Approximation algorithm for uniform bounded facility location problem

The uniform bounded facility location problem (UBFLP) seeks for the optimal way of locating facilities to minimize total costs (opening costs plus routing costs), while the maximal routing costs of all clients are at most a given bound M. After building a mixed 0–1 integer programming model for UBFLP, we present the first constant-factor approximation algorithm with an approximation guarantee of 6.853+? for UBFLP on plane, which is composed of the algorithm by Dai and Yu (Theor. Comp. Sci. 410:756–765, 2009) and the schema of Xu and Xu (J. Comb. Optim. 17:424–436, 2008). We also provide a heuristic algorithm based on Benders decomposition to solve UBFLP on general graphes, and the computational experience shows that the heuristic works well.     

Cost sharing and strategyproof mechanisms for set cover games

We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, in the core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budget-balanced mechanism in the core. We show that there is no cost allocation method that can always recover more than $\frac{1}{\ln n}$ of the total cost and in the core. Here n is the number of all players to be served. We give a cost allocation method that always recovers $\frac{1}{\ln d_{\mathit{max}}}$ of the total cost, where d _max is the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than $\frac{1}{n}$ of the total cost for every subset of players. We give an efficient cost sharing scheme that always recovers at least $\frac{1}{2n}$ of the total cost for every subset of players and furthermore, our scheme is cross-monotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets; further, the total cost of the set cover is no more than ln?d _max times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism to them. We also show how to fairly share the payments to all sets among the elements.     

Shifting strategy for geometric graphs without?geometry

We give a simple framework which is an alternative to the celebrated and widely used shifting strategy of Hochbaum and Maass (J. ACM 32(1):103?C136, 1985) which has yielded efficient algorithms with good approximation bounds for numerous optimization problems in low-dimensional Euclidean space. Our framework does not require the input graph/metric to have a geometric realization??it only requires that the input graph satisfy some weak property referred to as growth boundedness. Growth bounded graphs form an important graph class that has been used to model wireless networks. We show how to apply the framework to obtain a polynomial time approximation scheme (PTAS) for the maximum (weighted) independent set problem on this important graph class; the problem is W[1]-complete. Via a more sophisticated application of our framework, we show how to obtain a PTAS for the maximum (weighted) independent set for intersection graphs of (low-dimensional) fat objects that are expressed without geometry. Erlebach et al. (SIAM J. Comput. 34(6):1302?C1323, 2005) and Chan (J. Algorithms 46(2):178?C189, 2003) independently gave a PTAS for maximum weighted independent set problem for intersection graphs of fat geometric objects, say ball graphs, which required a geometric representation of the input. Our result gives a positive answer to a question of Erlebach et al. (SIAM J. Comput. 34(6):1302?C1323, 2005) who asked if a PTAS for this problem can be obtained without access to a geometric representation.     

Approximating soft-capacitated facility location problem with uncertainty

In this paper we devise the stochastic and robust approaches to study the soft-capacitated facility location problem with uncertainty. We first present a new stochastic soft-capacitated model called The 2-Stage Soft Capacitated Facility Location Problem and solve it via an approximation algorithm by reducing it to linear-cost version of 2-stage facility location problem and dynamic facility location problem. We then present a novel robust model of soft-capacitated facility location, The Robust Soft Capacitated Facility Location Problem. To solve it, we improve the approximation algorithm proposed by Byrka et al. (LP-rounding algorithms for facility-location problems. CoRR, 2010a) for RFTFL and then treat it similarly as in the stochastic case. The improvement results in an approximation factor of \(\alpha + 4\) for the robust fault-tolerant facility location problem, which is best so far.     

Approximation strategy-proof mechanisms for obnoxious facility location on a line

In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible.     

Cooperation despite contingency: what accounts for cooperative behaviour of contingent managerial workers?

