Review of Empirical Studies in Multiobjective Mathematical Programming: Subject Reflection of Nonlinear Utility and Learning

Multiple objective programming provides a means of aiding decision makers facing complex decisions where trade-offs among conflicting objectives must be reconciled. Interactive multiobjective programming provides a means for decision makers to learn what these trade-offs involve, while the mathematical program generates solutions that seek improvement of the implied utility of the decision maker. A variety of multiobjective programming techniques have been presented in the multicriteria decision-making literature. This study reviews published studies with human subjects where some of these techniques were applied. While all of the techniques have the ability to support decision makers under conditions of multiple objectives, a number of features in applying these systems have been tested by these studies. A general evolution of techniques is traced, starting with methods relying upon linear combinations of value, to more recent methods capable of reflecting nonlinear trade-offs of value. Support of nonlinear utility and enhancing decision-maker learning are considered.     

MULTIPLE-CRITERIA DECISION MAKING INCLUDING QUALITATIVE FACTORS: THE POST-MODEL ANALYSIS APPROACH

As a method of solving multiple-criteria decision making problems with a single quantitative objective and multiple qualitative objectives, the post-model analysis (PMA) approach is proposed. The essence of PMA is to support the trade-offs between a quantitative objective and multiple qualitative objectives so that the decision maker can find a perceived most preferred nondominated solution. To this end, the optimal solution of a quantitative model is found first, without regard for qualitative factors. The solution is then evaluated in terms of qualitative objectives. When the initial quantitatively optimal solution is adjusted to allow improvement of qualitative goals, opportunity costs of achieving qualitative goals are incurred. In this process, an expert system and/or graphical display can be used. PMA therefore provides a way to incorporate quantitative models into knowledge-based expert systems.     

Enhancing knowledge construction processes within multicriteria decision analysis: The Collaborative Value Modelling framework

This paper proposes a new Collaborative Value Modelling framework, that combines Delphi and multicriteria decision conferencing, to build widely informed evaluation models. Multicriteria Decision Analysis (MCDA) is commonly used to help decision-makers and other stakeholders in complex evaluation contexts. Further to the technical soundness and meaningfulness of the methods and tools used, it is critical to design adequate social processes to promote shared understanding around key evaluation issues while capturing multiple stakeholders’ values and perspectives. Multicriteria decision conferencing processes have been typically adopted for collaborative modelling using MCDA methods in decision conferences with relatively small groups. Such a socio-technical approach has proven to be effective, in a variety of contexts, in creating a collaborative environment that enables surfacing individual beliefs, identifying common concerns, managing eventual value conflicts and promoting agreement in group model building. But, extending this framework to broader participatory contexts requires a different design of the social process, in order to ensure that model building captures the full panoply of points of view. This challenge can be tackled by enhancing multicriteria decision conferencing with an all-embracing (Web-)Delphi participatory process. We depart from the existing collaborative knowledge acquisition methodology to design, with the Delphi method, a participatory knowledge construction process that elicits and analyses individual judgemental knowledge from a (very) large and diverse number of stakeholders. The knowledge acquired is then digested by a small group of key-players, in a subsequent decision conferencing, to collaboratively develop a widely informed multicriteria evaluation model. This new Web-Delphi-decision conferencing social setting has been tested already in real complex evaluation contexts using a specific multicriteria method, the Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH), to develop a variety of value modelling activities. We call this socio-technical design the Collaborative Value Modelling framework. Here, we describe its real use to support the construction of value functions, focusing on how the judgemental knowledge collected flows between the participatory and collaborative stages of the framework. Results validate that enhancing MACBETH decision conferencing with an ex ante Web-Delphi process fosters higher participation and collaboration in multicriteria modelling.     

Entscheidungsunterstützung unter Berücksichtigung der Anforderungen von Entscheidungsträgern am Beispiel der Gestaltung von optionalen Girokonto-Tarifen

Quantitative decision models are used only if managers’ implementation conditions are met. Decision makers want tools that offer a set of good solutions so that they can evaluate different solutions according to various objectives without being forced to make their trade-offs explicit in a functional form. This also allows taking into account strategic aspects that cannot be modeled otherwise. In such situations, heuristics are needed which derive solutions from the structure and not so much from the mathematical properties. We present such a decision support tool for the problem of determining a menu of optional tariffs for checking accounts. The heuristic is based on the idea that for reasonably separable preferences across segments it is the best to offer for each segment the most preferred product. We use latent class choice-based conjoint analysis to estimate customer preferences and develop a customized choice-based conjoint design to take differences in individual demand into account. The proposed heuristic was used to support an actual decision problem for which the profit contribution has been increased substantially without having faced a considerable loss of customers.     

