Pooling Problem Research Articles

Target-based Inventory Pooling Problem

We study a stochastic inventory risk pooling problem, in which the objective is to minimize the risk that the remaining inventory and the unsatisfied demand exceed the pre-specified acceptable levels. We use the robustness optimization framework to model this problem, in which the decision maker does not need to determine the size of the ambiguity set. The model will then determine the most robust solution that satisfies the threshold levels. Moreover, we introduce a new utility-based probability distribution distance and formulate the problem as a convex optimization problem. A column and constraint generation (CCG) algorithm is derived to solve the model exactly. We conduct experiments to compare the performance of our model with two other benchmark models, and show that our model provides lower risk and more robustness to distribution ambiguity.

Water conservation and the common pool problem: Can pricing address free-riding in residential hot water consumption?

Water conservation and the common pool problem: Can pricing address free-riding in residential hot water consumption?

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

(1) Problem definition: Using patient-level data from 72 MRI hospitals in Ontario, Canada from 2013 to 2017, we find that over 60% of patients exceeded their wait time targets. We conduct a data-driven analysis to quantify the reduction in the Fraction Exceeding Target (FET) for MRI services through geographic resource sharing while controlling for the cost of patient driving. (2) Academic/Practical Relevance: Grouping hospitals in the same geographic region into resource-sharing pools can reduce waiting time but increase travel costs. We prove analytically that partial pooling typically dominates complete pooling and no pooling for a simple linear city model with homogeneous patients. We present a data-driven method to solve the generalized (practical but more difficult) geographic pooling problem of 72 hospitals with heterogeneous patients with different wait time targets located in a two-dimensional region. (3) Methodology: We propose a geographic resource sharing model that groups hospitals into clusters to reduce the FET while controlling for patient driving distance. For any given geographic cluster, using forecasted data generated by a neural network, we propose an advance scheduling mechanism that informs the patient of her service time when she requests an MRI scan, an ``augmented-priority queuing that ranks the patient based on her priority and waiting time target, and a routing algorithm that determines at which hospital she will receive the MRI scan. We then optimize clusters using modified K-means clustering and Genetic Algorithms. Lastly, we conduct a counterfactual analysis to determine the minimal capacity expansions needed to achieve the desired 10% FET. (4) Results: Our resource pooling model lowers the FET to 34% while limiting patients' driving time to maximally two hours. In addition, our model and method show that only eight additional scanners are needed to achieve 10% FET while 50 additional scanners would be needed without resource sharing. (5) Managerial Implication: Our paper provides a practical, data-driven geographical resource-sharing model that hospitals can readily implement. Our solution method achieves a near-optimal solution with low computational complexity. Using smart data-driven scheduling and routing, a little extra capacity placed at the right location is all we need to achieve the desired FET under geographic resource sharing.

History and Evolution of the North American Wildlife Conservation Model

The first section of this monograph describes the NAWCM and the difficulties it faces confronting circumstances very different from those that created it, namely the local overabundance of whitetail deer, wild hogs, and other wild game animals. It describes scientific wildlife management and argues that it constitutes the sole necessary cause of sustainable consumptive use of living natural resources. It concludes by showing that scientific wildlife management and markets for wild game meat can be compatible when commercial influences on wildlife managers are adequately checked. Section two reviews the history of wildlife management in North America, from American Indians through the development of the NAWCM in the late nineteenth century, and surveys the interplay between biology, ecology, markets, range, and population size of a dozen important types of wild animals. The key takeaway is that common pool problems and species-specific characteristics, like herding and flocking behaviors, endanger wild game populations far more than the scientifically-managed commercialization of their flesh does. The third section warns that the facile application of “democracy” to wildlife management poses grave risks for wildlife, especially wild game species, by threatening the authority of scientific wildlife management and further eroding the wildlife dollars volunteered by consumptive users. The fourth section suggests several ways that wildlife managers, short of reinstating markets for wild game meat, can increase the number of consumptive users and political support for the sustainable, consumptive use of wildlife. The most important suggestion is for the legalization of proxy hunting as a way, short of full-blown commercialization, of increasing wild game harvests where needed to meet local scientific wildlife management goals. The conclusion argues that by stressing the importance of scientific wildlife management over its other components, instead of making a fetish of prohibitions on wild game markets, the NAWCM can continue to protect North America’s wildlife throughout the twenty-first century.

