Pooling Problem Research Articles

Optimization of CO2 capture plants with surrogate model uncertainties

CO2 capture plants can help reduce the cost of deploying capture systems across the globe. However, the CO2 variability and model uncertainty represent operational challenges to capture CO2 from different sources. This work proposes a framework for analyzing the optimal plant design considering different flue gas sources. We show a methodology to generate large data sets from optimization runs using rigorous models in Aspen Plus®. The efficiency of the approach allows its application to large-scale optimization problems, with an average CPU time per run of 176 s.We additionally build surrogate models (SMs) for the capital and operating costs of the capture plants, employing an iterative procedure to generate SMs using ALAMO. We systematically reject SMs with high uncertainty in the estimated parameters. This approach results in SMs with favorable bias-variance tradeoffs, enabling their effective application to optimization problems under uncertainty, as demonstrated with a pooling problem of CO2 streams.

The fiscal effects of cross-prefectural border municipal mergers: evidence from Japan using the synthetic control method

ABSTRACTThe purpose of this paper is to investigate whether social connectedness can mitigate the fiscal common pool problem in municipal mergers, as many studies have primarily focused on whether this problem occurs. I employ the synthetic control method by using higher-level government borders to identify the moderating effects of social connectedness. The findings reveal that subordinate partners in cross-prefectural border mergers significantly reduce their bonds and construction expenses just before the mergers. Merger partners with strong incentives to merge do not create fiscal common pool problems, which is the opposite of previous studies. The result might imply the potential effectiveness of merger support policies that prioritize social connectedness.

Mathematical programming model for the optimal management of carbon intensity indicators in global supply chains

We propose a rigorous approach for the operational planning of supply chains considering carbon intensity limits in final products. Accurately tracking of these indicators along the value chain can be challenging when dealing with bulk products. Production, transportation, blending and separation of components yield a complex pooling problem within a network structure. A novel mixed-integer nonlinear model is developed to optimize shipping schedules, inventories, processing and distribution of products while complying with environmental constraints of different markets. The model allows for rigorous monitoring and managing of carbon indicators, as well as for drawing important conclusions about sourcing strategies. A decomposition algorithm is presented for this problem, which permits obtaining high quality solutions in reasonable times. A global scale case study is solved to illustrate the economic impact of operating under carbon intensity limits, as well as suggesting alternative operating modes when the penalties on exceeding carbon targets are high.

Capacity acquisition and PPE distribution planning during the COVID-19 pandemic

As demand for personal protective equipment (PPE) surged during the COVID-19 pandemic and healthcare facilities faced supply shortages, the availability and distribution of PPE, being critical in fighting the pandemic, required pooling resources from multiple sectors. We explore such a resource pooling problem and propose to build up capacity by acquiring distribution and storage capacity from private carriers in return for compensation. We present a capacity acquisition and PPE distribution planning model under sufficient supply to optimally acquire storage and distribution capacity from third parties to fulfill demand. We then consider insufficient supply and propose a priority-based model based on pandemic severity. Finally, we model uncertain demand through two-stage stochastic programming with recourse and solve it using Benders decomposition and sample average approximation. We build a test case for the province of Ontario, Canada and provide detailed analysis under varying supply and demand scenarios.

Health Expenditure Decentralization and Health Outcomes: The Importance of Governance

Abstract Does health expenditure decentralization improve a nation’s health? Should countries care about governance quality when they decentralize healthcare spending to local governments? We answer these questions using cross-country data comprising fifty countries from 1996 to 2018. We find that health spending decentralization worsens health outcomes, which are offset by better governance of government. We calibrate the maximum feasible degree of health expenditure decentralization to have positive effects on health outcomes for a given percentile distribution of governance quality. Countries should be mindful of this negative consequence of health spending decentralization and should ensure that the quality of their governance exceeds a certain threshold to offset this negative externality. We also find that vertical fiscal imbalance is negatively associated with health outcomes, underscoring the role of revenue decentralization in improving the fiscal discipline of local governments by avoiding moral hazard caused by soft budget constraints and the common pool problem.

