Welfare Maximization Problem Research Articles

Strategic behavior and social optimization in a constant retrial queue with the N-policy

We consider customers’ strategic behavior and the corresponding social maximization problem in an M/M/1 constant retrial queue with the N-policy. There is no waiting space in front of the server and customers who find the server busy have to abandon the system, but they can leave their contact details to stay on a waiting list. Consequently, after a service completion, the server will seek a customer from the waiting list at a constant retrial rate on an FCFS basis. The server is switched off whenever the system becomes empty, and is resumed only when the number of waitlisted customers reaches a given threshold. We assume that the arriving customers who find the server busy or down decide whether to leave their contact details or to balk based on a linear reward-cost structure. We examine customers’ strategic response to this mechanism and compare it to the social optimal behavior with delay information. It is shown that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system, and therefore, both multiple and unique equilibrium arrival rates could exist. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. The individual equilibrium strategies are compared with the social optimum and the Price of Anarchy (PoA) is studied as a measure to quantify the inefficiency of the equilibrium strategies. Finally, numerical examples are presented to illustrate the sensitivity of some key system performance measures.

Duration-Differentiated Energy Services With a Continuum of Loads

The problem of balancing supply and demand in the power grid becomes more challenging with the integration of uncertain and intermittent renewable supply. The usual scheme of supply following load may not be appropriate for large penetration levels of renewable supply. The reason is the increased level of reserves required to maintain a reliable grid, which affects both operational costs (reserves are expensive) and the environmental benefits of renewables (on-line reserves might increase CO 2 emissions). An alternative paradigm is to use demand side flexibility for power balance. In this paper, we focus on one particular way of exploiting the demand side flexibility. We consider a group of loads with each load requiring a constant power level for a specified duration within an operational period. The loads are differentiated in terms of the duration of service they require. The flexibility of a load resides in the fact that the power delivery may occur at any subset of the total operational period. We consider the problems of scheduling, control and market implementation for a continuum of these loads. If the loads and the available power are known in advance, we find conditions under which the available power can service all the loads, and we describe an algorithm that constructs an appropriate allocation. In the event the available supply is inadequate, we characterize the minimum amount of power that must be purchased to service the loads. In addition, we investigate the implementation of a forward market in which consumers can purchase duration differentiated services. We first characterize the social welfare maximization problem and then show the existence of an efficient competitive equilibrium in this forward market.

Whole-Page Optimization and Submodular Welfare Maximization with Online Bidders

In the context of online ad serving, display ads may appear on different types of web pages , where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various prespecified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current webpage respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page and may lead to highly suboptimal results in general. In this article, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world datasets. A key technical ingredient of our results is a novel primal-dual analysis for handling free disposal, which updates dual variables using a “level function” instead of a single level and unifies with previous analyses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 - 1 / e - o (1)-competitive ratio. Moreover, our experiments on real-world datasets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders and show how to solve this problem using our algorithm for whole-page optimization.

Optimal Fines under Announced and Surprise Inspections

AbstractThis paper examines optimal fines in a regulatory framework where the regulator can choose either surprise or announced inspections to monitor a firm for compliance. The firm can invest in detection avoidance, but it receives a fine if the regulator discovers that it is noncompliant. In the welfare maximization problem, we focus on the trade‐off between the frequency of inspections and the magnitude of the fine. We find that when inspections are unannounced, the optimal fine is maximal, but when they are announced, the optimal fine may be less than maximal.

Optimal Fines Under Announced and Surprise Inspections

This paper examines optimal fines in a regulatory framework where the regulator can choose either surprise or announced inspections to monitor a firm for compliance. The firm can invest in detection avoidance, but it receives a fine if the regulator discovers that it is non-compliant. In the welfare maximization problem, we focus on the trade-off between the frequency of inspections and the magnitude of the fine. We find that when inspections are unannounced, the optimal fine is maximal, but when they are announced, the optimal fine may be less than maximal.

