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We analyzed the planning problem for HIV screening, testing, and care. This problem consists of determining the optimal fraction of patients to be screened in every period as well as the optimum staffing level at each part of the healthcare system to maximize the total health benefits to the patients measured by quality-adjusted life-years (QALYs) gained. We modeled this problem as a nonlinear mixed integer programming program comprising disease progression (the transition of the patients across health states), system dynamics (the flow of patients in different health states across various parts of the healthcare delivery system), and budgetary and capacity constraints. We applied the model to the Greater Los Angeles (GLA) station in the Veterans Health Administration system. We found that a Centers for Disease Control and Prevention recommended routine screening policy in which all patients visiting the system are screened for HIV irrespective of risk factors may not be feasible because of budgetary constraints. Consequently, we used the model to develop and evaluate managerially relevant policies within existent capacity and budgetary constraints to improve upon the current risk based screening policy of screening only high risk patients. Our computational analysis showed that the GLA station can achieve substantial increase (20% to 300%) in the QALYs gained by using these policies over risk based screening. The GLA station has already adapted two of these policies that could yield better patient health outcomes over the next few years. In addition, our model insights have influenced the decision making process at this station.

Increased human life expectancy combined with declining birth rates around the globe has led to ageing populations, particularly in the developed world. This phenomenon brings about increased dependency ratios and calls for setting new policies for the elderly citizens. This comprises provision of a set of life-enhancing services in an accessible and equitable way. In this paper, we consider the multi-period problem of locating senior centres offering these services to the elderly population with budget constraints and capacity limitations. Both consistent and inconsistent versions of the problem are considered, aiming at identifying the set of facilities to operate in each region at each period, the service type(s) to be offered and the allocation of budget in each period to location and operation of facilities. A mixed integer mathematical programming model is presented, an efficient iterated local search procedure is proposed and managerial insights are provided. [ABSTRACT FROM AUTHOR]

Project planning and scheduling are one of the most important issues in construction engineering and management. It is being crucial to progress developed countries. One of the major challenges in construction project management is time and cost management. The traditional view lonely is not able to meet the needs of this field. Therefore, the use of modern management approaches can be greatly helpful. Time and cost are among the important objectives of each project. Cost and time trade-off is among the major important issues in projects planning and control and the main of solving this problem is actually analysis of interaction of different types of project costs and time of the project. In this paper, a time and cost trade off project scheduling problem under budget constraint is studied. For this purpose, a meta-heuristic genetic algorithm is developed to find the optimal solution in MATLAB. Completion time sensitivity analysis is done according to different budget level. In order to validate proposed algorithm, problem is solved by GAMS and the outputs between them are compared. The results show that proposed meta heuristic algorithm is able to solve problem optimally so that differences between samples solution were zero in different budget level.

Stochastic flexible flow shop scheduling problem (SFFSSP) is one the main focus of researchers due to the complexity arises from inherent uncertainties and also the difficulty of solving such NP-hard problems. Conventionally, in such problems each machine’s job process time may encounter uncertainty due to their relevant random behaviour. In order to examine such problems more realistically, fixed interval preventive maintenance (PM) and budget constraint are considered.PM activity is a crucial task to reduce the production efficiency. In the current research we focused on a scheduling problem which a job is processed at the upstream stage and all the downstream machines get busy or alternatively PM cost is significant, consequently the job waits inside the buffers and increases the associated holding cost. This paper proposes a new more realistic mathematical model which considers both the PM and holding cost of jobs inside the buffers in the stochastic flexible flow shop scheduling problem. The holding cost is controlled in the model via the budget constraint. In order to solve the proposedmodel, three hybrid metaheuristic algorithms are introduced. They include a couple of well-known metaheuristic algorithms which have efficient quality solutions in the literature. The two algorithms of them constructed byincorporationof the particle swarm optimization algorithm (PSO) and parallel simulated annealing (PSA) methods under different random generation policies. The third one enriched based on genetic algorithm (GA) with PSA. To evaluate the performance of the proposed algorithms, different numerical examples are presented. Computational experiments revealed that the proposed algorithms embedboth desirable accuracy and CPU time. Among them, the PSO-PSAП outperforms than other algorithms in terms of makespan and CPU time especially for large size problems.

