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We investigate whether smooth robust methods for forecasting can help mitigate pronounced and persistent failure across multiple forecast horizons. We demonstrate that naive predictors are interpretable as local estimators of the long-run relationship with the advantage of adapting quickly after a break, but at a cost of additional forecast error variance. Smoothing over naive estimates helps retain these advantages while reducing the costs, especially for longer forecast horizons. We derive the performance of these predictors after a location shift, and confirm the results using simulations. We apply smooth methods to forecasts of UK productivity and US 10-year Treasury yields and show that they can dramatically reduce persistent forecast failure exhibited by forecasts from macroeconomic models and professional forecasters.

This chapter suggests a robust Hausman and Taylor (1981), hereafter HT, estimator that deals with the possible presence of outliers. This entails two modifications of the classical HT estimator. The first modification uses the Bramati and Croux (2007) robust Within MS estimator instead of the Within estimator in the first stage of the HT estimator. The second modification uses the robust Wagenvoort and Waldmann (2002) two-stage generalized MS estimator instead of the 2SLS estimator in the second step of the HT estimator. Monte Carlo simulations show that, in the presence of vertical outliers or bad leverage points, the robust HT estimator yields large gains in MSE as compared to its classical Hausman–Taylor counterpart. We illustrate this robust version of the HT estimator using an empirical application.

Uncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors.

This research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model.

In this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities.

This study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

The purpose of this paper is to introduce robust optimization approaches to balance mixed model assembly lines with uncertain task times and daily model mix changes.

Scenario planning approach is used to represent the input data uncertainty in the decision model. Two kinds of robust criteria are provided: one is min‐max related; and the other is α‐worst scenario based. Corresponding optimization models are formulated, respectively. A genetic algorithm‐based robust optimization framework is designed. Comprehensive computational experiments are done to study the effect of these robust approaches.

With min‐max related robust criteria, the solutions can provide an optimal worst‐case hedge against uncertainties without a significant sacrifice in the long‐run performance; α‐worst scenario‐based criteria can generate flexible robust solutions: through rationally tuning the value of α, the decision maker can obtain a balance between robustness and conservatism of an assembly line task elements assignment.

This paper is an attempt to robust mixed model assembly line balancing. Some more efficient and effective robust approaches – including robust criteria and optimization algorithms – may be designed in the future.

In an assembly line with significant uncertainty, the robust approaches proposed in this paper can hedge against the risk of poor system performance in bad scenarios.

Using robust optimization approaches to balance mixed model assembly line.

This study aims to design a proper supply chain network for the vaccine industry in Iran, which considers several features such as uncertainties in demands and cost, perishability of vaccines, wastages in storage, limited capacity and different priorities for demands.

This study presents a mixed-integer linear programming (MILP) model and using a robust counterpart approach for coping with uncertainties of model.

The presented robust model in comparison with the deterministic model has a better performance and is more reliable for network design of vaccine supply chain.

This study considers uncertainty in the network design of vaccine supply chain for the first time in the vaccine context It presents an MILP model where strategic decisions for each echelon and tactical decisions among different echelons of supply chain are determined. Further, it models the difference between high- and low-priority demands for vaccine.

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

The principal concern of organization managers in the global rivalry of commerce environment is how to select the project portfolio among available projects. In this matter, organizations should consider the uncertainty intrinsic in the projects regarding an appropriate valuation technique within an optimization framework. In this research, the purpose of this paper is to formulate using a robust optimization algorithm to deal with the complexities and uncertainty inherent in the construction of the project portfolio.

First, a general mathematical formulation is presented, which in compound real options valuation is highlighted. This formulation gives managerial flexibility by correcting the deficiency of traditional discounted cash flow technique that excludes any form of flexibility. Then, considering a limitation on budget of the organization, an integer programming formulation to maximize the n-fold compound options for project portfolio selection is proposed. Finally, a robust optimization model is developed along with the robust combinatorial optimization algorithm, which is effective for solving problems under uncertainty.

Sensitivity analysis showed that projects in later phases of development, having survived several phases of pre-clinical and clinical tests, are worth more because they are more likely to pertain to business. However, the investment costs related to each project during development phases limit the number of projects that a company can bring to their final portfolio. Additionally, the analysis of conservatism level represented how project managers can quite easily determine their risk attitude and the corresponding portfolio composition. From a managerial point of view, the proposed framework is very useful because it requires only financial estimates. Hence, the proposed decision support tool can assist research and development (R&D) project managers in the pharmaceutical industry for making decisions.

The first is the application of the n-fold compound options on portfolio of R&D projects and the employment of compound options value of a project portfolio as an objective function. The second one is a mathematical formulation of these concepts and solving it by the robust combinatorial optimization algorithm. The literature is lacking in the application of the robust combinatorial optimization algorithm to R&D project portfolio selection based on the generalized n-fold compound option model of Cassimon et al. (2004). Every framework from calculation of the n-fold compound option to solving robust combinatorial algorithm is programmed in Matlab software, since it can be used as a business support tool.

The purpose of this paper is to develop a mathematical model for the design of robust layout for unequal area-dynamic facility layout problem with flexible bay structure (UA-DFLP with FBS) and test the suitability of generated robust layout in a dynamic environment.

This research adopts formulation of a mathematical model for generating a single layout for unequal area facility layout problems with flexible bay structure under dynamic environment. The formulated model for the robust layout formation is solved by developing a simulated annealing algorithm. The proposed robust approach model for UA-DFLP with FBS is validated by conducting numerical experiments on standard UA-DFLPs reported in the literature. The suitability of the generated robust layout in a dynamic environment is tested with total penalty cost criteria.

The proposed model has given a better solution for some UA-DFLPs with FBS in comparison with the adaptive approach’s solution reported in the literature. The total penalty cost is within the specified limit given in the literature, for most of the layouts generated for UA-DFLPs with FBS. In the proposed model, there is no rearrangement of facilities in various periods of planning horizon and thus no disruptions in operations.

The present work has limitations that when the area and aspect ratio of the facilities are required to change from one period to another, then it is not possible to make application of the robust approach-based formulation to the dynamic environment facility layout problems.

Rearrangement of facilities in adaptive approach disrupts the operations whereas in the proposed approach no disruption of production. The FBS approach is more suitable for layout planning where proper aisle structure is required. The solution of the proposed approach helps to create a proper aisle structure in the detailed layout plan. Thus, easy interaction of the material handling equipment, men and materials is possible.

This paper proposes a mathematical formulation for the design of robust layout for UA-FLPs with FBS in a dynamic environment and an efficient simulated annealing algorithm as its solution procedure. The proposed robust approach generates a single layout for the entire planning horizon. This approach is more useful for facilities which are difficult/sensitive to relocate in various periods of the planning horizon.

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of electromagnetic problems which may be sensitive to parameter variations. The purpose of this paper is to propose a robust objective function for topological design problems.

In this paper, a robust objective function for topology optimization is defined on an uncertainty set using the worst case analysis. The robustness of a topological design is defined as the worst response due to the variations of the location of the topology change. The approach is based on the definition of a topological gradient.

The robust topology optimization (RTO) was applied to eddy current crack reconstruction problems. The numerical applications showed that this method can provide more reliable results for the reconstruction in the presence of significant noise in the measured signal.

The RTO may be applied to some more complicated design problems; however large computational costs may result.

This paper has defined a robustness metric for topology design and a robust design model is proposed for topology optimization problems.