Economics of collective monitoring: a study of environmentally constrained electricity generators

This paper investigates the costs of monitoring of a distributed multi-agent economic activity in the presence of constraints on the agents’ joint outputs. If the regulator monitors agents individually she calculates each agent’s optimal contribution to the constrains by solving a constrained welfare-maximisation problem. This will maximise welfare but may be expensive because monitoring cost rises with the number of agents. Alternatively, the regulator could monitor agents collectively, using a detector, or detectors, to observe if each constraint is jointly satisfied. This will ease implementation cost, but lower welfare. We define the welfare difference between each regime of monitoring for a fairly inclusive electricity generation model and formulate some predictions. The behaviour of two generators in a coupled-constrained, three-node case study reproduces these predictions. We find that the welfare loss from collective monitoring can be small if the constraints are tight. We also learn that, under either regime, the imposition of transmission and environmental restrictions may benefit the less efficient generator and shift surplus share towards the emitters, decreasing consumer surplus.

Maximizing net benefits for conventional and flexible bus services

Transit ridership is usually sensitive to fares, travel times, waiting times, and access times, among other factors. Therefore, the elasticities of demand with respect to such factors should be considered in modeling bus transit services and must be considered when maximizing net benefits (i.e. “system welfare”=consumer surplus+producer surplus) rather just minimizing costs. In this paper welfare is maximized with elastic demand relations for both conventional (fixed route) and flexible-route services in systems with multiple dissimilar regions and periods. As maximum welfare formulations are usually too complex for exact solutions, they have only been used in a few studies focused on conventional transit services. This limitation is overcome here for both conventional and flexible transit services by using a Real Coded Genetic Algorithm to solve such mixed integer nonlinear welfare maximization problems with constraints on capacities and subsidies. The optimized variables include service type, zone sizes, headways and fares. We also determine the maximum welfare threshold between optimized conventional and flexible services) and explore the effects of subsidies. The proposed planning models should be useful in selecting the service type and optimizing other service characteristics based on local geographic characteristics and financial constraints.

Distributed and Optimal Resource Allocation for Power Beacon-Assisted Wireless-Powered Communications

In this paper, we investigate optimal resource allocation in a power beacon-assisted wireless-powered communication network (PB-WPCN), which consists of a set of hybrid access point (AP)-source pairs and a power beacon (PB). Each source, which has no embedded power supply, first harvests energy from its associated AP and/or the PB in the downlink (DL) and then uses the harvested energy to transmit information to its AP in the uplink (UL). We consider both cooperative and non-cooperative scenarios based on whether the PB is cooperative with the APs or not. For the cooperative scenario, we formulate a social welfare maximization problem to maximize the weighted sum-throughput of all AP-source pairs, which is subsequently solved by a water-filling based distributed algorithm. In the non-cooperative scenario, all the APs and the PB are assumed to be rational and self-interested such that incentives from each AP are needed for the PB to provide wireless charging service. We then formulate an auction game and propose an auction based distributed algorithm by considering the PB as the auctioneer and the APs as the bidders. Finally, numerical results are performed to validate the convergence of both the proposed algorithms and demonstrate the impacts of various system parameters.

Pollutant Abatement Investment under Ambiguity in a Two-Period Model

This paper investigates a pollutant abatement investment under ambiguity in a twoperiod setting. We consider there are representative consumer and firm in an economy and formulate the social welfare maximization problem. Then we numerically derive the optimal level of abatement investment. Furthermore, we analyze the comparative static effects of the model’s parameters and find an increase in the degree of ambiguity encourages pollutant abatement investment.

