Multiobjective simulation-based methodologies for medical decision making.

A variety of methodologies have been employed for decision making related to the treatment of diseases/injury. Decision trees are a functional way in which to examine problems under uncertainty by providing a method to analyze decisions under risk (Detsky, 1996, 97). However, conventional decision trees do not completely represent the real world since they cannot investigate problems that are cyclic in nature (Jaafari, 2003). The stochastic tree that developed Hazen during 1992-to-1996 is one of the most relevant methods and techniques related to decision analyses that append more incorporation for medical intervention related to recurring diseases/injuries. The approach combines features of continuous-time Markov chains with those of decision trees and that enable time to be modeled as a range where health state transitions can occur at any instant (Hazen 1992-to-96). It can also accommodate patients\u27 preferences regarding risk and quality of life. In this research we enhance Hazen\u27s stochastic tree by developing an analytical model, and we extend its capabilities more by developing multi-objective simulation based methodologists for medical decision making. First, with our enhancement on the Hazen\u27s stochastic tree, the model is improved by utilizing the Weibull Accelerated Failure Time model. This new technique will fill the gap between the experimental circumstances and the corresponding circumstances or conditions of standard/current treatment. Second, as simulation can be a final alternative for problems that are mathematically intractable for other techniques (Banks 1996), our multi-objective simulation based model for medical decision making extends the capabilities of Hazen stochastic tree. It adds more flexibility with the use of survival distributions for health states sojourn, and combines two sound theories: multi attribute utility (MAU) theory, and Ranking-Selection procedures. Indeed, our simulation model (considering patient\u27s profile/preferences and health states survival/quality/cost, QALY) presents an investigation of the use of simulation on the stochastic tree, with associated techniques related to ranking and selection, and multi-objectives decision analysis

Models, Theoretical Properties, and Solution Approaches for Stochastic Programming with Endogenous Uncertainty

In a typical optimization problem, uncertainty does not depend on the decisions being made in the optimization routine. But, in many application areas, decisions affect underlying uncertainty (endogenous uncertainty), either altering the probability distributions or the timing at which the uncertainty is resolved. Stochastic programming is a widely used method in optimization under uncertainty. Though plenty of research exists on stochastic programming where decisions affect the timing at which uncertainty is resolved, much less work has been done on stochastic programming where decisions alter probability distributions of uncertain parameters. Therefore, we propose methodologies for the latter category of optimization under endogenous uncertainty and demonstrate their benefits in some application areas. First, we develop a data-driven stochastic program (integrates a supervised machine learning algorithm to estimate probability distributions of uncertain parameters) for a wildfire risk reduction problem, where resource allocation decisions probabilistically affect uncertain human behavior. The nonconvex model is linearized using a reformulation approach. To solve a realistic-sized problem, we introduce a simulation program to efficiently compute the recourse objective value for a large number of scenarios. We present managerial insights derived from the results obtained based on Santa Fe National Forest data. Second, we develop a data-driven stochastic program with both endogenous and exogenous uncertainties with an application to combined infrastructure protection and network design problem. In the proposed model, some first-stage decision variables affect probability distributions, whereas others do not. We propose an exact reformulation for linearizing the nonconvex model and provide a theoretical justification of it. We designed an accelerated L-shaped decomposition algorithm to solve the linearized model. Results obtained using transportation networks created based on the southeastern U.S. provide several key insights for practitioners in using this proposed methodology. Finally, we study submodular optimization under endogenous uncertainty with an application to complex system reliability. Specifically, we prove that our stochastic program\u27s reliability maximization objective function is submodular under some probability distributions commonly used in reliability literature. Utilizing the submodularity, we implement a continuous approximation algorithm capable of solving large-scale problems. We conduct a case study demonstrating the computational efficiency of the algorithm and providing insights

Fuzzy Linear Programming in DSS for Energy System Planning

Energy system planning requires the use of planning tools. The mathematical models of real-world energy systems are usually multiperiod linear optimization programs. In these models, the objective function describes the total discounted costs of covering the demand for final energy or energy services. The demand for various forms of energy or energy services is the driving force of the models. By using such linear programming (LP) formulations, decision makers can elaborate suitable strategies for solving their planning problems, such as the development of emission reduction strategies. Uncertainties that affect the process of energy system planning can be divided into parameter and decision uncertainties. Data or parameter uncertainties can be addressed either by stochastic optimization or by the methodology of fuzzy linear programming (FLP). In addition, FLP allows explicit incorporation of decision uncertainties into a mathematical model. This paper therefore aims at evaluating the methodology of FLP with respect to the support that it offers the decision-making process in energy system planning under uncertainty. Employing the parallels between multi-objective linear programming (MOLP) and FLP, problems of FLP in decision support system applications are pointed out and solutions are offered. The proposed modifications are based on the methodology of aspiration-reservation based decision support and still enable modeling of uncertainties in a fuzzy sense. A case study is documented to show the application of the modified FLP approach

