As simple as possible but not simpler in Multiple Criteria Decision Aiding: the robust-stochastic level dependent Choquet integral approach

The level dependent Choquet integral has been proposed to handle decision making problems in which the importance and the interaction of criteria may depend on the level of the alternatives’ evaluations. This integral is based on a level dependent capacity, which is a family of single capacities associated to each level of evaluation for the considered criteria. We present two possible formulations of the level dependent capacity where importance and interaction of criteria are constant inside each one of the subintervals in which the interval of evaluations for considered criteria is split or vary with continuity inside the whole interval of evaluations. Since, in general, there is not only one but many level dependent capacities compatible with the preference information provided by the Decision Maker, we propose to take into account all of them by using the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). On one hand, ROR defines a necessary preference relation (if an alternative a is at least as good as an alternative b for all compatible level dependent capacities), and a possible preference relation (if a is at least as good as b for at least one compatible level dependent capacity). On the other hand, considering a random sampling of compatible level dependent capacities, SMAA gives the probability that each alternative reaches a certain ranking position as well as the probability that an alternative is preferred to another. A real-world decision problem on rankings of universities is provided to illustrate the proposed methodology.     

Numerical methods for determine the equilibrium point's stability of multidimensional nonlinear dynamic system

This work is concerned with the use of new nunumerical methods to establish some new criteria to determine the equilibrium point's stability of a multidimensional nonlinear dynamic system. Copyright © 2010 John Wiley & Sons, Ltd.     

Ship routing and scheduling in the new millennium

We review research on ship routing and scheduling and related problems during the new millennium and provide four basic models in this domain. The volume of research in this area about doubles every decade as does the number of research outlets. We have found over a hundred new refereed papers on this topic during the last decade. Problems of wider scope have been addressed as well as more specialized ones. However, complex critical problems remain wide open and provide challenging opportunities for future research.     

Coping with inefficiencies in a New Economic Geography model: The unintended consequences of policy interventions

This article introduces a social planner version of a central microfounded New Economic Geography model for explicitly answering whether the symmetric equilibrium of the decentralized market economy is socially desirable. We find that savings incentives are too weak, resulting in an inefficiently low capital stock and therefore an inadequate number of product varieties. We derive the appropriate subsidy and taxation scheme to remedy these distortions. Interestingly, implementing the associated policies crucially impacts on the stability of the symmetric equilibrium and has the potential to result in unintended agglomeration processes.     

Analysis of the M/G/1 queue with exponentially working vacations—a matrix analytic approach

In this paper, an M/G/1 queue with exponentially working vacations is analyzed. This queueing system is modeled as a two-dimensional embedded Markov chain which has an M/G/1-type transition probability matrix. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. Then, based on the classical vacation decomposition in the M/G/1 queue, we derive a conditional stochastic decomposition result. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by analyzing the semi-Markov process. Furthermore, we provide the stationary waiting time and busy period analysis. Finally, several special cases and numerical examples are presented.     

Multi-variable grey model based on dynamic background algorithm for forecasting the interval sequence

The multi-variable grey model based on dynamic background algorithm improves the forecasting performance of the multi-variable grey model on the precise number sequence. In order to make this model suitable for the interval sequence, the matrix form of the multi-variable grey model based on dynamic background algorithm is proposed in the paper. In the modeling process, the interval is treated as a two-dimensional column vector, the parameters of the multi-variable grey model are replaced by matrices, and the dynamic background algorithm for interval sequences is proposed. The analysis results of the matrix algorithm for the dynamic background value and the prediction formula show that the new model is essentially a way to predict one of the two bounds of an interval by combining them, reflecting the integrity and interaction between the lower and upper bounds. The interval predictions of industrial electricity consumption of Zhejiang Province, China national electricity consumption and consumer price index show that the new model can well predict the minimum and maximum values of the interval sequence and has better prediction performance compared with the method of predicting each boundary sequence separately.     

Pricing and equity in cross-regional green supply chains

This paper addresses the problem of the firms operating on cross-border or inter-regional platforms that are subject to the enforcement of each local government's carbon emissions regulatory policy, thus causing an imbalance in the sharing of the burden of the greening of the total supply chain. We introduce the concept of equity as the incentive mechanism to coordinate this green supply chain which is a function of the carbon emission permits and the revenue generated by the firms. Due to the complexity and imbalance in the original incentive mechanism to this problem, we provide a new equivalent supply chain network equilibrium model under elastic demand based on user equilibrium theory. We state the user equilibrium conditions and provide the equivalent formulation. We show the trade-offs under various carbon emissions regulatory policies. A product with higher price elasticity and carbon emission intensity not only hampers the firm from gaining a higher revenue, but it also reduces the equity of the system under an invariant emission regulatory policy.     

Non-zero-sum stochastic differential reinsurance and investment games with default risk

This paper investigates the implications of strategic interaction (i.e., competition) between two CARA insurers on their reinsurance-investment policies. The two insurers are concerned about their terminal wealth and the relative performance measured by the difference in their terminal wealth. The problem of finding optimal policies for both insurers is modelled as a non-zero-sum stochastic differential game. The reinsurance premium is calculated using the variance premium principle and the insurers can invest in a risk-free asset, a risky asset with Heston’s stochastic volatility and a defaultable corporate bond. We derive the Nash equilibrium reinsurance policy and investment policy explicitly for the game and prove the corresponding verification theorem. The equilibrium strategy indicates that the best response of each insurer to the competition is to mimic the strategy of its opponent. Consequently, either the reinsurance strategy or the investment strategy of an insurer with the relative performance concern is riskier than that without the concern. Numerical examples are provided to demonstrate the findings of this study.     

Family of numerical methods based on non-polynomial splines for solution of contact problems

In this paper a new technique based on quartic non-polynomial spline functions connecting spline functions values at mid knots and their corresponding values of the fourth-order derivatives is developed. This approach leads to a family of numerical methods for computing approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is shown that the present family of methods gives better approximations. Existing second and fourth-order finite-difference and spline functions based methods developed at mid knots become special cases of the new approach. Numerical examples are given to illustrate applicability and efficiency of the new methods.