Previous empirical results have revealed two particular mechanisms influencing cooperative or extra-role behaviour of contingent employees. These are the mechanism of instrumentality, mainly driven by contingent employees’ desire for a permanent position, and the mechanism of social exchange, based on the ‘norm of reciprocity’ (Gouldner in Am Sociol Rev 25:161–178, 1960) between employer and employee. For the most part the cooperative behaviour studied among contingent workers has been restricted to non-managerial positions. But is it also possible to transfer these mechanisms to contingent employees in managerial positions? A quantitative study of contingent (self-employed) workers in managerial positions (also called ‘interim managers’) was carried out among 133 German interim managers. The results of regression analysis reveal that social exchange as well as instrumentality mechanism can facilitate cooperative behaviour of contingent employees in managerial positions. However, the aspects of social exchange, especially task autonomy, seem to be more relevant to the cooperative behaviour of these individuals.     

The power of “mapping the territory”. Why economists should become more aware of the performativity of their models

Economics is not simply about representing reality; it is also about shaping it, an approach encapsulated in Donald MacKenzie’s aphorism that economics is best conceived as an “engine, not as a camera” (MacKenzie and Millo (Am J Sociol 109(1):107–145, 2003). The making and application of economic theories and models contribute actively and intentionally towards the making of our social world, by encouraging, guiding and legitimizing actions and decisions, or discouraging others, and by steering them in certain directions. It follows that economists do not simply draw maps of the economic territory within their compass: they are not straightforwardly the cartographers of the economy, and cannot be seen as the disinterested observers that they commonly represent themselves to be, and indeed are often thought of as. Their theoretical work has or aims at practical consequences for the economy, and indeed for society at large, and their interests and influence are thus by no means confined to academia alone. This article calls for a discussion of the ethical responsibilities of economists, and of economics, and challenges the discipline properly to assume those responsibilities; and it concludes by considering the key questions—what makes a ‘good’ economic model; and what criteria should be used to distinguish the good models, and the ‘good ways’ of handling models and their results, from the bad ones. As far as epistemology, the methodology of research programmes and the relation of theory and (social) practice are concerned, the insights of mainly von Hayek (Br J Philos Sci 6(23):209–225, 1955, The pretence of knowledge. Lecture to the memory of Alfred Nobel, 1974; Individualism and economic order, University of Chicago Press, Chicago, pp 33–56, 1980a; Individualism and economic order, University of Chicago Press, Chicago, pp 57–76, 1980b; The theory of complex phenomena. Readings in the philosophy of social science, MIT Press, Cambridge, 1994) and Popper (e.g. The myth of the framework: in defence of science and rationality, Routledge, New York 1994a; Models, instruments, and truth. The status of the rationality principle in the social sciences, pp 154–184, 1994b) provide the background of my discussion of the mentioned issues.     

Improved approximation algorithms for the max-bisection and the disjoint 2-catalog segmentation problems

We consider the max-bisection problem and the disjoint 2-catalog segmentation problem, two well-known NP-hard combinatorial optimization problems. For the first problem, we apply the semidefinite programming (SDP) relaxation and the RPR² technique of Feige and Langberg (J. Algorithms 60:1–23, 2006) to obtain a performance curve as a function of the ratio of the optimal SDP value over the total weight through finer analysis under the assumption of convexity of the RPR² function. This ratio is shown to be in the range of [0.5,1]. The performance curve implies better approximation performance when this ratio is away from 0.92, corresponding to the lowest point on this curve with the currently best approximation ratio of 0.7031 due to Feige and Langberg (J. Algorithms 60:1–23, 2006). For the second problem, similar technique results in an approximation ratio of 0.7469, improving the previously best known result 0.7317 due to Wu et al. (J. Ind. Manag. Optim. 8:117–126, 2012).     

An improved distributed data aggregation scheduling in wireless sensor networks

This paper focuses on the distributed data aggregation collision-free scheduling problem, which is one of very important issues in wireless sensor networks. Bo et al. (Proc. IEEE INFOCOM, 2009) proposed an approximate distributed algorithm for the problem and Xu et al. (Proc. ACM FOWANC, 2009) proposed a centralized algorithm and its distributed implementation to generate a collision-free scheduling for the problem, which are the only two existing distributed algorithms. Unfortunately, there are a few mistakes in their performance analysis in Bo et al. (Proc. IEEE INFOCOM, 2009), and the distributed algorithm can not get the same latency as the centralized algorithm because the distributed implementation was not an accurate implementation of the centralized algorithm (Xu et al. in Proc. ACM FOWANC, 2009). According to those, we propose an improved distributed algorithm to generate a collision-free schedule for data aggregation in wireless sensor networks. Not an arbitrary tree in Bo et al. (Proc. IEEE INFOCOM, 2009) but a breadth first search tree (BFS) rooted at the sink node is adopted, the bounded latency 61R+5Δ?67 of the schedule is obtained, where R is the radius of the network with respect to the sink node and Δ is the maximum node degree. We also correct the latency bound of the schedule in Bo et al. (Proc. IEEE INFOCOM, 2009) as 61D+5Δ?67, where D is a diameter of the network and prove that our algorithm is more efficient than the algorithm (Bo et al. in Proc. IEEE INFOCOM, 2009). We also give a latency bound for the distributed implementation in Xu et al. (Proc. ACM FOWANC, 2009).     