Sample average approximation for stochastic nonconvex mixed integer nonlinear programming via outer-approximation

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333–346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation algorithm where we iterate between a mixed-integer linear programming (MILP) master problem and a nonconvex nonlinear programming (NLP) subproblem. We prove that the optimal solutions and optimal value obtained by the SAAOA algorithm converge to the optimal solutions and the optimal value of the true SP problem as the sample size goes to infinity. The convergence rate is also given to estimate the sample size. Since the theoretical sample size estimate is too conservative in practice, we propose an SAAOA algorithm with confidence intervals for the upper bound and the lower bound at each iteration of the SAAOA algorithm. Two policies are proposed to update the sample sizes dynamically within the SAAOA algorithm with confidence intervals. The proposed algorithm works well for the special case of pure binary first stage variables and continuous stage two variables since in this case the nonconvex NLPs can be solved for each scenario independently. The proposed algorithm is tested with a stochastic pooling problem and is shown to outperform the external sampling approach where large scale MINLPs need to be solved.

Public investment and the fiscal common pool problem on municipal mergers in Japan

The purpose of this paper is to reveal the kinds of public investment that create a fiscal common pool problem through municipal mergers in Japan. In particular, we focus on whether municipal mergers increase road and public park construction immediately before the mergers because previous papers reveal that municipal mergers increase only local bonds. The empirical results show that subordinate merger partners rapidly increase their road and public park expenses just before mergers.

On the effect of the selection of suppliers on the design of formulated products

An extended pooling problem is developed for the design of detergents, that include process and product design together with suppliers’ selection. It is a multiperiod and multi-objective optimization problem since it considers the economic benefit and environmental impact as well as the contract length. This problem can be considered as a previous step to the integrated product, process and supply chain design. This type of problems is non-linear and non-convex. Two formulations are developed to tackle this problem. An MINLP and a reformulated NLP using a decision vector avoiding the use of binary variables. The NLP shows better computational performance in spite of the larger problem size. Furthermore, it is demonstrated that when considering different ingredients, formulations, pricing policies and suppliers, their selection can be adjusted until a reduction of almost 40% of CO2 emissions is achieved without the benefit decreasing more than 1.5%.

Municipal merger and debt issuance in South African municipalities

ABSTRACT Existing research reveals opportunistic free-riding behaviours by municipalities facing mergers; these behaviours include over-issuance of debt before mergers because their burden will be shared by newly constructed municipalities. Nevertheless, the literature presents few solutions to this problem. We therefore investigate whether South African municipalities that faced mergers engaged in free-riding behaviours before the mergers. In South Africa, the upper government of municipalities implemented the monitoring of borrowings before mergers. Using a difference-in-differences analysis and quarterly data of South African municipalities, we find that South African municipalities decreased the amount of borrowings before their mergers. This result contradicts previous research, indicating that proper policy for municipal mergers may prevent the fiscal common pool problem caused by free-riding behaviours. To the best of our knowledge, our study is the first to demonstrate a reduction in borrowings before municipal mergers.

Qualifying the common pool problem in government spending: the role of positional externalities

Under what circumstances do coalition partners tend to overspend? The so-far dominant explanation relies on the common pool resource theory—the more cabinet members there are, the higher the spending. While theoretically sound, this explanation seems to be more relevant for some cases and less for others. What could lie behind this discrepancy? While the literature to date has focused on institutional factors, we propose a mechanism that relates to voting behaviour. Relying on the concept of positional externalities, we argue that each coalition member wishes to spend relatively more resources than the other coalition member(s) to attract impressionable voters. Positional externalities, we claim, exhibit a direct positive effect on total spending and, perhaps more importantly, interact with the common pool resource factor, decreasing its relevance when they are weak.