Distributed Spectrum Sharing in Cognitive Radio Networks: A Pricing-Based Decomposition Approach

The limited radio spectrum has become a bottleneck for various wireless communications. To better utilize the scare radio spectrum, cognitive radios have recently attracted increasing attention, which makes spectrum sharing more viable. Sharing radio spectrum from primary users to secondary users is of great importance. A licensed primary user (PU) can lease its spectrum to secondary users (SUs) for wireless communications. This paper studies the problem of social welfare maximization of distributed spectrum sharing among a PU and SUs. We first formulate the problem of social welfare maximization which takes into account both the cost of the PU and the utility gained by each SU. The social welfare maximization is a convex optimization problem and thus can be solved by a centralized algorithm. However, the utility function of each SU may contain the private information. To avoid privacy leakage of SUs, we propose an iterative distributed algorithm based on a pricing-based decomposition framework. It is theoretically proved that our algorithm converges to the optimal solution. Simulation results are presented to show that our algorithm achieves the optimal social welfare and converges quickly in a practical setting.

Black-Box Randomized Reductions in Algorithmic Mechanism Design

We give the first black-box reduction from approximation algorithms to truthful approximation mechanisms for a non-trivial class of multi-parameter problems. Specifically, we prove that every welfare-maximization problem that admits a fully polynomial-time approximation scheme (FPTAS) and can be encoded as a packing problem also admits a truthful-in-expectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis by employing small perturbations as a tool in algorithmic mechanism design. We develop a “duality” between linear perturbations of the objective function of an optimization problem and of its feasible set, and we use the “primal” and “dual” viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.

Determination of Transmission Capacity for a Two-node Market

We examine a two-node competitive market, taking into account the losses under transmission and the costs of transmission line construction. We state a welfare maximization problem and show how to solve it. Moreover, we analyze how the flow of good between markets affects the benefit of transmission system, consumer surplus and producers’ profit. We also consider a two-node market under imperfect competition and study the Cournot equilibrium depending on the transmission capacity.

Improved cost–benefit analysis for market-based transmission planning, a European perspective

This paper addresses the problem of transmission planning in interconnected power systems under the uncertainty of future generation parks and fast varying marginal production costs. The decision maker has to consider many different aspects during the definition of different transmission planning strategies that sometimes might even be contradicting. Major contributions are the incorporation of energy policy measurements in the evaluation process of candidate transmission plans and the inclusion of short- and long-term uncertainties. The proposed methodology, so-called C-TRAP, is based on a semi-dynamic heuristic approach that solves the social welfare maximization problem for several discrete steps considering different preferences for energy policy and transmission network reinforcements. The flexibility provided through the heuristic analysis is very important for decision makers in the new uncertain environment in power systems.

A Study on Reliability Differentiated Pricing of Firm Capacity

It is known that Reliability Differentiated Pricing (RDP) can improve the efficiency and benefits of consumers and producers. This paper examines the long-run social welfare maximization problem of the utility and presents a long-term reliability differentiated prices for firm capacity, based on customer outage costs. Then the applicability of the proposed pricing scheme is verified with a case study.

On the design of public infrastructure systems with elastic demand

This paper considers the optimization of public infrastructure systems, recognizing that these systems serve multiple user classes. Example application domains include: public transportation systems, electricity distribution grids, urban water distribution systems, and maintenance of pavement and bridge systems. Under the guidance of a policy-making body, the analyst chooses both the system design, including its layout and control, and the prices to be charged for the service. The goal of the optimization is to maximize society’s welfare recognizing that the system’s performance will in general depend on the system’s demand, and vice versa.The optimization problem is first formulated in its full complexity, where the prices, the demand and the system design are to be determined. It is then shown that if the user classes recognized in the analysis can be priced independently, and if the policy setting body specifies either the demand levels or the generalized prices experienced by each user group, then the resulting welfare maximization problem decomposes into three sub-problems that can be solved sequentially: demand estimation, system design and pricing. It also turns out that the optimum design can always be obtained by minimizing the generalized cost of the system to society for the known fixed demand, as is conventionally done in practice. The resulting design is independent of how net user benefits are measured and of the pricing scheme.If the policy-making body does not specify cost or demand targets, and instead assesses benefits by means of consumer surplus then the optimum design is still the solution of a conventional design problem with fixed demand. In this case, however, the demand has to be obtained iteratively using a marginal cost pricing rule.The paper finally shows how government can structure payments to a for-profit agency so it will be induced to design and operate the system optimally for society.