逆向供应链中电子废弃产品回收定价和补贴策略研究

随着废弃电子产品的大量涌现和社会环保意识的增强,废弃电子产品的回收处理成为社会关注的热点问题之一。在现有的文献研究中,更多的是从逆向供应链系统化的视角关注价格或税收政策对回收商或处理商的运营效率、积极性的影响,逆向供应链激励的关键问题即如何确定回收价格和补贴方面的研究却较少见。本文基于社会福利最大化的视角,建立斯塔克伯格博弈模型（社会福利模型）来确定逆向供应链分散管理中的回收价格和社会最优补贴费,该模型可以检验分散管理系统（环保局作为领导者、MIS和回收商作为追随者）中回收逆向供应链的回收价格和补贴的激励效应。通过社会福利模型和资金平衡模型的比较,以及比较案例的数值演算,结果发现：达到市场最优销售数量和向顾客提供回收废弃电子产品的最优奖金的状况下,销售商和回收商处于平衡状态;社会福利模型中窒息价格、零奖金对应的基准收集数量、相对于奖金的收集量敏感度等因素对社会福利的影响均优于资金平衡模型。     

Scheduling Packets with Values and Deadlines in Size-Bounded Buffers

Motivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of multiple size-bounded buffers such that at any time, the number of packets residing in each individual buffer cannot exceed its capacity. Packets arrive at the network switch over time; they have values, deadlines, and designated buffers. In each time step, at most one pending packet is allowed to be sent and this packet can be from any buffer. The objective is to maximize the total value of the packets sent by their respective deadlines. A 9.82-competitive online algorithm (Azar and Levy in Lect Notes Comput Sci 4059:5–16 2006) and a 4.73-competitive online algorithm (Li in Lect Notes Comput Sci 5564:265–278, 2009) have been provided for this model, but no offline algorithms have yet been described. In this paper, we study the offline setting of the multi-buffer model. Our contributions include a few optimal offline algorithms for some variants of the model. Each variant has its unique and interesting algorithmic feature.     

Optimal key tree structure for two-user replacement and deletion problems

We study the optimal tree structure for the key management problem. In the key tree, when two or more leaves are deleted or replaced, the updating cost is defined to be the number of encryptions needed to securely update the remaining keys. The objective is to find the optimal tree structure where the worst case updating cost is minimum. We extend the result of 1-replacement problem in Snoeyink et al. (Proceedings of the twentieth annual IEEE conference on computer communications, pp. 422–431, 2001) to the k-user case. We first show that the k-deletion problem can be solved by handling k-replacement problem. Focusing on the k-replacement problem, we show that the optimal tree can be computed in $O(n^{(k+1)^{2}})$ time given a constant k. Then we derive a tight degree bound for optimal tree when replacing two users. By investigating the maximum number of leaves that can be placed on the tree given a fixed worst case replacement cost, we prove that a balanced tree with certain root degree 5≤d≤7 where the number of leaves in the subtrees differs by at most one and each subtree is a 2-3 tree can always achieve the minimum worst case 2-replacement cost. Thus the optimal tree for two-user replacement problem can be efficiently constructed in O(n) time.     

Optimal Descending Mechanisms for Constrained Procurement

Descending mechanisms for procurement (or, ascending mechanisms for selling) have been well‐recognized for their simplicity from the viewpoint of bidders—they require less bidder sophistication as compared to sealed‐bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms.     

