A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron

A study was made of the global minimization of a general quasiconcave function on a convex polyhedron. This nonconvex problem arises in economies of scale environments and in alternative formulations of other well-known problems, as in the case of bilinear programming.Although not very important in our final results, a local minimum can be easily obtained. However, a major aspect is the existence of two families of lower bounds on the optimal functional value: one is provided by non-linear programming duality, the other is derived from a lexicographic ordering of basic solutions which allows the use of relaxation concepts. These results were exploited in a finite algorithm for obtaining the global minimum whose initial implementation has had encouraging performance.     

The telephonic switching centre network problem: formalization and computational experience

The switching centre network problem consists of looking for a topology on the urban street network that minimizes the total cost of cables and subterranean piping infrastructure necessary to link a telephonic centre and it subscribers. A simple version of the real model can be viewed as a mixture of Steiner's problem on graphs and a transhipment problem with a single source. We show that a very good initial solution for the problem can be obtained using Dijkstra's minimum distance algorithm. We discuss the theoretical background and the computational experience concerning a software for microcomputers that uses such initialization strategy and that is running quite well in practice. We present the heuristic that looks for scale economies provenient from trajectory coincidences, a local optimum strategy, and also discuss global optimum strategies which should be tested following recent experience concerning Steiner's problem.     

Depot location: A technique for the avoidance of local optima

This paper is concerned with facility location as exemplified by the depot-siting problem. In particular it considers the problem of achieving only locally-optimal locations and describes a readily-available technique which greatly increases the chance of attaining the global solution. The technique is exemplified on two data sets using a depot cost function which is linear in throughput and also one displaying economies of scale.     

Computing economies of vertical integration,economies of scope and economies of scale using partial frontier nonparametric methods

So far, in the nonparametric literature only full frontier nonparametric methods have been applied to search for economies of scope and scale, particularly the data envelopment analysis method (DEA). However, these methods present some drawbacks that might lead to biased results. This paper proposes a methodology based on more robust partial frontier nonparametric methods to look for scope and scale economies. Through this methodology it is possible to assess the robustness of these economies, and in particular to assess the influence that extreme data or outliers might have on them. The influence of the imposition of convexity on the production set of firms was also investigated. This methodology was applied to the water utilities that operated in Portugal between 2002 and 2008. There is evidence of economies of vertical integration and economies of scale in drinking water supply utilities and in water and wastewater utilities operating mainly in the retail segment. Economies of scale were found in water and wastewater utilities operating exclusively in the wholesale, and in some of these utilities diseconomies of scope were also found. The proposed methodology also allowed us to conclude that the existence of some smaller utilities makes the minimum optimal scales go down.     

Bargaining sets with small coalitions

We study two alternative definitions of the bargaining set in large (atomless) economies; the local bargaining by MasColell (1989) and the global bargaining set by Vind (1992). We alter these definitions to limit the size of the permitted size of the involved coalitions. It turns out that the local bargaining set becomes very large, whereas the global bargaining set is unaltered.     

关于二阶椭圆方程区域分裂法的最优预处理

§0.引言 区域分裂是与微分方程数值解的并行计算的数学基础密切相关的,预处理共轭梯度法是区域分裂的一个主要途径,寻找好的预处理子是关键问题,本文给出一个较一般性的方法,预处理过程包括一个整体小规模问题和若干个独立的局部子问题,整体问题和局部问题的选取均有极大的任意性,预处理条件数的估计是由整体问题和局部问题的一些特     

中国上市建筑企业规模经济和范围经济评价——一种随机边界成本函数方法

目前对于企业规模经济和范围经济的研究大多数是在不存在X无效的假设下进行的。即认为企业始终是在它们的有效边界内的,因此对企业规模经济和范围经济的实证研究也都是X有效的前提下的。本文试图采用一种成本非有效的随机边界成本函数,建立广义超越对数成本函数模型对企业规模经济和范围经济进行评价。数据来源于深沪两市建筑业板块25家上市公司2003-2007年的年度报告。研究结果表明:我国上市建筑企业中同时存在着规模不经济和范围不经济,而不存在X无效性假设条件下的估计结果使得规模经济值被提高。     

The Optimal Preconditioning in the Domain Decomposition Method for Wilson Element

1.TheCollstructionofPreconditionerLetfil)eapolygolldolllaillillR',feL'(fl).Consi(lertheholllogeneousDiricllletboulldaryvalueProblenlofPoissonequation,Assllmethat,fordomainfi,thereareacoarsersubdivisionTHwitllIneshsizeHalldananotheroneThwithmeshsizeh,whichisobtainedbyrefiningTH'Thebotllsubdivisionssatisfythequasi-uniformityandtheillversehypothesis.FOragivenelemelltT,Pm(T)dellotesthespaceofallpolynomialswiththedegreenotgreaterthanm,Qm(T)denotesthespaceofallpolynomialswiththedegreecorres…     

Location of slaughterhouses under economies of scale

The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale.We present an approach based on linearization of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.     

