Pareto Efficient Frontier Research Articles

A Bi-Objective Mixed-Integer Linear Programming Model for a Sustainable Agro-Food Supply Chain with Product Perishability and Environmental Considerations

Background: Agro-food supply chains possess specific characteristics due to the diverse nature of products involved and contribute to all three pillars of sustainability, making the optimal design of a sustainable agro-food supply chain a complex problem. Therefore, efficient models incorporating the unique characteristics of such chains are essential for making optimal supply chain decisions and achieving economically and environmentally sustainable agro-food supply chains that contribute to global food security. Methods: This article presents a multi-objective mixed-integer linear programing model that integrates agricultural-related strategic decisions into the tactical design of an agro-food supply chain. The model considers transportation, inventory, processing, demand fulfilment, and waste disposal decisions. It also accounts for seasonality and perishability, ensuring a comprehensive approach to sustainability. The model aims to maximize the total generated profits across the supply chain while simultaneously minimizing CO2 emissions as a measure of environmental impact. Results: By implementing the model on a sugar beet supply chain in the Netherlands, strategic crop rotation farm schedules for the crop rotation cycle and the optimum supply network decisions are obtained. Furthermore, different objectives are analyzed and the Pareto-efficient frontier is investigated to analyze the underlying trade-offs. Additionally, the model serves as a decision support tool for managers facilitating informed investment decisions in technologies that prolong product shelf life while maintaining profitability. Conclusions: The proposed multi-objective model offers a valuable framework for designing economically and environmentally sustainable agro-food supply chains. By aligning with sustainability goals and providing decision support, this research contributes to enhancing global food security and promoting sustainable resource utilization.

A simultaneous balancing and sequencing algorithm to plan assembly lines in the fashion industry

PurposeThe purpose of the study is to fill a gap in the literature on mathematical production planning (joint balancing and sequencing) in the fashion industry. It considers in particular situations of mass customization, made-to-measure or small lot sizes.Design/methodology/approachThe paper develops a mathematical model based on product options and attributes instead of fixed variants. It proposes an easy-to-use genetic algorithm to solve the resulting optimization problem. Functionality and performance of the algorithm are illustrated via a computational study.FindingsAn easy-to-implement, yet efficient algorithm to solve the multi-objective implementation of a problem structure that becomes increasingly relevant in the fashion industry is proposed. Implementation of the algorithm revealed that the algorithm is ideally suited to generate significant savings and that these savings are impervious to problem and thus company size.Practical implicationsThe solutions from the algorithm (Pareto-efficient frontier) offer decision-makers more flexibility in selecting those solutions they deem most fitting for their situation. The computational study illustrates the significant monetary savings possible by implementing the proposed algorithm to practical situations.Originality/valueIn contrast to existing papers, for the first time, to the best of the author’s knowledge, the focus of the joint balancing and sequencing approach has been applied in the fashion instead of the automotive industry. The applicability of the approach to specific fields of the fashion industry is discussed. An option and attributes-based model, rarely used in general assembly line sequencing per se, is used for more flexibility in representing a diverse set of model types.

Risk-averse rehabilitation decision framework for roadside slopes vulnerable to rainfall-induced geohazards

Rainfall-induced slope failures disrupt the traffic and warrant urgent slope repair works. The impact of roadside slope failures can be minimized if slopes are proactively rehabilitated. Nonetheless, transportation agencies are constrained in their budget to rehabilitate a limited number of slope segments due to competing maintenance needs among different transportation assets. Therefore, the transportation agencies should identify the critical slope combination that should be proactively rehabilitated under constraint budgets to lessen the impact on the transportation network during extreme rainfall events. The decision-making approach for slope rehabilitation should also ensure low risk associated with the selected rehabilitation strategy. Current slope-rehabilitation decision models do not consider the risk associated with the rehabilitation strategies in the decision-making process. The objective of this study is to develop a risk-averse stochastic combinatorial optimization to facilitate the selection of slope rehabilitation strategies, which leads to the least expected cost and conditional value at risk (CVaR) for extreme rainfall events. The simulated annealing approach is used to solve the risk-averse combinatorial optimization rehabilitation problem with the objective function that measures the total cost of traffic disruption and slope restoration post-failures. The approach is demonstrated using a transportation network in Lamar County, Texas. Unlike a genetic algorithm-based approach in the literature that yields a single slope rehabilitation strategy, the proposed risk-averse simulated annealing approach identifies rehabilitation strategies along the Pareto efficient frontier facilitating the rehabilitation decisions based on the tradeoff between expected cost and CVaR. For the network in Lamar County, the proposed risk-averse simulated annealing provided a solution in the Pareto front that reduced CVaR by 2.0% compared to the solution obtained from the genetic algorithm-based approach while only increasing the expected cost by 0.8%. The risk-averse optimization approach will aid transportation agencies in determining slope rehabilitation strategies for minimizing the impact of rainfall-induced failures at appropriate risk aversion levels.