Competitive analysis for make-to-order scheduling with reliable lead time quotation

This paper makes extended studies on the discrete problem of online scheduling and reliable lead time quotation (discrete Q-SLTQ) introduced by Keskinocak et al. (Manag. Sci. 47(2):264–279, 2001). We first relax the assumption on revenue function from a linear decreasing function to any decreasing function. We present an online deterministic strategy which is optimal in competitiveness for concave revenue functions. The above results are further extended to the continuous Q-SLTQ model where orders are released at arbitrary time points. For the discrete Q-SLTQ problem, if orders are with nonuniform lengths, we prove the nonexistence of online strategies with bounded competitive ratios; otherwise if orders are with unit length but various weights, we present an optimal online strategy.     

Bounds of Relative Regret Limit in p‐Robust Supply Chain Network Design

This research studies the p‐robust supply chain network design with uncertain demand and cost scenarios. The optimal design integrates the supplier selection together with the facility location and capacity problem. We provide a new framework to obtain the relative regret limit, which is critical in the robust supply chain design but is assumed to be a known value in the existing literature. We obtain lower and upper bounds for relative regret limit and obtain a sequence of optimal solutions for series relative regret limits between the upper and lower bounds. An algorithm for p‐robust supply chain network design is provided. A series of numerical examples are designed to find the properties of the bottleneck scenarios. A scenario with low probability and a low optimal objective function value for the scenario has a greater chance of being a bottleneck. To focus only on the influence from the relative regret, we also introduce three separate new objective functions in p‐robust design. The proposed new theories and approaches provide a sequence of options for decision makers to reduce the marketing risks effectively in supply chain network design.     

Tight approximation bounds for combinatorial frugal coverage algorithms

We consider the frugal coverage problem, an interesting variation of set cover defined as follows. Instances of the problem consist of a universe of elements and a collection of sets over these elements; the objective is to compute a subcollection of sets so that the number of elements it covers plus the number of sets not chosen is maximized. The problem was introduced and studied by Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009) due to its connections to the donation center location problem. We prove that the greedy algorithm has approximation ratio at least 0.782, improving a previous bound of 0.731 in Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009). We also present a further improvement that is obtained by adding a simple corrective phase at the end of the execution of the greedy algorithm. The approximation ratio achieved in this way is at least 0.806. Finally, we consider a packing based algorithm that uses semi-local optimization, and show that its approximation ratio is not less than 0.872. Our analysis is based on the use of linear programs which capture the behavior of the algorithms in worst-case examples. The obtained bounds are proved to be tight.     

Valuing high technology growth firms

For the valuation of fast growing innovative firms Schwartz and Moon (Financ Anal J 56:62–75, 2000), (Financ Rev 36:7–26, 2001) develop a fundamental valuation model where key parameters follow stochastic processes. While prior research shows promising potential for this model, it has never been tested on a large scale dataset. Thus, guided by economic theory, this paper is the first to design a large-scale applicable implementation on around 30,000 technology firm quarter observations from 1992 to 2009 for the US to assess this model. Evaluating the feasibility and performance of the Schwartz-Moon model reveals that it is comparably accurate to the traditional sales multiple with key advantages in valuing small and non-listed firms. Most importantly, however, the model is able to indicate severe market over- or undervaluation from a fundamental perspective. We demonstrate that a trading strategy based on our implementation has significant investment value. Consequently, the model seems suitable for detecting misvaluations as the dot-com bubble.     

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.     

Pricing in a Transportation Station with Strategic Customers

We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.     

Some results on the target set selection problem

In this paper we consider a fundamental problem in the area of viral marketing, called Target Set Selection problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the Target Set Selection problem can be solved in linear time, which generalizes Chen’s result (Discrete Math. 23:1400–1415, 2009) for trees, and the time complexity is much better than the algorithm in Ben-Zwi et al. (Discrete Optim., 2010) (for bounded treewidth graphs) when restricted to block-cactus graphs. We show that if the underlying graph G is a chordal graph with thresholds θ(v)≤2 for each vertex v in G, then the problem can be solved in linear time. For a Hamming graph G having thresholds θ(v)=2 for each vertex v of G, we precisely determine an optimal target set S for (G,θ). These results partially answer an open problem raised by Dreyer and Roberts (Discrete Appl. Math. 157:1615–1627, 2009).