A multiobjective metaheuristic for a mean-risk multistage capacity investment problem

We propose a multiobjective local search metaheuristic for a mean-risk multistage capacity investment problem with irreversibility, lumpiness and economies of scale in capacity costs. Conditional value-at-risk is considered as a risk measure. Results of a computational study are presented and indicate that the approach is capable of producing high-quality approximations to the efficient sets with a modest computational effort. The best results are achieved with a new hybrid approach, combining Tabu Search and Variable Neighbourhood Search.     

The capacitated p-hub median problem with integral constraints: An application to a Chinese air cargo network

Consolidation at hubs in a pure hub-and-spoke network eliminates partial center-to-center direct loads, resulting in savings in transportation costs. In this research, we propose a general capacitated p-hub median model, with economies of scale and integral constraints on the paths. This model requires the selection of a specific p among a set of candidate hubs so that the total cost on the resulting pure capacitated hub-and-spoke network is minimized while simultaneously meeting origin–destination demands, operational capacity and singular path constraints. We explored the problem structure and developed a genetic algorithm using the path for encoding. This algorithm is capable of determining local optimality within less than 0.1% of the Lagrangian relaxation lower bounds on our Chinese air cargo network testing case and has reasonable computational times. The study showed that designating airports with high pickups or deliveries as hubs resulted in a high percentage of origin–destination pairs (ODs) in direct deliveries. Furthermore, the more hubs there are, the higher the direct share and the less likely for double rehandles. Sensitivity analysis on the discount rate showed that the economies of scale on trunk lines of hub-and-spoke networks may have a substantial impact on both the operating costs and the route patterns.     

Local and global returns to scale in performance measurement

In data envelopment analysis, the type of local returns to scale (RTS) exhibited by a technically efficient unit indicates whether an increase or reduction of the scale of operations could improve the productivity of the unit. One of the approaches to testing RTS is based on the comparison of the efficiency of the unit in specially constructed reference technologies. It has been suggested that this approach is equally suitable for convex and non-convex, including the free disposal hull, technologies. In this paper, we construct examples that show that this suggestion in the case of non-convex technologies is not correct. We show that the type of RTS obtained by this approach is not a local, but global, characteristic of the technology, as it indicates the direction to the most productive scale size of the unit. In non-convex technologies, the local and global classifications of RTS are generally different.     

An efficient algorithm for large scale global optimization of continuous functions

A fast descent algorithm, resorting to a “stretching” function technique and built on one hybrid method (GRSA) which combines simulated annealing (SA) algorithm and gradient based methods for large scale global optimizations, is proposed. Unlike the previously proposed method in which the original objective functions remain unchanged during the whole course of optimization, the new method firstly constructs an auxiliary function on one local minimizer obtained by gradient based methods and then SA is executed on this constructed auxiliary function instead of on the original objective function in order that we can improve the jumping ability of SA algorithm to escape from the currently discovered local minimum to a better one from which the gradient based methods restart a new local search. The above procedure is repeated until a global minimum is detected. In addition, corresponding to the adopted “stretching” technique, a new next trial point generating scheme is designed. It is verified by simulation especially on large scale problems that the convergence speed is greatly accelerated, which is its main difference from many other reported methods that mostly cope with functions with less than 50 variables and does not apply to large scale optimization problems. Furthermore, the new algorithm functions as a global optimization procedure with a high success probability and high solution precision.     

A note on competitive supply chains with generalised supply costs

This note generalises models from two influential papers in the theory of supply chain outsourcing under competition: 9 and 1. The first paper studies the impact of competitive intensity on the outsourcing decision from the supplier’s point of view for linear supply cost; the second paper examines the impact of supply economies of scale from the retailer’s point of view when selling perfectly substitutable products. By considering competitive intensity and supply economies of scale simultaneously, we find that equilibrium channel structures are primarily determined by the competitive intensity, which is true even under supply diseconomies of scale; the key message in the second paper of scale economies driving retailer’s outsourcing supply decision is highly dependent on the assumption of perfect substitutes. Our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions.     