Performance measurement of decision making units through interval efficiency with slacks-based measure: an application to tourist hotels in Taipei

Data envelopment analysis (DEA) is widely used to evaluate the performance of a group of homogeneous decision making units (DMUs). Considering the uncertainty, interval DEA has been introduced to fit into more situations. In this paper, an interval efficiency method based on slacks-based measure is proposed to solve the uncertain problems in DEA. Firstly, the maximum and minimum efficiency values of the evaluated DMU are calculated by the furthest and closest distance from the evaluated DMU to the projection points on the Pareto-efficient frontier, respectively. Then, the AHP method is used for the full ranking of DMUs. The paper uses the pairwise comparison relationship between each pair of DMUs to construct the interval multiplicative preference relations (IMPRs) matrix. If the matrix does not meet the consistency condition, a method to obtain consistency IMPRs is introduced. According to the consistency judgment matrix, the full ranking of DMUs can be obtained. Finally, we apply our method to the performance evaluation of 12 tourist hotels in Taipei in 2019.

Quality Expectation-Variance Tradeoffs in Crowdsourcing Contests

We examine designs for crowdsourcing contests, where participants compete for rewards given to superior solutions of a task. We theoretically analyze tradeoffs between the expectation and variance of the principal's utility (i.e. the best solution's quality), and empirically test our theoretical predictions using a controlled experiment on Amazon Mechanical Turk. Our evaluation method is also crowdsourcing based and relies on the peer prediction mechanism. Our theoretical analysis shows an expectation-variance tradeoff of the principal's utility in such contests through a Pareto efficient frontier. In particular, we show that the simple contest with 2 authors and the 2-pair contest have good theoretical properties. In contrast, our empirical results show that the 2-pair contest is the superior design among all designs tested, achieving the highest expectation and lowest variance of the principal's utility.

Pareto efficient buy and hold investment strategies under order book linked constraints

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of “golden strategies”, i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.

Managerial Ability and R&D Investment: An Empirical Analysis Based on DEA-Tobit Model

DEA is a statistical procedure used to evaluate the relative efficiency of separable entities, termed “decision-making units” (DMUs), where each DMU converts certain inputs into outputs. The DEA efficiency methodology can provides an ordinal ranking of relative efficiency compared to the Pareto-efficient frontier, and the widely used efficiency measure require that weights be explicitly set, which is more advantageous than the conventional measures of efficiency. The Tobit model is a dependent variable limited model. Since the efficiency value measured by the DEA model is a truncated discrete distribution value between 0 and 1, the Tobit model can effectively avoid the problems of bias and inconsistency in parameter estimation. Based on this, this paper takes Chinese A-share listed companies from 2008 to 2018 as samples, adopts DEA-Tobit model to measure managerial ability, and studies the impact of managerial ability on firm innovation investment. It is found that managerial ability is negatively correlated with R&D investment. Further research shows that the negative relationship between managerial ability and firm innovation investment is more significant in non-state-owned companies. Transparency of accounting information can alleviate the restraining effect of managers ability on innovation input. This study not only enriches the research literature in the field of managerial ability and firm innovation input, but also has important enlightenment significance on how to improve managerial innovation willingness in reality and further promote firm innovation behavior.