지방의회의 규모는 재정 지출에 영향을 미치는가

This paper examines whether there exists an impact of the size of local councils on government spending in Japanese local governments. I focus on the fact that the maximum number of council members of municipal councils in Japan has been bound by law, and estimates this by RDD. Then, we examine the existence and positivity or negativity of the effect of council size. My estimation results show that an increase in council size leads to an increase in government spending for the “small and medium-sized groups,” while the opposite is true for the “medium and large groups. The author believes that the common pool problem of increasing government spending does not change with the size of the municipality. Therefore, the difference in the estimated results may be due to differences in the oversight function of councils. A result of this paper suggest that the size of local council members may contribute to the achievement of sound public finances.

Renewable resource use with imperfect self-control

We investigate renewable resource use when the harvesting agents face self-control problems. Individuals are conceptualized as dual selves. The rational long-run self plans for the infinite future while the affective short-run self desires to maximize instantaneous profits or utility. Depending on the degree of self-control, actual behavior is partly driven by short-run desires. In a model of a single harvesting agent (e.g. a fishery), we discuss how self-control problems affect harvesting behavior, resource conservation, and sustainability and discuss policies to curb overuse and potential collapse of the resource due to limited self-control. We then extend the model to several harvesting agents and show how limited self-control exacerbates the common pool problem. Finally, we investigate heterogenous agents and show that there are spillover effects of limited self-control in the sense that perfectly rational agents also behave less conservatively when they interact with agents with imperfect self-control.

Geographic Virtual Pooling of Hospital Resources: Data-Driven Trade-off Between Waiting and Traveling

Problem definition: Patient-level data from 72 magnetic resonance imaging (MRI) hospitals in Ontario, Canada from 2013 to 2017 show that over 60% of patients exceeded their wait time targets. We conduct a data-driven analysis to quantify the reduction in the patient fraction exceeding (FET) target for MRI services through geographic virtual resource-sharing while limiting incremental driving time. We present a data-driven method to solve the geographic pooling problem of partitioning 72 hospitals with heterogeneous patients with different wait time targets located in a two-dimensional region into a set of clusters. Methodology/results: We propose an “augmented-priority rule,” which is a sequencing rule that balances the patient’s initial priority class and the number of days until her wait time target. We then use neural networks to predict patient arrival and service times. We combine this predicted information and the sequencing rule to implement “advance scheduling,” which informs the patient of her treatment day and location when requesting an MRI scan. We then optimize the number of geographic resource pools among the 72 hospitals using genetic algorithms. Our resource-pooling model lowers the FET from 66% to 36% while constraining the average incremental travel time below three hours. In addition, our model shows that only 10 additional scanners are needed to achieve 10% FET, whereas 50 additional scanners would be needed without resource sharing. Over 70% of the hospitals are not worse off financially. Each individual hospital, measured over at least two weeks, achieves a higher machine utilization and a lower FET. Managerial implications: Our paper provides a practical, data-driven geographical resource-sharing model that hospitals can readily implement. Our method achieves a near-optimal solution with low computational complexity. Using smart data-driven scheduling, a little extra capacity placed at the right location is all we need to achieve the desired FET under geographic resource-sharing. Funding: This paper is supported by the following grant: Canadian Institutes of Health Research (CIHR) [Grant CIHR-950-231935]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1225 .

Target‐based resource pooling problem

We study a two‐stage resource pooling problem with multiple resources and customers. The central decision‐maker decides the capacity level of the resources within a total budget before the realization of uncertain demand. Then, the fulfillment policy is determined by individual service‐level requirements. We use a robust satisficing framework to formulate the problem and allow ambiguity in the distribution of demand. Moreover, we introduce a new utility‐based probability distance allowing the model to be solved exactly using a column and constraint generation algorithm. We also provide a more efficient solution method for some special cases. Finally, we conduct experiments for a process flexibility problem, which is an example of the resource pooling problem. We show the advantage of our model over some benchmark approaches, and show the impact of the flexibility structure and correlation between demands.

Games with possibly naive present-biased players

We propose a solution concept for games that are played among players with present-biased preferences that are possibly naive about their own, or about their opponent’s future time inconsistency. Our perception-perfect outcome essentially requires each player to take an action consistent with the subgame perfect equilibrium, given her perceptions concerning future types, and under the assumption that other present and future players have the same perceptions. Applications include a common pool problem and Rubinstein bargaining. When players are naive about their own time inconsistency and sophisticated about their opponent’s, the common pool problem is exacerbated, and Rubinstein bargaining breaks down completely.