A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

CLIMATE CHANGE AND FISHERIES: ASSESSING THE ECONOMIC IMPACT IN ICELAND AND GREENLAND

ABSTRACT. . Climate changes in the 21st century are expected to significantly increase ocean temperatures and modify other oceanographic conditions in the North Atlantic. Marine biological research suggests that the impacts on the commercially most important fish stocks in the Icelandic‐Greenland ecosystem may well be quite substantial. This will obviously lead to a corresponding impact on the economies of these two countries. However, the timing, extent and biological impact of global warming is quite uncertain. As a result the economic impact is similarly uncertain. This paper attempts to provide estimates of the impact of altered fish stocks due to global warming on the Icelandic and Greenland economies. The approach is one of stochastic simulations. This involves essentially three steps. The first is to obtain predictions of the impact of global warming on fish stocks and the associated probability distribution. For this we rely on recent marine biological predictions. The second step is to estimate the role of the fisheries sector in the two economies. This is done with the help of modern econometric techniques based on economic growth theory and historical data. Obviously these estimates are also subject to stochastic errors and uncertainty. The third step is to carry out Monte Carlo simulations on the basis of the above model and the associated uncertainties. The result of the Monte Carlo simulations consists of a set of dynamic paths for GDP over time with an expected value and a probability distribution for each future year. On this basis it is possible to calculate confidence intervals for the most likely path of GDP over time. The results indicate that the fisheries impact of global warming on the Icelandic GDP is more likely to be positive than negative but unlikely to be of significant magnitude compared to historical economic growth rates and fluctuations. The uncertainty of this prediction, however, is large. For Greenland, the impact on fish stocks and the GDP is highly likely to be positive and quite substantial relative to the current GDP. Due to less knowledge of the relationship between the fisheries sector and the Greenland economy, however, the confidence interval of this prediction is even wider than in the case of Iceland.     

Regional concentration and efficiency in Mexican manufacturing

This paper explores the link between industrial location, concentration, and economic efficiency in Mexican manufacturing. Using a linear programming approach, the authors calculate indices of overall, technical, allocative, and scale efficiency for Mexican manufacturing industries by state to test whether, in 1985, those regions with high levels of industrial concentration were suffering from the costs of congestion. The evidence suggests that, at least at the aggregate level, there continued to be a positive relationship between industry concentration and efficiency in production. There is also evidence that overall efficiency was related to scale efficiency, although highly industrialized regions on the production frontier often operated at inefficient scales. In particular, the most concentrated regions (the Federal District, the state of Mexico, Jalisco, and Nuevo León) consistently display decreasing returns to scale, indicating that the process of industrial concentration may be leading to diseconomies of scale. Finally, an econometric analysis suggests that scale, urbanization, and agglomeration economies are positively related to overall and technical efficiency at the regional level, while foreign ownership is negatively related. Agglomeration economies at the industry level were not significant. The paper also makes a methodological contribution. It is the first application of a distance-function production methodology to measuring regional efficiency in a developing country. It demonstrates how to conduct distance-function efficiency analysis using the newly developed GAMS mathematical programming environment. These tools should be of considerable interest to applied microeconomists.     

A Profit-maximizing Plant-loading Model with Demand Fill-rate Constraints

This paper discusses a new formulation of a class of plant product-mix loading problems which are characterized by capacitated production facilities, demand fill-rate requirements, fixed facility costs, concave variable production costs and an integrated network structure which encompasses inbound supply and outbound distribution flows. In particular, we are interested in assigning product lines and volumes to a set of capacitated plants under the demand fill-rate constraints. Fixed costs are incurred when a product line is assigned to a plant. The variable production-cost function also exhibits concavity with respect to each product-line volume. Thus both scale economies and plant focus effect are considered explicitly in the model. The model also can be used to determine which market to serve in order to best allocate the firm's resources. The problem formulation leads to a concave mixed-integer mathematical programme. Given the state of the art of non-linear programming techniques, it is often not possible to find global optima for reasonably sized problems. We develop an optimization algorithm within the framework of Benders' decomposition for the case of a piecewise linear concave cost function. Our algorithm generates optimal solutions efficiently.     

Trudinger–Moser Type Inequalities with Vanishing Weights in the Unit Ball

We introduce local and global generalized Herz spaces. As one of the main results we show that Morrey type spaces and complementary Morrey type spaces are included into the scale of these Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized Herz spaces with application to Morrey type spaces and their complementary spaces, based on the mentioned inclusion.