1DCNN Fault Diagnosis Based on Cubic Spline Interpolation Pooling

The conventional pooling method for processing one-dimensional vibration signals may lead to certain issues, such as weakening and loss of feature information. The present study proposes the cubic spline interpolation pooling method. The method is appropriate for processing one-dimensional signals. The proposed method can transform the pooling problem into a linear fitting problem, use the cubic spline interpolation method with outstanding fitting effects, and calculate the fitting function of the input signals. Moreover, the values of the interpolation points are sequentially taken as the feature value output. Furthermore, the network using the conventional pooling method and the pooling network model proposed in the present study are compared, tested, and analyzed on the constructed simulation signals and the measured bearing dataset. It is concluded that the proposed pooling method can reduce the data dimension while improving the network feature extraction capability and is more appropriate for pooling one-dimensional signals.

Renewable Resource Use with Imperfect Self-Control

We investigate renewable resources 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. This modeling represents impatience and present bias without causing time inconsistent decision making. 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 present-biased harvesting behavior. 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.

The role of research in common pool problems

Significant amounts of public spending are allocated towards research on climate change, but considerable uncertainties remain. We analyze the strategic role of information acquisition and the determinants of investments in information in a common pool game. In the first stage, countries can acquire a signal about their own environmental damages caused by total emissions. Because signals are public, there are information spillovers between countries. In the second stage, the countries decide how much pollution to emit. We show that there can be an inefficiently high amount of investments in information in the non-cooperative equilibrium compared to the cooperative solution if the countries are risk averse and the expected emissions are sufficiently large. In addition, we analyze what happens if the countries cooperate in one of the stages but not in the other. We show numerically that if the emissions are decided non-cooperatively, countries might agree not to acquire any information at all. But if the emissions levels are decided cooperatively, investments in the non-cooperative equilibrium are always too low.

A multi-commodity flow formulation for the optimal design of wastewater treatment networks

The wastewater treatment network (WWTN) optimization problem can be viewed as an extension of the generalized pooling problem (GPP), where not only the different streams are mixed and split, but also some chemical components are removed from the system. It is well known that a strong formulation is key to efficient global solution of GPP, and multi-commodity flow formulations have been recognized as such strong formulations. The paper presents the first multi-commodity flow formulation for the WWTN optimization problem. We discuss the challenges in adapting the classical multi-commodity flow approaches for a WWTN, and propose the conditions under which the selected commodities are adequate for modeling a WWTN. We prove that the proposed formulation is at least as strong as a classical component based formulation. We show the significant computational advantage of the proposed formulation over the component based formulation through 16 problem instances from the literature.

An extended mixed-effects framework for meta-analysis.

Standard methods for meta-analysis are limited to pooling tasks in which a single effect size is estimated from a set of independent studies. However, this setting can be too restrictive for modern meta-analytical applications. In this contribution, we illustrate a general framework for meta-analysis based on linear mixed-effects models, where potentially complex patterns of effect sizes are modeled through an extended and flexible structure of fixed and random terms. This definition includes, as special cases, a variety of meta-analytical models that have been separately proposed in the literature, such as multivariate, network, multilevel, dose-response, and longitudinal meta-analysis and meta-regression. The availability of a unified framework for meta-analysis, complemented with the implementation in a freely available and fully documented software, will provide researchers with a flexible tool for addressing nonstandard pooling problems.

Convexifications of rank-one-based substructures in QCQPs and applications to the pooling problem

We study sets defined as the intersection of a rank-one constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-one set is polyhedral or second-order cone representable. In all these cases, we also show that a linear objective can be optimized in polynomial time over these sets. Towards the application side, we show how these sets relate to commonly occurring substructures of a general quadratically constrained quadratic program. To further illustrate the benefit of studying quadratically constrained quadratic programs from a rank-one perspective, we propose new rank-one formulations for the generalized pooling problem and use our convexification results to obtain several new convex relaxations for the pooling problem. Finally, we run a comprehensive set of computational experiments and show that our convexification results together with discretization significantly help in improving dual bounds for the generalized pooling problem.