Labeling samples manually is a laborious, error-prone, and cost-consuming process, which is a traditional approach to preparing training data for supervised learning. Crowdsourcing provides an effective way to acquire labeled training data. In this paper, we propose an adaptive crowd labeling method to construct a set of the pairs of opinion target and opinion term iteratively under certain budget constraint. First, we assess the workers' reliabilities with a small number of labeled samples based on an EM process, since the worker's expertise varies widely on an open crowdsourcing platform. And then, the tasks are assigned to the high reliable workers for labeling the pairs of opinion target and opinion term. Finally, the responds of a sample from multiple workers are integrated to generate a final result based on the labelers' reliabilities as well as the dependency relation between opinion target and opinion term in this sample. A series of the experimental results show that the proposed method can achieve better extracting effectiveness compared with the baselines and the state-of-the-art methods.

Owing to the accuracy and flexibility, mobile advertising has become a very attractive marketing method based on smart mobile terminals. The more common mobile advertisement distribution methods are based on location and content. But most of them donart take into account the limited duration time of mobile users and the timeliness of advertising, which makes mobile advertisement distribution suffer from low propagation efficiency. To make up for this deficiency, we propose the advertisement platformars expected income maximization problem (EIMP), and prove its NP-hardness. As far as we know, EIMP is a combination of the 0–1 multi-dimensional and multiple knapsack problem, which is even harder. In dealing with this difficulty, we fortunately find that this problem could be transformed into a maximizing monotone submodular set function, which is subject to partition matroid constraints. Then we propose a simple but effective greedy algorithm TIMAO (Time-sensitive Mobile Advertisement Offloading) which has a constant approximation ratio of 1/3 to provide a performance guarantee for this issue. Finally, extensive evaluations are conducted. The results show that compared with the random selection method, TIMAO increases the expected income of the platform by about two times. And it achieves 99.2% of the near optimal results obtained by the CPLEX tool-box. Moreover, we propose an important metric, the duty cycle, to evaluate system performance in time domain. The results show that our scheme could increase the time duty cycle by about average 10% compared with the random selection.

Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output's income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services. [ABSTRACT FROM AUTHOR]

Procuring the correct materials at the right time and for the lowest cost is essential in construction. This fact underlines the importance of an optimized material procurement schedule integrated with the construction schedule/program. However, few studies examine the development of a material procurement schedule by integrating the construction schedule and optimizing material costs as well as any material shortage impact. In addition, budget constraints and maximum storage capacity are rarely captured in existing models for material procurement optimization. To address these shortcomings, an optimization model is developed using the nondominated sorting genetic algorithm II (NSGA-II) and executed in MATLAB R2017a. This model was implemented in a construction project that developed a material delivery schedule based on the budget constraints and maximum storage capacity for five majorly used building materials, resulting in a costs saving of 31.17% and a reduction in shortage impact of 83.47% compared with the actual delivery schedule. The developed model also incorporates the minimum order quantity and standard shipping size as well as avoiding surplus materials, leading to sustainable procurement of materials. Construction practitioners can use this model for procuring materials when facing budget constraints in a construction project with the lowest cost and least shortage and without excess or insufficient purchasing. The model will aid in completing the project within the stipulated time and budgeted cost. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of the moderate growth of government borrowing on debt sustainability in 11 Russian regions over about 10 years, starting in 2010. The current study aims to assess the debt sustainability of the Russian region’s budget by determining Euclidean distance budget constraints and cluster analysis. This study is based on the methodology of hierarchical cluster analysis, which makes it possible to isolate regions of accumulation of objects from the aggregate data and combine them into homogeneous segments. The central hypothesis of this study is that by using this method, it is possible to increase the accuracy of the values that limit budget constraints in a region’s financial system. This study, using open data from the Federal State Statistics Service, is based on a database of statistical, financial, and economic indicators of the Russian economy. The calculations include about 45 macroeconomic indicators, which reflect the ratios of socio-economic development of the region’s financial system. The methodology described in the paper for assessing the debt sustainability of budget policy proves the need to calculate six indicators and determine the debt limits for the regions of each cluster. It finds a need to reduce the high debt burden of 46% of the regions belonging to the Northwestern Federal District. Confidence intervals for the debt limit suggest that the negative growth effect of high debt may start from levels of around 5% of the debt-to-GDP ratio and about 43% of the debt-to-revenue ratio. The results indicate that regions with a high level of debt sustainability include St. Petersburg city, the Leningrad region, and the Kaliningrad region. From a state debt policy perspective, the results provide additional arguments for debt reduction for the Republic of Komi, the Republic of Karelia, the Arkhangelsk region, and the Pskov region. The general conclusion of the study boils down to the need to reduce the debt burden of the budgets of some regions of the SFZO, as well as to the need to change the upper limits of debt, which are equally set for all regions by the Budget Code of the Russian Federation, to differentiated values of public domestic debt, taking into account the results obtained in the study.