A mathematical model for allocating project managers to projects

In multi-project environments, the decision of which project manager to allocate to which project directly affects organizational performance and therefore, it needs to be taken in a fair, robust and consistent manner. We argue that such a manner can be facilitated by a mathematical model that brings together all the relevant factors in an effective way. Content and thematic analyses of extant literature on optimization modelling were conducted to identify the major issues related to formulating a relevant mathematical model. A total of 200 articles covering the period 1959 to 2015 were reviewed. A deterministic integer programming model was formulated and implemented in OpenSolver. The utility of the model was demonstrated with an illustrative example to optimize the allocation of six project managers to six projects. The results indicate that the model is capable of making optimal allocations in less than one second, with a solution precision of 99%. These results compare well with some intuitive verification checks on certain expectations. For example, the most competent project manager was allocated to the highest priority project while the least competent project manager was allocated to the lowest priority project. Through this study, we have proposed a comprehensive and balanced approach by incorporating both hard and soft issues in our mathematical modelling, to address gaps in existing project manager-to-project (PM2P) allocation models as well as extending applications of mathematical modelling of the PM2P allocation problem to a “new” country and industry, with a view to complement managerial intuition. In an attempt to address gaps in existing mathematical models associated with challenges related to acceptance by industry practitioners, future work includes developing a graphical user interface to separate the model base and optimization software details from users, as part of a complete product to be validated as an industry application

The SIMRAND methodology: Theory and application for the simulation of research and development projects

A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions

A General Overview of Multi-objective Multiple-participant Decision Making for Flood Management

Decision-making problems in water resources are often associated with multiple objectives and multiple stakeholders. To enable more effective and acceptable decision outcome, it is required that more participation is ensured in the decision making process. This is particularly relevant for flood management problems where the number of stakeholders could be very large. Although application of multi-objective decision-making tools in water resources is very wide, application with the consideration of multiple stakeholders is much more limited. The solution methodologies adapted for multi-objective multi-participant decision problems are generally based on aggregation of decisions obtained for individual decision makers. This approach seems somewhat inadequate when the number of stakeholders is very large, as often is the case in flood management. The present study has been performed to have an overview of existing solution methodologies for multi-objective decision making approaches in water resources. Decision making by single and multiple stakeholders has been considered under both deterministic and uncertain conditions. It has been found that the use of fuzzy set theory to represent various uncertainties associated with decision making situations under multi-objective multiple-participant environment is very promising. Coupled with multi-objective methods (e. g. compromise programming and goal programming), fuzzy approach has also the ability to support group decisions, to reflect collective opinions and conflicting judgments.https://ir.lib.uwo.ca/wrrr/1003/thumbnail.jp

A Methodological Guide to Multiobjective Optimization

During the last few years, multiobjective optimization has received growing attention: the number of publications related to this subject between 1974 and 1979 exceeds 120. There are many approaches, techniques and tools related to multiobjective decision-making and optimization; however, not all approaches are equally developed, and the resulting tools are often applied because of certain traditions rather than their suitability for solving a given problem. Therefore, this paper is devoted to a comparative evaluation of various approaches and tools. This evaluation is based, however, first on a classification of problems of multiobjective decision making and optimization. Thereafter, the available approaches, methods, techniques and tools are shortly presented and evaluated in terms of suitability for various classes of problems. The final part of the paper presents a broader description of a relatively new approach based on reference objective levels, not fully developed yet but applicable in many classes of problems. A new notion of extended threshold utility functions, other basic theoretical results, applicational examples and directions of further research related to this approach are presented

Conflicting Objectives in Decisions

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem

On-Farm Costos of Reducing environmental degradation under risk

Farmers respond to environmental regulations by adjusting production practices so as to comply while minimizing their loss in expected income. Ultimately the cost of agro environmental regulation is determined by farm level adjust¬ments. Our farm level simulation framework assesses economic and environmental impacts of hypothetical pesticide restrictions in the context of continuing soil conservation efforts.