Modeling biodiversity benefits and external costs from a keystone predator reintroduction policy

In this paper, an economic model was constructed to determine the optimal wolf population and distribution across the Northern Rocky Mountains. Both ecological and economic concepts were incorporated in an implicitly spatial social welfare maximization problem. This interdisciplinary model relies on multiple data sources, including current wolf population and distribution information, opportunity cost to local landowners, and contingent valuation studies to determine willingness-to-pay for wolves. Economic models tend to externalize ecological concerns and ecological models often omit the complex human dimensions of conservation policy. Accordingly, this model can serve as a guide for integrating best practices from both fields. The model presented here is sufficiently general to apply to wolves in other ecosystems and to other highly interacting species such as beavers and bison. The Northern Rocky Mountain wolf was used as an example of how this economic model works, but this model can be applied far more broadly.

Price of Correlations in Stochastic Optimization

When decisions are made in the presence of high-dimensional stochastic data, handling joint distribution of correlated random variables can present a formidable task, both in terms of sampling and estimation as well as algorithmic complexity. A common heuristic is to estimate only marginal distributions and substitute joint distribution by independent (product) distribution. In this paper, we study possible loss incurred on ignoring correlations through a distributionally robust stochastic programming model, and we quantify that loss as price of correlations (POC). Using techniques of cost sharing from game theory, we identify a wide class of problems for which POC has a small upper bound. To our interest, this class will include many stochastic convex programs, uncapacitated facility location, Steiner tree, and submodular functions, suggesting that the intuitive approach of assuming independent distribution acceptably approximates the robust model for these stochastic optimization problems. Additionally, we demonstrate hardness of bounding POC via examples of subadditive and supermodular functions that have large POC. We find that our results are also useful for solving many deterministic optimization problems like welfare maximization, k-dimensional matching, and transportation problems, under certain conditions.

A Fuzzy-based Genetic Algorithm for Social Welfare Maximization by Placement and Sizing of Static Synchronous Series Compensator

This article presents a fuzzy-based genetic algorithm to maximize total social welfare and alleviate congestion by placement and sizing of one static synchronous series compensator device, considering its investment cost in a double-sided auction market. The generating units cost curves are considered to be quadratic with sine components to show the impacts of valve point loading. By adding the valve point effect, the model presents non-differentiable and convex regions that challenge most gradient-based optimization algorithms. In addition, the impact of distribution companies on the social welfare maximization and congestion management is presented as a quadratic function. The proposed approach makes use of the fuzzy-based genetic algorithm to optimal schedule generating companies and distribution companies and setting the static synchronous series compensator location and its size while the Newton–Raphson algorithm minimizes the mismatch of the power flow equations. Simulation results on the modified IEEE 14- and 30-bus test systems (with/without line flow constraints, before/after compensation) are used to examine the impacts of the static synchronous series compensator on the total system social welfare improvement versus its cost. Several cases are considered to test and validate the consistency of detecting best solutions. Simulation results are compared to solutions obtained by the genetic algorithm and sequential quadratic programming approach, which has been used in MATPOWER (available on-line; see [1]). The aim of this article is the utilization of static synchronous series compensator for the social welfare maximization problem considering the impact of valve point loading effect on the operation point of the generating companies by inclusion of fuzzy rules in the genetic algorithm to guarantee fast convergence for locating/sizing the static synchronous series compensator. The proposed method shows the benefits of the static synchronous series compensator in a deregulated power market and demonstrates how it can be utilized by the independent system operator to improve the total social welfare and prevent congestion.