Hyperbolic Discounting in Fiscal Policy: The Case of Malaysian Government Budget

Thispaper examines the lag effect of interest payments on the national output represented by GDP. The lag effectimplies the observation of hyperbolic discounting in the fiscal policy. The idea is round-eyed;that the government takes on high debts to finance their spending while not factoring or placing less importanceon the cost of the interest payments. The concept of hyperbolic discounting of behavioral economics is used in this paper to explain this phenomenon in the present path of public policy which operates under an interest-based system. We conduct this analysis by examiningthe present fiscal model and its effect on the economy, wherein debt is preferredin fiscal policy framework.It appears from the findings that the trend in Malaysia’s fiscal policy shows the presence of hyperbolic discounting.Shifting the debt burden to future governments and spending above revenue capacity can be seen as a manifestation of the common pool problem. Two main policy recommendations can be made. Firstly, the fiscal policy structure has to move away from the current interest-based borrowing. This is because an intrinsic feature of the interest-based system is that the risks of a debt transaction are transferred from the lender to the borrower.Secondly, the current tax structure can be simplied to improve tax compliance so as to improve tax revenue collection.Both the above policy recommendations have the potential of reducing the effect of hyperbolic discounting. The first increases the interaction between the government and the public thus enhances the governance structure of the government. The government will have to be more transparent in its dealing as the public has a vested interest in the development projects. The second enhances the first effect by providing a potential increase in tax revenue which will reduce the stress on debt servicing and the need for borrowing.

A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables

In this paper, we propose a generalized Benders decomposition-based branch and cut algorithm for solving two stage stochastic mixed-integer nonlinear programs (SMINLPs) with mixed binary first and second stage variables. At a high level, the proposed decomposition algorithm performs spatial branch and bound search on the first stage variables. Each node in the branch and bound search is solved with a Benders-like decomposition algorithm where both Lagrangean cuts and Benders cuts are included in the Benders master problem. The Lagrangean cuts are derived from Lagrangean decomposition. The Benders cuts are derived from the Benders subproblems, which are convexified by cutting planes, such as rank-one lift-and-project cuts. We prove that the proposed algorithm converges in the limit. We apply the proposed algorithm to a stochastic pooling problem, a crude selection problem, and a storage design problem. The performance of the proposed algorithm is compared with a Lagrangean decomposition-based branch and bound algorithm and solving the corresponding deterministic equivalent with the solvers including BARON, ANTIGONE, and SCIP.

Generic modeling framework of Multi-Energy Systems (MES) within the Upstream Oil Supply Chain (USOSC) network

Persistent decline in energy return on energy invested (EROEI) of crude oil production has challenged researchers to find solutions to a sustainable supporting energy framework. This study looks at determining the economic profit of integrating renewable energy sources to support crude oil production, formulated as a pooling problem, while mitigating carbon dioxide emissions from each sector of the USOSC. General Algebraic Modeling Systems was used to develop a MILP multi-period model to evaluate optimal energy distribution based on an integrated renewable energy infrastructure, using the multi-energy hub approach. A case study was carried out on Abu Dhabi, where 10 oil producing wells of varying quality were considered. Different scenarios, including varying EROI, implementation of EOR+ technology (i.e. carbon capture and re-injection) and employment of carbon cap and trade program (CC&T), were considered. Major findings from each of these scenarios depict the energy system configuration along with optimum flow rates whilst maximizing economic profit.

Robust Optimization for the Pooling Problem

The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of parametric uncertainty. This paper applies two robust optimization approaches, reformulation and cutting planes, to the non-linear, non-convex pooling problem. Most applications of robust optimization have been either convex or mixed-integer linear problems. We explore the suitability of robust optimization in the context of global optimization problems which are concave in the uncertain parameters by considering the pooling problem with uncertain inlet concentrations. We compare the computational efficiency of reformulation and cutting plane approaches for three commonly-used uncertainty set geometries on 14 pooling problem instances and demonstrate how accounting for uncertainty changes the optimal solution.

Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods

The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For the pooling problem with time discretization, we propose second order cone programming (SOCP) and linear programming (LP) relaxations and prove that they obtain the same optimal value as the semidefinite programming relaxation. Moreover, a rescheduling method is proposed to efficiently refine the solution obtained by the SOCP or LP relaxation. The efficiency of the SOCP and the LP relaxation and the proposed rescheduling method is illustrated with numerical results on the test instances from the work of Nishi in 2010, some large instances and Foulds 3, 4 and 5 test problems.