Social media networks have been playing an increasingly more important role for both socialization and information diffusion. Political campaign can gain more supporters by attracting more mass attention and influencing them directly, while commercial campaigns can increase their companies' profits by expanding social media connection with new users. To build the optimal network structure to influence the whole, this paper studies mathematical models to simulate the users' behaviours interacting with others in the information provider's network. The behaviours of concerns include information re-posting and following/unfollowing other users. Linear threshold propagation model is used to determine the re-posting actions, Boundedly Rational User Equilibrium (BRUE) models are used to determine the following or unfollowing actions. Hence, the topology of the network changes and depends on the information provider's plan to post various kinds of information. A three-level optimization model is proposed to maximize total number of connections, the goal of the top level. The second level simulates user behaviours under BRUE. The third level maximizes the each user's utility defined in the second level. This paper solves this problem using exact algorithms for a small-scale synthetic network. For a large-scale problem, this paper uses heuristic algorithms based on large neighbourhood search. This paper also discusses possible reasons why the BRUE model may be a more accurate simulation of users' actions compared to game theory. Comparisons from the BRUE model to game theoretical model show that the BRUE model performs significantly better than game theoretical model. [ABSTRACT FROM AUTHOR]

This document aims to determine the empirical link between current account balances and a set of economic variables proposed by the theoretical and empirical literature. To do this, we first use a generalized method of moments (GMM) dynamic panel regression technique to identify the key fundamentals of current account balances in certain economies in the Middle East and North Africa (MENA) region. Next, we estimate the link between exports and imports in order to test the sustainability of current account balances. To do this, the authors estimate a threshold cointegration model on a sample of 12 countries from the MENA region over the period 1970–2018. Nevertheless, the results show that the countries of the MENA region must put in place policies aimed at reducing their current account deficits in order to regain their external stability. [ABSTRACT FROM AUTHOR]

Background The current economic constraints cause hospital management to use the available public resources as rationally as possible. At the same time, there is the necessity to improve current scientific knowledge. This is even more relevant in the case of patients with malignant pleural mesothelioma (MPM), given the severity of the disease, its dismal prognosis, and the cost of chemotherapy drugs. This work aims to evaluate the standard cost of patients with MPM, supporting physicians in their decision-making process in relation to budget constraints, as well as policymakers with respect research policy. Methods The authors conducted a retrospective cost analysis on all the patients with MPM who were first admitted to a reference hospital specialized in MPM care between 2014 and 2015, collecting data on their diagnostic pathways and active treatments, as well as on the related official fees for each procedure. Then, using a multiple regression model, we estimated the overall expected cost of a patient with MPM treated in our hospital, to be born by the Regional Healthcare System based on the chosen clinical pathway. Results According to results, the economic impact of caring for a patient with MPM is mostly related to the selected active treatments, with drug and hospitalization costs as main drivers. Our analysis suggests that the expected reimbursed fee to care for a patient with MPM is equal to € 18 214.99, with chemotherapy and monitoring costs equal to € 12 861.43 and hospitalization cost equal to € 5353.55. This cost decreases to € 320.18 in the case of enrollment in an experimental trial of first-line treatment. In the other cases (second-line or third-line trials), the expected cost borne by the healthcare system for treating patients grows exponentially (€ 40,124.18 and € 59 839.94, respectively). Conclusion Experimental trials might be a solution to decrease the economic burden for the public healthcare system only in the case of first-line treatments, where the cost of chemotherapy is relevant. Nevertheless, policy-makers have to accept the sharing of this economic burden between society and the pharmaceutical industry to broaden the current scientific knowledge.