Geometric and LP-based heuristics for angular travelling salesman problems in the plane

The angular-metric travelling salesman problem (AngleTSP) asks for a Hamiltonian cycle for given points in the Euclidean plane mimimizing the sum of all turning angles. Setting as objective the linear combination of these angles with the distances of the classical TSP, gives rise to the angular-distance-metric travelling salesman problem (AngleDistanceTSP).Since both problems are NP-hard, we first introduce a wide range of heuristic approaches, motivated by the typical geometric structure of optimal solutions. In particular, we exploit lens-shaped neighbourhoods of edges and a decomposition of the graph into layers of convex hulls, which are then merged into a tour. Secondly, we consider an ILP model based on the more general quadratic travelling salesman problem (QTSP). By rounding its fractional solutions we obtain a collection of subtours, paths and isolated points, which are then combined into a tour by various strategies, all of them involving auxiliary ILP models. Finally, different improvement heuristics are proposed, most notably a matheuristic which locally reoptimizes the solution for rectangular sectors of the given point set by an ILP approach.Results of extensive computational experiments using benchmark instances from the literature illustrate the Pareto-efficient frontier of algorithms in a (running time, objective value)-space. It turns out that our new methods clearly dominate previously published heuristics.

Strategy-proof Pareto-improvement

We consider a model where each agent has an outside option of privately known value. At a given allocation, we call the set of agents who do not exercise their outside options the “participants.” We show that one strategy-proof and individually rational mechanism weakly Pareto-improves another if and only if, at each preference profile, it weakly expands (in terms of set inclusion) the set of participants. Corollaries include: a sufficient condition for a mechanism to be on the Pareto-efficient frontier of strategy-proof mechanisms; uniqueness of strategy-proof Pareto-improvements under true preferences over certain normatively meaningful benchmark allocation rules; and a characterization of the pivotal mechanism.

Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere

This paper discusses isotropic sparse regularization for a random field on the unit sphere S 2 in R 3 , where the field is expanded in terms of a spherical harmonic basis. A key feature is that the norm used in the regularization term, a hybrid of the ℓ 1 and ℓ 2 -norms, is chosen so that the regularization preserves isotropy, in the sense that if the observed random field is strongly isotropic then so too is the regularized field. The Pareto efficient frontier is used to display the trade-off between the sparsity-inducing norm and the data discrepancy term, in order to help in the choice of a suitable regularization parameter. A numerical example using Cosmic Microwave Background (CMB) data is considered in detail. In particular, the numerical results explore the trade-off between regularization and discrepancy, and show that substantial sparsity can be achieved along with small L 2 error.

Integrating harvesting decisions in the design of agro-food supply chains

The inefficiencies observed in current agro-food supply chains, and recent trends in agro-food industry such as consolidation, increase the need for further studies on supply chain management in this field. Models are required for the complex task of determining the optimal supply chain configuration in order to improve their economic and environmental performance, while taking into account the specific characteristics of agro-food supply chains. This paper provides a general description of the supply chain design problem in agro-food industrial chains, considering the role of seasonality and harvesting decisions, perishability, and processing. A general model formulation is presented, which accommodates for these characteristics and for forward and backward flows along the chain. The general model is applied to a case study of the sugar beet processing chain in the Netherlands. The pareto-efficient frontier between maximizing the total gross margin and minimizing the global warming potential in CO2-eq is explored. Uncertainties in demand and harvest yield are taken into account using a stochastic version of the model. Results show that a supply chain design model tailored to the specific characteristics of an agro-food supply chain with its uncertainties leads to identifying better performing supply chain configurations. In the case study, supply chain configurations can be found in which the performance on both the economic and the environmental objective is better than the modelled current performance. Additionally, we observe that supply chain configurations with decentralized processing or pre-processing are an interesting topic for future research in the context of agro-food industry.

Integrating encounter theory with decision analysis to evaluate collision risk and determine optimal protection zones for wildlife

