Robust Multi-Objective Sustainable Reverse Supply Chain Planning: An Application in the Steel Industry

In the design of the supply chain, the use of the returned products and their recycling in the production and consumption network is called reverse logistics. The proposed model aims to optimize the flow of materials in the supply chain network (SCN), and determine the amount and location of facilities and the planning of transportation in conditions of demand uncertainty. Thus, maximizing the total profit of operation, minimizing adverse environmental effects, and maximizing customer and supplier service levels have been considered as the main objectives. Accordingly, finding symmetry (balance) among the profit of operation, the environmental effects and customer and supplier service levels is considered in this research. To deal with the uncertainty of the model, scenario-based robust planning is employed alongside a meta-heuristic algorithm (NSGA-II) to solve the model with actual data from a case study of the steel industry in Iran. The results obtained from the model, solving and validating, compared with actual data indicated that the model could optimize the objectives seamlessly and determine the amount and location of the necessary facilities for the steel industry more appropriately.This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problem

Inequality and Uncertainty: Theory and Legal Applications

Welfarism is the principle that social policy should be based solely on individual well-being, with no reference to \u27fairness or rights. The propriety of this approach has recently been the subject of extensive debate within legal scholarship. Rather than contributing (directly) to this debate, we identify and analyze a problem within welfarism that has received far too little attentioncall this the ex ante/ex post problem. The problem arises from the combination of uncertainty-an inevitable feature of real policy choice-and a social preference for equality. If the policymaker is not a utilitarian, but rather has a social welfare function that is equity regarding to some degree, then she faces a critical choice. Should she care about the equalization of expected well-being (the ex ante approach), or should she care about the expected equalization of actual well-being (the ex post approach)? Should she focus on the equality of prospects or the prospects for equality? In this Article, we bring the ex ante/ex post problem to the attention of legal academics, provide novel insight into when and why the problem arises, and highlight legal applications where the problem figures prominently. We ultimately conclude that welfarism requires an ex post approach. This is a counterintuitive conclusion, because the ex post approach can conflict with ex ante Pareto superiority. Indeed, this Article demonstrates that the ex post application of every equity-regarding social welfare function-whatever its particular form-must conflict with ex ante Pareto superiority in specific situations. Among other things, then, this Article shows that legal academics who care about equity must abandon either their commitment to welfarism or their commitment to ex ante Pareto superiorit

Robust Mission Design Through Evidence Theory and Multi-Agent Collaborative Search

In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are modelled through evidence theory and the belief, or credibility, in the successful achievement of mission goals is maximised along with the reliability of constraint satisfaction. The multiobjective optimisation problem is solved through a novel algorithm based on the collaboration of a population of agents in search for the set of highly reliable solutions. Two typical problems in mission analysis are used to illustrate the proposed methodology

Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, the lowest upper bound on costs). However, hedging against an unlikely worst case may lead to losses in other situations. In general, one is interested in policies that behave well in all situations which results in a multi-objective view on decision making. In this paper, we consider policies for the expected discounted reward measure of MDPs with uncertain parameters. In particular, the approach is defined for bounded-parameter MDPs (BMDPs) [8]. In this setting the worst, best and average case performances of a policy are analyzed simultaneously, which yields a multi-scenario multi-objective optimization problem. The paper presents and evaluates approaches to compute the pure Pareto optimal policies in the value vector space.Comment: 9 pages, 5 figures, preprint for VALUETOOLS 201

Well-Being, Inequality and Time: The Time-Slice Problem and its Policy Implications

Should equality be viewed from a lifetime or sublifetime perspective? In measuring the inequality of income, for example, should we measure the inequality of lifetime income or of annual income? In characterizing a tax as progressive or regressive, should we look to whether the annual tax burden increases with annual income, or instead to whether the lifetime tax burden increases with lifetime income? Should the overriding aim of anti-poverty programs be to reduce chronic poverty: being badly off for many years, because of low human capital or other long-run factors? Or is the moral claim of the impoverished person a function of her current state - meaning that someone who is badly nourished, badly housed, or in pain at present has a strong claim on our aid regardless of whether this is a chronic or transient state? Should we think of the aged as a suspect class, a low-well-being group? From the sublifetime perspective, the aged are indeed a kind of suspect class, because they tend to have low current incomes and health and to be socially isolated. But the aged have lived for many years and are therefore, as a matter of lifetime well-being, relatively rich compared to the rest of the population. This Article addresses the time-slice question. I use the framework of welfarism and the formal apparatus of social welfare functions to sharpen analysis. The first half of the Article argues for the lifetime perspective. The second half surveys the implications of that perspective for a host of legal and policy issues: the measurement of equality; the measurement of poverty; the design of redistributive taxes; the question whether non-tax instruments, such as environmental regulations or tort law, should also be used for redistribution; and how the suspect class framework and other distributively sensitive policy tools should be structured. Above all, the Article aims to raise the profile of a foundational question which has been insufficiently discussed - a question that anyone who cares about equality should grapple with