Budget constraints may cause delays in the development of transmission expansion projects. These delays increase the probability of congestion in power systems. The congestions preclude a non‐discriminatory access of Generation Companies (GenCos) to transmission network, thus leading to financial losses to certain GenCos. On the other hand, a higher degree of risk is involved in transmission investment, and a long time period is required to return the capital cost. It would, therefore, be effective to offer structures to promote merchant investments in order to lighten the financial burden on the transmission service provider to avoid lengthy delays. This paper proposes a structure to involve the GenCos in merchant transmission investment. The rationale for engaging in such projects is that, as well as the profit from the merchant investment, the GenCos could make further profit from energy production by gaining improved access to load areas. The merchant investment cost of the transmission project is returned through long‐term firm contracts together with revenues from financial transmission right. The most profitable plan of the GenCo is identified by conducting a cost‐benefit analysis among expansion plans specified by the transmission system operator. [ABSTRACT FROM AUTHOR]

This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces the standard optimization approach by a probabilistic description of both the entire system and agents' behaviors. This is done in two distinct steps. A first step considers an interacting system involving an arbitrary number of agents, where each agent's utility function is subject to unpredictable shocks. In such a setting, individual optimization problems need not be resolved. Each agent is described by a time-dependent probability distribution centered around his utility optimum. The entire system of agents is thus defined by a composite probability depending on time, agents' interactions and forward-looking behaviors. This dynamic system is described by a path integral formalism in an abstract space—the space of economic variables—and is very similar to a statistical physics or quantum mechanics system. The usual utility optimization of a representative agent is recovered as a particular case. Compared to a standard optimization, such a description eases the treatment of systems with small number of agents. It becomes however useless for a large number of agents. In a second step therefore, we show that for a large number of agents, the previous description is equivalent to a more compact description in terms of field theory. This yields an analytical though approximate treatment of the system. This field theory does not model the aggregation of a microeconomic system in the usual sense. It rather describes an environment of a large number of interacting agents. From this description, various phases or equilibria may be retrieved, along with individual agents' behaviors and their interactions with the environment. For illustrative purposes, this paper studies a business cycle model with a large number of agents. [ABSTRACT FROM AUTHOR]

This paper presents uncertain interval programming models for multi-objective multi-item fixed charge solid transportation problem with budget constraint and safety measure (MOMIFCSTPBCSM). The human languages usually involve imperfect or unknown information and are in the lack of certainty, and often, it is impossible to exactly describe an existing state or a future outcome. In using the probability theory, we must have enough historical information to estimate the probability distributions and in the case of fuzzy theory, we must have a trustworthy membership function, which is not easy to do. Thus, we often estimate the degree of belief with some hesitation that each condition may occur. To deal with such a situation, the uncertain interval theory may be very useful. Based on these facts, the parameters of the formulated problem are chosen as uncertain intervals. We consider unit transportation costs, fixed charges, transportation times, deterioration of items, supplies at origins, demands at destinations, conveyance capacities, budget at each destination, selling prices and purchasing costs, and we assume the safety factor and the desired safety measure are interval uncertain parameters. To formulate the proposed MOMIFCSTPBCSM, we use interval theory and uncertain programming techniques to develop two different models: an Expected Value Model and a Chance-Constrained Model. The equivalent deterministic models are formulated and solved using a linear weighted method, a fuzzy programming method and the goal programming method. [ABSTRACT FROM AUTHOR]

