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A Consumption and Investment Problem via a Markov Decision Processes Approach with Random Horizon
This work is devoted to a consumption and investment problem, in which there is an investor with certain initial wealth with the possibility of deciding how much of such wealth will be consumed and how much will be invested in each of a series of successive times. The key issue is to find a wealth assignation rule in order to maximize the performance criteria; such dilemma will be achieved by the dynamic programming technique for the Markov decision processes with random horizon.
Multiobjective Green Time-Dependent Location-Routing Problem and Algorithms
To reduce the logistic cost and carbon emission and improve customer satisfaction, this study proposes a multiobjective green time-dependent location routing problem (MOGTDLRP) model in which the objectives are to minimize the distribution total cost, delivery time, and fuel consumption. This model will be solved by several hyperheuristic algorithms which include the high-level heuristics and the low-level heuristics. There are three acceptance criterions for the solution: improving and equal, all moves and accept all solutions, and dynamic acceptance criteria. Through the case, the performance of the algorithm and the influence of various factors on the solution are analyzed in this study. The experimental results show that the proposed model can effectively reduce logistic costs, carbon emissions, and vehicle travel time.
Development of a Bounded Two-Stage Data Envelopment Analysis Model in the Intuitionistic Fuzzy Environment
Data Envelopment Analysis is a powerful tool for evaluating the efficiency of decision-making units for the purpose of ranking, comparing, and differentiating efficient and inefficient units. Classical Data Envelopment Analysis methods operate by measuring the efficiency of each DMU compared to similar units without considering their internal workings and structures, which make them unsuitable for cases where DMUs are multistaged processes with intermediate products or when inputs and outputs are ambiguous or nonconfigurable. In problems that involve uncertainty, intuitionistic fuzzy sets can offer a better representation and interpretation of information than classic sets. In this paper, the noncooperative network data envelopment analysis model of Liang et al. (2008), which is based on Stackelberg game theory and efficiency decomposition, is expanded using the concepts of best and worst relative returns Data Envelopment Analysis model of Azizi et al. (2013) into an interval efficiency estimation model with α-β cuts for two-stage DMUs with trapezoidal intuitionistic fuzzy data. Furthermore, the method of Yue (2011) is used to rank these DMUs in terms of their intuitionistic fuzzy interval efficiency. A numerical example is also provided to illustrate the application of the proposed bounded two-stage intuitionistic Data Envelopment Analysis model.
Optimal HARA Investments with Terminal VaR Constraints
This paper studies the impact of Value at Risk (VaR) constraints on investors with hyperbolic absolute risk aversion (HARA) risk preferences. We derive closed-form representations for the “triplet”: optimal investment, terminal wealth, and value function, via extending the Bellman-based methodology from constant relative risk aversion (CRRA) utilities to HARA utilities. In the numerical part, we compare our solution (HARA-VaR) to three critical embedded cases, namely, CRRA, CRRA-VaR, and HARA, assessing the influence of key parameters like the VaR probability and floor on the optimal wealth distribution and allocations. The comparison highlights a stronger impact of VaR on a CRRA-VaR investor compared to a HARA-VaR (HV). This is in terms of not only lower Sharpe ratios but also higher tail risk and lower returns on wealth. The HV analysis demonstrates that combining both, capital guarantee and VaR, may lead to a correction of the partially adverse effects of the VaR constraint on the risk appetite. Moreover, the HV portfolio strategy also does not show the high kurtosis observed for the PV strategy. A wealth-equivalent loss (WEL) analysis is also implemented demonstrating that, for a HV investor, losses would be more serious if adopting a CRRA-VaR strategy as compared to a HARA strategy.
Decision-Making Methods in the Public Sector during 2010–2020: A Systematic Review
The aim of this article is to analyze the scientific developments in public sector decision making during the period 2010–2020, to identify which decision-making methods are preferred in different sectors of the public sector, and to determine which integrated methods are applied in this sector. In total, 468 scholarly articles were selected covering a near comprehensive review of the literature, as described below in the search process. We found that 271studies utilized a single method, whereas 180 studies utilized integrated methods. Data envelopment analysis (DEA) was the most common, used by 97 studies. However, an analytic hierarchy process (AHP) was utilized by 178 studies when counting both simple and integrated methods. It was shown that single methods were more commonly used in education, environment, health, and public services, and integrated methods were relatively favored in economics/finance, energy, site selection, and waste management. We conclude that multiple decision-making methods are used in the public sector, and during2010–2020, there has been a tendency to use unified methods in decision-making processes.
Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations
Achieving a high-resolution approximation and hitting the Pareto optimal set with some if not all members of the population is the goal for multi- and many-objective optimization problems, and more so in real-world applications where there is also the desire to extract knowledge about the problem from this set. The task requires not only to reach the Pareto optimal set but also to be able to continue discovering new solutions, even if the population is filled with them. Particularly in many-objective problems where the population may not be able to accommodate the full Pareto optimal set. In this work, our goal is to investigate some tools to understand the behavior of algorithms once they converge and how their population size and particularities of their selection mechanism aid or hinder their ability to keep finding optimal solutions. Through the use of features that look into the population composition during the search process, we will look into the algorithm’s behavior and dynamics and extract some insights. Features are defined in terms of dominance status, membership to the Pareto optimal set, recentness of discovery, and replacement of optimal solutions. Complementing the study with features, we also look at the approximation through the accumulated number of Pareto optimal solutions found and its relationship to a common metric, the hypervolume. To generate the data for analysis, the chosen problem is MNK-landscapes with settings that make it easy to converge, enumerable for instances with 3 to 6 objectives. Studied algorithms were selected from representative multi- and many-objective optimization approaches such as Pareto dominance, relaxation of Pareto dominance, indicator-based, and decomposition.