Abstract Better understanding human–wildlife interactions and their links with management can help improve the design of wildlife protection zones. One example is the problem of wildlife collisions with vehicles or human‐built structures (e.g., power lines, wind farms). In fact, collisions between marine wildlife and watercraft are among the major threats faced by several endangered species of marine mammals. Natural resource managers are therefore interested in finding cost‐effective solutions to mitigate these threats. We combined abundance estimators with encounter rate theory to estimate relative lethal collision risk of the Florida manatee (Trichechus manatus latirostris) from watercraft. We first modelled seasonal abundance of watercraft and manatees using a Bayesian analysis of aerial survey count data. We then modelled relative lethal collision risk in space and across seasons. Finally, we applied decision analysis and Linear Integer Programming to determine the optimal design of speed zones in terms of relative risk to manatees and costs to waterway users. We used a Pareto efficient frontier approach to evaluate the performance of alternative zones, which included additional practical considerations (e.g., spatial aggregation of speed zones) in relation to the optimal zone configurations. Under the various relationships for probability of death given strike speed that we considered, the current speed zones reduced the relative lethal collision risk by an average of 51.5% to 70.0% compared to the scenario in which all speed regulations were removed (i.e., the no‐protection scenario). We identified optimal zones and near‐optimal zones with additional management considerations that improved upon the current zones in terms of cost or relative risk. Policy implications. Our analytical framework combines encounter rate theory and decision analysis to quantify the effectiveness of speed zones in protecting manatees while accounting for uncertainty. Our approach can be used to optimize the design of protection zones intended to reduce conflicts between human waterborne activity and marine mammals. This framework could be extended to address many other problems of human–wildlife interactions, such as the optimal placement of wind farms to minimize collisions with wildlife or the optimal allocation of ranger effort to mitigate poaching threats.

Optimal fee structures in hedge funds

This paper proposes a framework to analyze hedge funds fee arrangements in which the portfolio construction is determined by the hedge fund manager and the fees are determined via an optimal equilibrium between the manager and the investor. In this setting, fees include management fees ( $$\alpha$$ ) and performance fees ( $$\beta$$ ). We select the paradigm of Expected Utility Theory to determine the managers optimal strategy. Benefiting from the dependence of the optimal terminal payoff on the fee structure, we explore two criteria producing an equilibrium fee mutually satisfying the investor and the manager, one based on Pareto Optimality and the second on negotiable regions. The former also leads to a Pareto efficient frontier of fee structures. We obtain evidence that the popular fee structure of $$(\alpha , \beta )=(2\%, 20\%)$$ is not an equilibrium fee between manager and investor. Although such equilibrium heavily depends on risk aversion levels and market conditions, the pair $$(\alpha , \beta )=(0.5\%, 30.7\%)$$ stands out as a fair choice. Moreover, the expected utility of the investor is not monotone in the performance fee for many market conditions. In other words, we prove that fee arrangements which include performance fees are usually beneficial for the investor.

Optimising embodied carbon and U-value in load bearing walls: A mathematical bi-objective mixed integer programming approach

The construction and building industry is known to be a carbon intensive sector. Of the various opportunities present for minimising the carbon footprint of buildings, optimising the material selection of building components is one plausible avenue for significant carbon reductions. In the construction of opaque load-bearing walls, the thermal performance of the construction build up is the parameter that has the greatest influence over building operational carbon emissions, with thicker profile walls leading to lower U-values and hence lower operational carbon from heating and cooling. Conversely, the extra wall material contributes to increased embodied carbon. The aim of this study is to capture such trade-off between embodied carbon and U-value by presenting a practical optimisation model to design load bearing walls in commercial and residential buildings. In particular, two objective functions are incorporated within the proposed model for the structural design and material selection of the wall layers; the first objective minimises the embodied carbon of the wall while the other minimises the U-value of the wall. The variables forming the optimisation model include the thickness of each wall layer, and the choice of material forming each layer. The proposed model is tested on a practical case example applicable in Australia and the UK, involving a load bearing wall. Results are reported in the form of a Pareto efficient frontier. Utilising the model enables the realisation of the impacts of material selection and wall layering on embodied carbon and U-value of the building structure.

Closest target for the orientation-free context-dependent DEA under variable returns to scale

An important branch of data envelopment analysis (DEA) is context-dependent DEA, which evaluates efficiency by combining the attractiveness and progress for a particular decision-making unit (DMU). Traditionally, context-dependent DEA models are based on the assumption of constant returns to scale. Two limitations are found when directly extending original radial context-dependent DEA (ORCD-DEA) models into variable returns to scale versions. One is that it may not be possible to determine the attractiveness of a DMU that logically must be attractive in that context. The other problem is that the progress measure cannot ensure an inefficient DMU projects to a Pareto-efficient frontier. A small numerical example is used to illustrate these two issues. In order to overcome these deficiencies, the concept of closest target is introduced to determine the attractiveness and progress for each DMU. The closest target method can further improve DMUs’ performance with less wastes in inputs or underproduction in outputs. Finally, a practical application involving computer printers is presented.