We experimentally investigate the effects of conflict budget on conflict intensity. We run a between-subjects Tullock contest in which we vary the contest budget from Low to Medium to High, while keeping the risk-neutral Nash equilibrium bid the same. We find a non-monotonic relationship: bids increase when the budget increases from Low to Medium, but decrease when the budget further increases from Medium to High. This can happen for players with concave utility, if a high budget has a wealth effect that reduces the marginal utility of winning resulting in lower bids. To test this, we run a Wealth treatment in which the budget remains the Medium, but contestants receive a fixed payment (as wealth) independent of the contest outcome. The bids in the Wealth treatment are lower than the Medium treatment, but are not different from the High treatment, supporting the hypothesis of a wealth effect. We then support this empirical observation by a theoretical model with risk-aversion. [ABSTRACT FROM AUTHOR]

Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where the upper level of a hierarchy may have his objective function and decision space partly determined by other levels. In addition, each planner's control instruments may allow him to influence the policies at other levels and thereby to improve his own objective function. As a tool, bi-level programming is applied for modeling decentralized decisions in which two decision makers make decisions successively. In this paper, we specifically address bi-level decision-making problems with budget constraint as an attractive feature in the context of enterprise-wide supply chain. We first describe the typical bi-level linear programming problem (BLLPP) and its optimal solution to the penalty function problem, and then, a cooperative decision-making problem in supply chain is modeled as BLLPP. A particle swarm optimization-based computational algorithm is designed to solve the problem, and the numerical example is presented to illustrate the proposed framework. [ABSTRACT FROM AUTHOR]

Expected utility models have been extensively used in the literature to model risk behaviour and estimate producers' risk preferences where producers are assumed to maximise their expected utility in their production decisions. However, suboptimal behaviour due to budget or non-budget constraints is common, which, if not addressed, could result in biased and inconsistent estimates of parameters in behavioural choice models. A generalised model and an approximation approach are used to correct biases in the estimation of producers' risk preferences by accounting for suboptimal behaviours. We conducted a Monte Carlo simulation to evaluate the bias correction performance of the proposed model using the generalised method of moments. Our results show that the proposed model and estimation procedure produce unbiased risk preference estimates. [ABSTRACT FROM AUTHOR]

Background: With modern methods in biotechnology, the search for biomarkers has advanced to a challenging statistical task exploring high dimensional data sets. Feature selection is a widely researched preprocessing step to handle huge numbers of biomarker candidates and has special importance for the analysis of biomedical data. Such data sets often include many input features not related to the diagnostic or therapeutic target variable. A less researched, but also relevant aspect for medical applications are costs of different biomarker candidates. These costs are often financial costs, but can also refer to other aspects, for example the decision between a painful biopsy marker and a simple urine test. In this paper, we propose extensions to two feature selection methods to control the total amount of such costs: greedy forward selection and genetic algorithms. In comprehensive simulation studies of binary classification tasks, we compare the predictive performance, the run-time and the detection rate of relevant features for the new proposed methods and five baseline alternatives to handle budget constraints. Results: In simulations with a predefined budget constraint, our proposed methods outperform the baseline alternatives, with just minor differences between them. Only in the scenario without an actual budget constraint, our adapted greedy forward selection approach showed a clear drop in performance compared to the other methods. However, introducing a hyperparameter to adapt the benefit-cost trade-off in this method could overcome this weakness. Conclusions: In feature cost scenarios, where a total budget has to be met, common feature selection algorithms are often not suitable to identify well performing subsets for a modelling task. Adaptations of these algorithms such as the ones proposed in this paper can help to tackle this problem. [ABSTRACT FROM AUTHOR]

The prevalence of mobile internet techniques stimulates the emergence of various spatial crowdsourcing applications. Certain of the applications serve for the requesters, budget providers, who submit a batch of tasks and a fixed budget to platform with the desire to search suitable workers to complete the tasks in maximum quantity. Platform lays stress on optimizing assignment strategies on seeking less budget-consumed worker-task pairs to meet the requesters' demands. Existing research on the task assignment with budget constraints mostly focuses on static offline scenarios, where the spatiotemporal information of all workers and tasks is known in advance. However, workers usually appear dynamically on real spatial crowdsourcing platforms, where existing solutions can hardly handle it. In this paper, we formally define a novel problem called B udget-aware O nline task A ssignment(BOA) in spatial crowdsourcing applications. BOA aims to maximize the number of assigned worker-task pairs under budget constraints where workers appear dynamically on platforms. To address the BOA problem, we first propose an efficient threshold-based greedy algorithm called Greedy-RT which utilizes a random generated threshold to prune the pairs with large travel cost. Greedy-RT performs well in the adversarial model when compared with simple greedy algorithm, but it is unstable in the random model for its random generated threshold may produce poor quality in matching size. We then propose a revised algorithm called Greedy-OT which could learn near optimal threshold from historical data, and consequently improves matching size significantly in both models. Finally, we verify the effectiveness and efficiency of the proposed methods through extensive experiments on real and synthetic datasets. [ABSTRACT FROM AUTHOR]