Cross-Layer Resource Allocation Model for Cellular-Relaying Network Performance Evaluation

The enhancement of cellular networks with relaying technologies is expected to bring significant technoeconomic benefits at the expense of more complex resource allocation. Suitable models for solving network dimensioning problems in cellular-relaying networks must handle radio resource allocation among hundreds of links and tackle interactions between networking layers. For this purpose, we propose a novel cross-layer resource allocation model based on average interference and ideal rate adaptation for the physical layer (PHY), time shares for the medium access layer, and fluid flows for the transport and network layers. We formulate a centralized social welfare maximization problem. When the routes are selected with an a priori algorithm, we show that the resource allocation problem admits an equivalent convex formulation. We show a numerical example for how to use the proposed framework for configuring the backhaul link in a practical relaying network. The overall problem of selecting routes and allocating time shares and link rates is nonconvex. We propose an iterative suboptimal algorithm to solve the problem based on a novel approximation of PHY. We state and prove several convergence properties of the algorithm and show that it typically outperforms routing based on signal-to-noise ratio only.

OPTIMAL BAIL AND THE VALUE OF FREEDOM: EVIDENCE FROM THE PHILADELPHIA BAIL EXPERIMENT

I. INTRODUCTION On a typical day in the United States, roughly 300,000 untried defendants are incarcerated and 700,000 are free on bail. (1) While the tradeoffs a judge must consider when setting bail are well-recognized, what level of bail is optimal is an open question. Our objective is to provide a rigorous framework for understanding bail policy and to estimate socially optimal levels of bail. The objectives of this study are to provide a rigorous framework for understanding bail policy, to estimate socially optimal levels of bail, and to contribute to the literature on policy evaluation by exploring the welfare implications of one specific publicly provided good with externalities (freedom from jail) that has measurable costs and benefits. Following Landes (1973, 1974), we explicitly model the process of bail setting as a welfare maximization problem in which an optimal social planner would seek to minimize the total cost incurred by society. The four costs that enter the planner's problem are the social cost of jailing the defendant, the private cost to the defendant from being incarcerated, the cost of crimes a defendant may commit while awaiting trial, and the cost to society of a criminal absconding. An increase in bail levels would lead to higher numbers of defendants who could not afford to post bail and would have to remain in jail until their trials. Detaining these additional individuals would impose costs on the justice system (who must feed, house, and monitor the incarcerated defendants) and also on the defendants, who would suffer from lost freedom. A decrease in bail levels would increase the number of defendants who could afford to post bail. The justice system and potential victims would then face the risks of these defendants possibly absconding and/or committing new crimes. The current study examines how to optimally balance these various consequences of changing the level of bail. First, we empirically estimate the effects of bail levels on the fraction of defendants posting, fleeing, and committing crimes during pre-trial release. Next, we assemble estimates of the per-unit costs associated with each of these pre-trial outcomes. We then combine these per-unit costs with our estimated causal relationships to measure the total cost incurred by society as a causal function of bail levels. Finally, using our estimates, we calculate optimal bail levels for different types of defendants, and we make recommendations for social welfare-maximizing bail policies. Ordinary least squares estimates of the effects of bail are likely to suffer from omitted variables bias. For example, judges assign higher bail levels to defendants deemed as dangerous in ways that may be unobservable to the econometrician. These defendants will also be more likely to commit subsequent crimes or to abscond. The omission of the dangerous variable will cause ordinary least squares to understate the effects of bail on flight and rearrest risk. We address this concern by using data from the 1981 Philadelphia Bail Experiment (Goldkamp and Gottfredson 1982). In this experiment, judges randomly assigned to the treatment group were given bail guidelines to use, while members of the control group set bail as they had previously. The bail guidelines caused the treatment judges to set considerably lower levels of bail than those set by the control group. Since defendants were randomly assigned to judges, the experiment induced exogenous variation in the bail levels faced by defendants. This experiment allows us to obtain unbiased estimates of the effects of bail on posting, failure-to-appear at trial, and rearrests. In addition to estimating optimal bail policies, this study contributes to the economics of crime literature by estimating the value that defendants place on 90 d of freedom. This parameter is a necessary input into our estimates of the socially optimal bail and is of interest in its own right. …