Pool Palms: Children and Swimming Pool Problems

Pool Palms: Children and Swimming Pool Problems

Is prorationing efficiency-enhancing or rent-seeking?: Evidence from a natural experiment

Prorationing is used as a textbook definition of a solution to the market failure presented by the common pool aspects of oil and natural gas (see, for example, Spulber, 1989, 59). Yet, at the same time, the academic literature on this question is severely limited. To fill this void, we analyze a recent natural experiment in Oklahoma to determine the impact of rule changes that increased the stringency of prorationing and constrained natural gas production at the well level for one year. Prorationing in Oklahoma no longer serves to address common pool problems, as the affected hydraulically fractured wells do not suffer from common pool problems. Instead, we show that prorationing reduced natural gas production by large companies but had a significantly weaker impact on the production by small companies as well as those headquartered in Oklahoma. This gave the less affected companies an important competitive advantage. These findings are generally consistent with the positions that companies took to advocate for and against prorationing. The regulations can therefore be interpreted as a form of rent-seeking, with their proponents benefitting by imposing production limitations on their rivals. This work stimulates questions about the implications of prorationing in other states.

On the P-formulation and the split-fraction-formulation for the generalized pooling problem

The formulations of the generalized pooling problem (GPP) use either quality variables (the P-formulation and its variants) or split-fraction variables (the SF-formulation and its variants) to model the material balance at the pools. Although the strength of the formulations among the category of the P-formulation is well understood and so is the strength of the formulations among the category of the SF-formulation, the strength of a P-formulation in comparison to a SF-formulation has not been well understood. This paper provides a formal analysis to compare the strength of the P-formulation and the SF-formulation, which leads to the conditions under which the P-formulation is at least as strong as the SF-formulation. These conditions also explain why the P-formulation is often no weaker than the SF-formulation at the root node of branch-and-bound search. The theoretical results are verified by a computational study of 26 problem instances.

The Role of Learning in Adaptation to Technology: The Case of Groundwater Extraction

Learning may play an important role in adopting new technology. While the role of learning in the decision to adopt has been widely investigated in the literature, to the best of our knowledge its role in knowing how to best use technology and the speed of learning has not been studied extensively. An example of this situation is when farmers adopt groundwater extraction technology. In this case, they need to learn the exact cost and benefit of extracting water in is relation to how they use it in practice. By comparing the extraction behavior of farmers who own new wells with farmers who own old wells, this paper explores the role of experience in shaping farmers’ decisions. Three identification strategies are used in this study to test the hypothesis that owners with less experience (owners of new wells) with groundwater technology are able to extract more water than experienced owners. The first strategy employs panel data. The results of this model show that groundwater extraction rises as the growth rate in the number of new wells increases. The second strategy uses the exogenous variation in precipitation shocks in a double-difference approach. Employing census data at the well level, this study shows that 6–13% more water is extracted from new wells than from older wells, and that the difference in extraction increases in areas that experience negative precipitation shocks. The third strategy uses the nearest-neighbor matching method, which shows that new wells extract 11% more groundwater per year compared to old wells, indicating that old wells are more efficient in maintaining their inter-temporal extraction. These findings have important implications for discussions of regulating a common pool resource. In the literature regarding the common pool problem, firms are often considered entities with complete information about their true abatement costs. An implication of findings of this paper is that quantity instruments for regulating groundwater extraction fail to guarantee productive efficiency when farmers face uncertainty about their marginal abatement cost. The results of this study show that it takes a few years for farmers to adapt to new technologies. According to this finding, a recommendation to policy makers, therefore, is that they must consider this time lag in learning how to use new technologies when proposing policies to mitigate the effects of climate change.

The Fiscal Common Pool Problem, Municipal Mergers, and Spillovers

Mergers of local governments, commonly referred to as municipal mergers, have been widely implemented to internalize spillover effects. Many empirical studies point out that municipalities change the intertemporal budget allocation by increasing their debt issuance before mergers and they consider that this debt issuance is induced by the “fiscal common pool problem” because of pooled budgets after mergers. However, this phenomenon has yet to be analyzed theoretically. Therefore, this paper examines the mechanism of increased debt issuance before municipal mergers. We compare the debt issuance in the merger case with the level in the socially optimal and nonmerger cases. We find that the amount of debt issuance is larger in the merger case than in both other cases. The difference vanishes when spillovers are perfect.