Using a novel data collection device so-called smart cart" which gathers in-store sequential goods choices log data, we study the effects of prior purchase behavior on subsequent goods choices. Analyzing 45,094 shopping trips by 8,924 unique customers, we found that they were more likely to choose high-priced goods i) when they have priorly purchased discounted or coupon products, and/or ii) when they stayed in the store longer before choosing them. By using a hierarchical modeling approach to understand consumer heterogeneity, we also show that customers who have been more likely to purchase discounted goods tend to show the tendency ii). [ABSTRACT FROM AUTHOR]

The theory of inverse location involves modifying parameters in such a way that the total cost is minimized and one/several prespecified facilities become optimal based on these perturbed parameters. When the modifying parameters are grouped into sets, with each group's cost measured under the rectilinear norm and the overall cost measured under the Chebyshev norm, the resulting problem is known as the max-sum inverse location problem. This paper addresses the max-sum inverse median location problem on trees with a budget constraint, where the objective is to modify the vertex weights so that a specified vertex becomes a 1-median, while minimizing the max-sum objective within the available budget. To solve this problem, a uni-variable optimization problem is first induced, where the objective function for each specified value of the variable can be obtained through a continuous knapsack problem. Leveraging the monotonicity of the cost function, a combinatorial algorithm is developed, which solves the problem in O (n log ⁡ n) time, where n denotes the number of vertices present in the tree. • We address the max-sum inverse median location problem on trees. • We reformulate the problem as a univariate optimization problem. • The objective of the induced optimization problem is a piecewise linear monotone function. • A combinatorial algorithm is developed to solve the problem in O (n log ⁡ n) time. [ABSTRACT FROM AUTHOR]

We investigate how to leverage limited local information for mobile advertisement popularization, where users are motivated to propagate advertisements with rewards or credits distributed from a centralized platform. Previous solutions on social networks failed to be applicable for mobile advertisement propagation because of the mobility, which would lead to extremely high overhead and low propagation efficiency. Participants need to be selected carefully and efficiently in dealing with the highly dynamic network and uncertain contacts among users. Even worse, the propagation effects are difficult to quantify with the increased number of mobile users. In tackling these difficulties, we propose αMAP (α here means efficient mobile advertisement popularization with local information), a lightweight but effective propagation user selection scheme with local information. Two key technologies inspire us to achieve efficient and effective mobile advertisement propagation. First, we advocate propagation effects instead of influence for user selection, where mobile users with strong information dissemination ability could be selected. Second, we use local information instead of the global information to achieve near optimal performance for propagation. In our proposed scheme, the information potentials proposed by Loukas et al. are leveraged to find the influential users with local information. With extensive experimental study, we find that αMAP could effectively improve the mobile advertisements delivery ratio. Using the propagation instead of popularization is validated with different aspects of investigations when the budget is constrained. To evaluate the impact of mobility, we leverage the mobile trace data set for comprehensive evaluations. αMAP performs fairly well when more realistic experimental settings are incorporated.

Several heterogeneous items are to be sold to a group of potentially budget- constrained bidders. Every bidder has private knowledge of his own valuation of the items and his own budget. Due to budget constraints, bidders may not be able to pay up to their values and typically no Walrasian equilibrium exists. To deal with such markets, we propose the notion of 'equilibrium under allotment' and develop an ascending auction mechanism that always finds such an equilibrium assignment and a corresponding system of prices in finite time. The auction can be viewed as a novel generalization of the ascending auction of Demange et al. (1986) from settings without financial constraints to settings with financial constraints. We examine various strategic and efficiency properties of the auction and its outcome.