Interactive Multiple Objective Decision Support for Sales Force Sizing and Deployment*

An interactive decision aid is introduced for the deployment of two sales resources: salespeople and sales support staff. The aid consists of a normative sales resource allocation model with five objectives and an interactive multiple objective programming solution procedure. The specific decision problem addressed involves the assignment of salespeople and sales support people to customer accounts and the allocation of the time they spend on these accounts. The authors contribute to the existing sales resource modeling literature by dealing with the deployment of two sales resources and interactively solving this problem with respect to five short-run and long-run objectives of the firm. This approach differs from existing sales force modeling efforts in which the solution is found noninteractively by optimizing a single sales resource model with respect to a single objective, often short-run sales. An application of the decision aid to the deployment problem of an industrial sales force manager is presented. Furthermore, useful extensions of the basic sales resource allocation model are discussed.     

Planning a sustainable reverse logistics system: Balancing costs with environmental and social concerns

The present work aims to support tactical and operational planning decisions of reverse logistics systems while considering economic, environmental and social objectives. In the literature, when addressing such systems economic aspects have been often used, while environmental concerns have emerged only recently. The social component is the one less studied and rarely the combination of the three concerns has been analyzed. This work considers the three objectives and was motivated by the challenge of supporting decision makers when managing a real case study of a recyclable waste collection system, where strategic decisions on the number and location of depots, vehicles and containers were taken beforehand. Tactical and operational decisions are studied involving the establishment of service areas for each depot and the definition and scheduling of collection routes for each vehicle. Such decisions should represent a compromise solution between the three objectives translating a sustainable reverse logistics plan. The problem is modeled as a multi-objective, multi-depot periodic vehicle routing problem with inter-depot routes. A mathematical formulation and a solution approach are proposed. An approximation to the Pareto front is obtained for the case study and the trade-offs between the objectives are discussed. A balanced solution is proposed.     

An Interactive Framework for Multi-Person,Multiobjective Decisions

Group decision making in the presence of multiple conflicting objectives is complex and difficult. This paper describes and evaluates an iterative technique to facilitate multiple objective decision making by multiple decision makers. The proposed method augments an interactive multiobjective optimization procedure with a preference ranking tool and a consensus ranking heuristic. Two multiple objective linear programming (MOLP) solution approaches, the SIMOLP method of Reeves and Franz [39] and the interactive weighted Tchebycheff procedure of Steuer and Choo [49], are recommended optimization strategies to be used independently or in concert. Computational experience suggests that the proposed framework is an effective decision-making tool. The procedure quickly located excellent compromise solutions in a series of test problems with hypothetical decision makers. In addition, human decision makers gave positive evaluations of the procedure and the production plans the procedure provided for a resource allocation case problem.     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

Data and Model Management in a Generalized MCDM-DSS*

Drawing upon the choice models developed in the multiple criteria decision making (MCDM) area, this paper proposes an architecture for designing an intelligent decision support system (DSS) that is intended to aid in making choices among multiple alternatives along multiple dimensions. It argues that effective support can be provided to the decision maker when the knowledge-based DSS is capable of dynamically selecting choice models appropriate to the domain and context of a particular problem being specified by the decision maker, and of properly applying them to the problem solution. Development of a prototype intended to partially represent application of the architecture is described. The paper concludes with suggestions for research extensions.     