A simulation–optimization strategy to deal simultaneously with tens of decision variables and multiple performance measures in manufacturing

This work addresses the multiple criteria simulation–optimization problem. This problem entails using an optimization strategy to manipulate the parameters of a simulation model to arrive at the best possible configurations in the presence of several performance measures in conflict. Pareto Efficiency conditions are used in an iterative framework based on experimental design and pairwise comparison. In particular, this work improves upon and replaces the use of Data Envelopment Analysis to determine the efficient frontier, and replaces the use of a single-pass algorithm previously proposed by our research group. The results show a rapid convergence to a more precise characterization of the Pareto-efficient frontier. In addition, the capability of the method to deal with fifty decision variables simultaneously is demonstrated through a study regarding the fine-tuning of a manufacturing line.

Estimating and decomposing overall inefficiency by determining the least distance to the strongly efficient frontier in data envelopment analysis

This paper proposes a new method to measure economic inefficiency of decision making units based on the calculation of the least distance to the Pareto-efficient frontier in data envelopment analysis. While all previously published approaches that have dealt with the problem of determining least distances to the efficient frontier are focus on exclusively technical inefficiency, the new methodology opens the door to applications of this approach when market prices, together with inputs and outputs, are available. Finally, the paper empirically illustrates the new method using recent data on the mandarins’ production in a Spanish eastern province.

Estimating and Decomposing Overall Inefficiency by Determining the Least Distance to the Strongly Efficient Frontier in Data Envelopment Analysis

This paper proposes a new method to measure economic inefficiency of decision making units based on the calculation of the least distance to the Pareto-efficient frontier in Data Envelopment Analysis (DEA). While all previously published approaches that have dealt with the problem of determining least distances to the efficient frontier are focus on exclusively technical inefficiency, the new methodology opens the door to applications of this approach when market prices, together with inputs and outputs, are available. Finally, the paper empirically illustrates the new method using recent data on the mandarins' production in a Spanish eastern province.

A validation scheme for intelligent and effective multiple criteria decision-making

Multiple criteria decision-making (MCDM) methods have various practical applications. Decision-makers face MCDM problems with conflicting criteria daily. Hence, MCDM methods have been developed to enable decision-makers to enhance decision quality. MCDM methods use various calculation approaches to evaluate the rank of alternatives. However, little evidence supports the consistency between the alternative chosen by the MCDM method and the decision-maker’s intuitive ideal alternative. Therefore, the objective of this study is to develop an operational validation scheme to examine and compare the effectiveness of MCDM methods. In the validation scheme, control variables include the number of alternatives, number of criteria, data set distributions, and nondominated data set options (Pareto efficient frontier or complete data set). We also add three weight distributions, namely uniform weights, rank order centroid weights, and rank sum weights, to determine the effect of weights on the MCDM methods We test linear, quadratic, Chebycheff, and prospect utility functions. In addition to the compensatory, noncompensatory, and partially compensatory utility functions, we use the prospect theory utility function. Mean absolute rank deviation and Kendall’s statistical rank test, are applied to examine the effectiveness of the methods To show the viability, this study illustrates the proposed scheme by an evaluation process of numerical comparisons among common MCDM methods including technique for order preference by similarity to ideal solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), elimination et choix traduisant la realité (ELECTRE), the piecewise linear prospect (PLP) theory method, and Analytic Hierarchy Process (AHP). Moreover, method-oriented parameter settings such as normalization methods, distance functions, VIKOR’s v, and ELECTRE’s thresholds are examined. Through the aforementioned settings, we compare the MCDM methods’ ranks with the decision-maker’s ranks by using assumed preference utility functions. The results reveal that interactive MCDM methods such as PLP and AHP outperform the others in terms of rank consistency. However, the performance of the MCDM methods is affected by the percentage of existing efficient solutions. More investigations into the applicability of the utility functions in various situations are suggested.

Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis

This paper proposes a new method to measure productivity change of decision making units in the full input-output space. The new approach is based on the calculation of the least distance to the Pareto-efficient frontier and hence provides the closest targets for evaluated decision making units to reach the strongly efficient frontier with least effort. Another advantage of the new methodology is that it always leads to feasible solutions. The productivity change in the new approach is operationalized as a Luenberger-type indicator in the Data Envelopment Analysis framework and it is decomposed into efficiency change and technical change. The paper empirically illustrates the new method using recent data on the Spanish quality wine sector.