Solving the pooling problem at scale with extensible solver GALINI

This paper presents a Python library to model pooling problems, a class of network flow problems with many engineering applications. The library automatically generates a mixed-integer quadratically-constrained quadratic optimization problem from a given network structure. The library additionally uses the network structure to build 1) a convex linear relaxation of the non-convex quadratic program and 2) a mixed-integer linear restriction of the problem. We integrate the pooling network library with GALINI, an open-source extensible global solver for quadratic optimization. We demonstrate GALINI’s extensible characteristics by using the pooling library to develop two GALINI plug-ins: 1) a cut generator plug-in that adds valid inequalities in the GALINI cut loop and 2) a primal heuristic plug-in that uses the mixed-integer linear restriction. We test GALINI on large scale pooling problems and show that, thanks to the good upper bound provided by the mixed-integer linear restriction and the good lower bounds provided by the convex relaxation, we obtain optimality gaps that are competitive with Gurobi 9.1 on the largest problem instances.

R&D INVESTMENTS IN PLANT BREEDING UNDER CHANGING INTELLECTUAL PROPERTY RIGHTS

In a Cournot duopoly model, we examine three policy regimes relevant to current international plant breeding: patents alone, patents with a farmer exemption to use saved seed, and patents with research collaboration. In the symmetric version of the model where firms are identical, we show that the social planner prefers patents with research collaboration over patents alone and prefers the patents alone to patents with a farmer exemption. We examine two variations of the model where firms are asymmetric i. due to cost differences and ii. due to the different endowments of germplasm. Situations develop where the research collaboration resolves the common pool problem and increases R&D investment and where it creates free riding problem and decreases R&D investment. We show that the lower cost (more endowed) breeder invests more in R&D under the research collaboration than patents if variety differentiation is high and cost (knowledge endowment) dispersion is low. On the other hand, the higher cost (less endowed) breeder, generally, invests less in R&D under a research collaboration if variety differentiation or cost (knowledge endowment) dispersion is low. These findings suggest new gains are likely from the adoption of international conventions of plant breeders' rights. Keywords: Plant breeding, farmer exemption, research collaboration, Intellectual Property Rights, product differentiation, Cournot oligopoly.JEL Classifications: D21, D43, D60, D82, L13, L24, O34, O38, Q16, Q18DOI: https://doi.org/10.32479/ijefi.11544

Democracy and Corruption

I examine the relationship between democracy and the perceived risk of corruption in a panel of 130 countries. My panel model controls for country fixed effects and enables the estimation of a within-country relationship between democracy and corruption. My main finding is that democracy significantly reduces the risk of corruption, but only in countries where ethnic fractionalization is low. In strongly fractionalized countries a transition from autocracy to democracy does not significantly reduce corruption. One explanation for these findings is that the corruption-reducing effect of greater accountability of politicians under democracy is undermined by the common pool problem; fractionalization increases the severity of the common pool problem.

Common Pool Problem: South Pars-North Dome Gas Field

The aim of this paper is to investigate possible problems of efficiency arising from the joint exploitation of the common gas pool (South Pars - North Dome, the largest natural gas reservoir in the world) by Iran and Qatar. The problem is related to the difference between private incentives and common goals. In the case of non-renewable resources, a Pareto-optimal joint extraction path could exist, but it is unlikely to occur in reality. We studied the difference in incentives for an optimal exploitation path for Iran and Qatar and found that their joint behavior was likely suboptimal from the perspective of the optimal dynamics of gas resource exploitation. In part, this is related to the difference in wealth, and in part to the sanctions against Iran, which have so far not allowed Iran to participate freely in the world market. Considering that the cost of future gas extraction in Russia's northern fields is likely to increase, a delay in the optimal presence of Iranian gas on the world market may lead to a suboptimal sequence of exploitation of various gas fields, which would mean both problems for the profitability of investments in Russia and higher world prices for natural gas in the future.

Federalism, but how? The impact of vertical fiscal imbalance on economic growth. Evidence from Belgium*

AbstractThis paper applies both parametric and nonparametric synthetic control methods in the case of a specific federal reform. It evaluates the impact of Belgium's constitutional federalism reform of 1993 on GDP per capita. The findings show a negative impact of the reform on economic growth. This negative impact ceases soon after 2001, when a subsequent reform reduced the vertical fiscal imbalance that characterized the 1993 federal reform. It is argued that the presence of a strong federalism with subnational spending autonomy and, conversely, a centralized tax system, enhanced pork barrel spending, a common pool problem, thus damaging economic growth.