A Dominance-Based Rough Set Approach for an Enhanced Assessment of Seasonal Influenza Risk

Accounting for about 290,000–650,000 deaths across the globe, seasonal influenza is estimated by the World Health Organization to be a major cause of mortality. Hence, there is a need for a reliable and robust epidemiological surveillance decision-making system to understand and combat this epidemic disease. In a previous study, the authors proposed a decision support system to fight against seasonal influenza. This system is composed of three subsystems: (i) modeling and simulation, (ii) data warehousing, and (iii) analysis. The analysis subsystem relies on spatial online analytical processing (S-OLAP) technology. Although the S-OLAP technology is useful in analyzing multidimensional spatial data sets, it cannot take into account the inherent multicriteria nature of seasonal influenza risk assessment by itself. Therefore, the objective of this article is to extend the existing decision support system by adding advanced multicriteria analysis capabilities for enhanced seasonal influenza risk assessment and monitoring. Bearing in mind the characteristics of the decision problem considered in this article, a well-known multicriteria classification method, the dominance-based rough set approach (DRSA), was selected to boost the existing decision support system. Combining the S-OLAP technology and the multicriteria classification method DRSA in the same decision support system will largely improve and extend the scope of analysis capabilities. The extended decision support system has been validated by its application to assess seasonal influenza risk in the northwest region of Algeria.     

多目标决策的β-较重最优解

对目标带有权重的多目标决策问题,从“锥有效性”的意义上提出一类β-较重最优解,并对有限方案情形给出了求解方法。     

Scenario Discovery with Multiple Criteria: An Evaluation of the Robust Decision‐Making Framework for Climate Change Adaptation

There is increasing concern over deep uncertainty in the risk analysis field as probabilistic models of uncertainty cannot always be confidently determined or agreed upon for many of our most pressing contemporary risk challenges. This is particularly true in the climate change adaptation field, and has prompted the development of a number of frameworks aiming to characterize system vulnerabilities and identify robust alternatives. One such methodology is robust decision making (RDM), which uses simulation models to assess how strategies perform over many plausible conditions and then identifies and characterizes those where the strategy fails in a process termed scenario discovery. While many of the problems to which RDM has been applied are characterized by multiple objectives, research to date has provided little insight into how treatment of multiple criteria impacts the failure scenarios identified. In this research, we compare different methods for incorporating multiple objectives into the scenario discovery process to evaluate how they impact the resulting failure scenarios. We use the Lake Tana basin in Ethiopia as a case study, where climatic and environmental uncertainties could impact multiple planned water infrastructure projects, and find that failure scenarios may vary depending on the method used to aggregate multiple criteria. Common methods used to convert multiple attributes into a single utility score can obscure connections between failure scenarios and system performance, limiting the information provided to support decision making. Applying scenario discovery over each performance metric separately provides more nuanced information regarding the relative sensitivity of the objectives to different uncertain parameters, leading to clearer insights on measures that could be taken to improve system robustness and areas where additional research might prove useful.     

Decisional Conflict and User Acceptance of Multicriteria Decision-Making Aids*

Despite the development of increasingly sophisticated and refined multicriteria decision-making (MCDM) methods, an examination of the experimental evidence indicates that users most often prefer relatively unsophisticated methods. In this paper, we synthesize theories and empirical findings from the psychology of judgment and choice to provide a new theoretical explanation for such user preferences. Our argument centers on the assertion that the MCDM method preferred by decision makers is a function of the degree to which the method tends to introduce decisional conflict. The model we develop relates response mode, decision strategy, and the salience of decisional conflict to user preferences among decision aids. We then show that the model is consistent with empirical results in MCDM studies. Next, the role of decisional conflict in problem formulation aids is briefly discussed. Finally, we outline future research needed to thoroughly test the theoretical mechanisms we have proposed.     

On multi-criteria chance-constrained capacitated single-source discrete facility location problems

This work aims at investigating multi-criteria modeling frameworks for discrete stochastic facility location problems with single sourcing. We assume that demand is stochastic and also that a service level is imposed. This situation is modeled using a set of probabilistic constraints. We also consider a minimum throughput at the facilities to justify opening them. We investigate two paradigms in terms of multi-criteria optimization: vectorial optimization and goal programming. Additionally, we discuss the joint use of objective functions that are relevant in the context of some humanitarian logistics problems. We apply the general modeling frameworks proposed to the so-called stochastic shelter site location problem. This is a problem emerging in the context of preventive disaster management. We test the models proposed using two real benchmark data sets. The results show that considering uncertainty and multiple objectives in the type of facility location problems investigated leads to solutions that may better support decision making.     

