward investment in Montenegro from other countries was US 3.3 billion in 2016. This level is low in absolute terms, particularly compared to other countries in the region (behind Serbia, Bosnia, Macedonia and Albania), but relatively high on a per capita basis. We undertook a survey of aspiring entrepreneurs across Montenegro. The sample was largely self-selected based on previous telephone surveys where respondents had expressed an interest in entrepreneurship, plus a review of the commercial register and referrals from respondents. The age distribution of aspiring entrepreneurs was under represented in younger age groups but higher in the 25–34 year old group compared with the population. Entrepreneurship aspirations are positive. There are very few problems with structural issues such as ease of forming a company. For example, establishing a business in Montenegro can be a time-consuming process. According to the World Bank’s Doing Business Report (2018), Montenegro was ranked 42nd globally for ease of doing business, a clear improvement on its previous ranking of 51st. Results from our survey, indicate five key issues stand out: 1. Access to finance is very challenging and acts as a significant barrier to both innovation and entrepreneurship. There is a particular need for access to affordable seed capital. This is a similar to the challenge being addressed by some of the rural micro-finance programs in Asia. 2. Connection to markets outside Montenegro and the Western Balkans region is challenging for new entrepreneurs. 3. There is a considerable amount of energy and effort already being injected, but significant scope for improving the skills of entrepreneurial teams. 4. The trading channels and payment methods accepted suggest our entrepreneurs are using basic business models, almost entirely face-to-face and strongly cash-based. 5. Three quarters of all businesses in the survey supplied larger organisations, which may be accounted by the very large public-sector base

Academic Libraries Without Print

Librarians from four university library environments— Western Oregon University, University of California Merced, Brigham Young University, and Cleveland State University—discussed changes occurring in their library operations as they transition to services centered in e‐resources. They explored, through the evidence of their changing library operations, a range of topics including trends in collection development and usage; developments in open access publishing; instruction; and evolving peer review and publication processes. The moderator initiated the discussion with a review of a few of the year’s relevant technology changes. Overall the cadence of change is brisk and has become the familiar norm

The Wiltshire Wills Feasibility Study

The Wiltshire and Swindon Record Office has nearly ninety thousand wills in its care. These records are neither adequately catalogued nor secured against loss by facsimile microfilm copies. With support from the Heritage Lottery Fund the Record Office has begun to produce suitable finding aids for the material. Beginning with this feasibility study the Record Office is developing a strategy to ensure the that facsimiles to protect the collection against risk of loss or damage and to improve public access are created.<p></p> This feasibility study explores the different methodologies that can be used to assist the preservation and conservation of the collection and improve public access to it. The study aims to produce a strategy that will enable the Record Office to create digital facsimiles of the Wills in its care for access purposes and to also create preservation quality microfilms. The strategy aims to seek the most cost effective and time efficient approach to the problem and identifies ways to optimise the processes by drawing on the experience of other similar projects. This report provides a set of guidelines and recommendations to ensure the best use of the resources available for to provide the most robust preservation strategy and to ensure that future access to the Wills as an information resource can be flexible, both local and remote, and sustainable