Robust,multi-objective optimization for the military medical evacuation location-allocation problem

Determining where to locate mobile aeromedical staging facilities (MASFs) as well as identifying how many aeromedical helicopters to allocate to each MASF, commonly referred to as the medical evacuation (MEDEVAC) location-allocation problem, is vital to the success of a deployed MEDEVAC system. Within this research, we develop an integer mathematical programming formulation to determine the location and allocation of MEDEVAC assets over the phases of a military deployment to support operations ranging from peacekeeping through combat to post-combat resolution. Our model seeks to address the multi-objective problem of maximizing the expected demand coverage as a measure of solution effectiveness, minimizing the maximum number of located MASFs in any deployment phase as a measure of solution efficiency, and minimizing the total number of MASF relocations throughout the deployment as a measure of solution robustness. This research makes two contributions. First, it formulates a representative mathematical programming formulation and identifies an accompanying solution methodology (i.e., the ε-constraint Method) to assess and recommend improvements to deployed military MEDEVAC systems designed to provide large-scale emergency medical response for contingency operations that range in casualty-inducing intensity (i.e., demand) over the phases of a deployment. Second, the research illustrates the application of the model for a realistic, synthetically generated medical planning scenario in southern Azerbaijan. Comparisons are made between the model’s (multi-phase) optimal solution and the phase-specific optimal solutions that disregard concerns of transitions between phases. The results highlight the conflicting nature between the objectives and illustrate the trade-offs between objectives as restrictions applied to the second and third objectives are respectively tightened or relaxed.     

An Integrated Framework for Environmental Multi‐Impact Spatial Risk Analysis

Quantitative risk analysis is being extensively employed to support policymakers and provides a strong conceptual framework for evaluating decision alternatives under uncertainty. Many problems involving environmental risks are, however, of a spatial nature, i.e., containing spatial impacts, spatial vulnerabilities, and spatial risk‐mitigation alternatives. Recent developments in multicriteria spatial analysis have enabled the assessment and aggregation of multiple impacts, supporting policymakers in spatial evaluation problems. However, recent attempts to conduct spatial multicriteria risk analysis have generally been weakly conceptualized, without adequate roots in quantitative risk analysis. Moreover, assessments of spatial risk often neglect the multidimensional nature of spatial impacts (e.g., social, economic, human) that are typically occurring in such decision problems. The aim of this article is therefore to suggest a conceptual quantitative framework for environmental multicriteria spatial risk analysis based on expected multi‐attribute utility theory. The framework proposes: (i) the formal assessment of multiple spatial impacts; (ii) the aggregation of these multiple spatial impacts; (iii) the assessment of spatial vulnerabilities and probabilities of occurrence of adverse events; (iv) the computation of spatial risks; (v) the assessment of spatial risk mitigation alternatives; and (vi) the design and comparison of spatial risk mitigation alternatives (e.g., reductions of vulnerabilities and/or impacts). We illustrate the use of the framework in practice with a case study based on a flood‐prone area in northern Italy.     

Single machine scheduling: A comparison of two solution procedures

Recent research on the single machine scheduling problem has focused on the treatment of multiple scheduling objectives. Most works have used some combination of mean flowtime, maximum tardiness, or total tardiness as scheduling criteria. Previous research has largely ignored earliness as a scheduling criterion. This paper presents a model that employs the criteria of flowtime as a measure of work-in-process (WIP) inventory and total job earliness to represent finished goods inventory. Total tardiness is used to represent customer satisfaction. The three criteria are used to form a single, weighted-sum objective function for guiding the choice of the best processing sequence. Two procedures are presented that might be used to solve this problem. The first is an enumeration scheme using bounding and dominance criteria that have been developed to aid efficient solution, and the second is a mixed integer linear programming (LP) formulation. Computational experience with the two models is also presented.     

A review on airport gate assignment problems: Single versus multi objective approaches

Assigning aircraft to gates is an important decision problem that airport professionals face every day. The solution of this problem has raised a significant research effort and many variants of this problem have been studied. In this paper, we review past work with a focus on identifying types of formulations, classifying objectives, and categorising solution methods. The review indicates that there is no standard formulation, that passenger oriented objectives are most common, and that more recent work are multi-objective. In terms of solution methods, heuristic and metaheuristic approaches are dominant which provides an opportunity to develop exact and approximate approaches both for the single and multi-objective problems.