Aggregate–disaggregate approach to an airfreight forwarder’s planning under uncertainty: a case study

Resource planning of airfreight forwarders is a complex endeavor, requiring decisions to be made in a dynamic and uncertain environment. Airfreight forwarders acquire airfreight spaces from three sources: allotment from carriers, retail from carriers and subcontracting to partners, all of which differ in terms of cost, flexibility and timing of booking. This real-life problem has many planning decisions (bookings in terms of carriers, route, time, ULDs, etc.). In this case study, we propose an aggregate–disaggregate approach and focus on the most critical decisions. A two-stage stochastic dynamic program first determines, in aggregates, the amount of allotment bookings, retail resources, and subcontracting or surplus co-loading. Then, a heuristic is used to disaggregate resource requirements into specific bookings. An analysis is provided to examine the relevant managerial issues. Based on real-life data, we show several patterns of aggregate resource bookings with respect to different levels of demand uncertainty and cost parameters. We show that resource disaggregation has to balance cost-effectiveness, capacity flexibility and routing flexibility of a resource plan.     

Blow-up for Joseph–Egri equation: Theoretical approach and numerical analysis

This work develops the theory of the blow-up phenomena for Joseph–Egri equation. The existence of the nonextendable solution of two initial-boundary value problems (on a segment and a half-line) is demonstrated. Sufficient conditions of the finite-time blow-up of these solutions, as well as the analytical estimates of the blow-up time, are obtained. A numerical method that allows to precise the blow-up moment for specified initial data is proposed.     

On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli–Euler beam

The equilibrium and kinematic equations of an arbitrarily curved spatial Bernoulli–Euler beam are derived with respect to a parametric coordinate and compared with those of the Timoshenko beam. It is shown that the beam analogy follows from the fact that the left-hand side in all the four sets of beam equations are the covariant derivatives of unknown vector. Furthermore, an elegant primal form of the equilibrium equations is composed. No additional assumptions, besides those of the linear Bernoulli–Euler theory, are introduced, which makes the theory ideally suited for the analytical assessment of big-curvature beams. The curvature change is derived with respect to both convective and material/spatial coordinates, and some aspects of its definition are discussed. Additionally, the stiffness matrix of an arbitrarily curved spatial beam is calculated with the flexibility approach utilizing the relative coordinate system. The numerical analysis of the carefully selected set of examples proved that the present analytical formulation can deliver valid benchmark results for testing of the purely numeric methods.     

An inference–proof approach to privacy-preserving horizontally partitioned linear programs

Mangasarian (Optim. Lett., 6(3), 431–436, 2012) proposed a constraints transformation based approach to securely solving the horizontally partitioned linear programs among multiple entities—every entity holds its own private equality constraints. More recently, Li et al. (Optim. Lett., doi:10.1007/s11590-011-0403-2, 2012) extended the transformation approach to horizontally partitioned linear programs with inequality constraints. However, such transformation approach is not sufficiently secure – occasionally, the privately owned constraints are still under high risk of inference. In this paper, we present an inference–proof algorithm to enhance the security for privacy-preserving horizontally partitioned linear program with arbitrary number of equality and inequality constraints. Our approach reveals significantly less information than the prior work and resolves the potential inference attack.     

An information‐theoretic‐based (MaxEnt) approach to social dynamical systems

Jeffreys‐Jaynes’ Predictive Statistics appears to provide a promising approach for the study of general dynamical systems. We describe an application of such theory to the analysis of the dynamics of interacting social groups. For that purpose the said statistical theory is redirected towards the construction of an equivalent stochastic theory. The working of the formalism is illustrated by applying it to a simplified case of opinion forming in a two‐candidates election.     

Displacement structure approach to Cauchy and Cauchy–Vandermonde matrices: inversion formulas and fast algorithms

The confluent Cauchy and Cauchy–Vandermonde matrices are considered, which were studied earlier by various authors in different ways. In this paper, we use another way called displacement structure approach to deal with matrices of this kind. We show that the Cauchy and Cauchy–Vandermonde matrices satisfy some special type of matrix equations. This leads quite naturally to the inversion formulas and fast algorithms for matrices of this kind.     

An alternative approach to solving cost minimization problem with Cobb–Douglas technology

Central European Journal of Operations Research - We propose a new method for solving the production cost minimization problem with Cobb–Douglas technology. The method is based on weighted...     

Lagrangian approach to a generalized coupled Lane–Emden system: Symmetries and first integrals

This paper aims to classify a generalized coupled Lane–Emden system and to compute the Noether operators corresponding to a Lagrangian for a generalized coupled Lane–Emden system which occurs in the modelling of several physical phenomena such as pattern formation, population evolution and chemical reactions. In addition the first integrals for the Lane–Emden system are constructed with respect to Noether operators.     

Localized waves and interaction solutions to an extended (3+1)-dimensional Jimbo–Miwa equation

Based on Hirota bilinear method, four kinds of localized waves, solitons, breathers, lumps and rogue waves of the extended (3+1)-dimensional Jimbo–Miwa equation are constructed. Breathers are obtained through choosing appropriate parameters on soliton solutions, while lumps and rogue waves are derived via the long wave limit on the soliton solutions. The energy, phase shift, shape, and propagation direction of these localized waves can be influenced and controlled by parameters. Considering mixed cases of the above four types of solutions, we also give many kinds of interaction solutions in the same plane with different parameters or different planes with the same parameters. Dynamical characteristics of these localized waves and interaction solutions are further analyzed and vividly demonstrated through figures.     

Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

From a cellular automaton model of tumor–immune interactions to its macroscopic dynamical equation: A drift–diffusion data analysis approach

Several models of tumor growth have been developed from various perspectives and for multiple scales. Due to the complexity of interactions, how the macroscopic dynamics formed by such interactions at the microscopic level is a difficult problem. In this paper, we focus on reconstructing a model from the output of an experimental model. This is carried out by the data analysis approach. We simulate the growth process of tumor with immune competition by using cellular automata technique adapted from previous studies. We employ an analysis of data given by the simulation output to derive an evolution equation of macroscopic dynamics of tumor growth. In a numerical example we show that the dynamics of tumor at stationary state can be described by an Ornstein–Uhlenbeck process. We show further how the result can be linked to the stochastic Gompertz model.     

Qualitative and quantitative combined nonlinear dynamics model and its application in analysis of price,supply–demand ratio and selling rate

The qualitative and quantitative combined nonlinear dynamics model proposed in this paper fill the gap in nonlinear dynamics model in terms of qualitative and quantitative combined methods, allowing the qualitative model and quantitative model to perfectly combine and overcome their weaknesses by learning from each other. These two types of models use their strengths to make up for the other’s deficiencies. The qualitative and quantitative combined models can surmount the weakness that the qualitative model cannot be applied and verified in a quantitative manner, and the high costs and long time of multiple construction as well as verification of the quantitative model. The combined model is more practical and efficient, which is of great significance for nonlinear dynamics. The qualitative and quantitative combined modeling and model analytical method raised in this paper is not only applied to nonlinear dynamics, but can be adopted and drawn on in the modeling and model analysis of other fields. Additionally, the analytical method of qualitative and quantitative combined nonlinear dynamics model proposed in this paper can satisfactorily resolve the problems with the price system’s existing nonlinear dynamics model analytical method. The three-dimensional dynamics model of price, supply–demand ratio and selling rate established in this paper make estimates about the best commodity prices using the model results, thereby providing a theoretical basis for the government’s macro-control of price. Meanwhile, this model also offer theoretical guidance to how to enhance people’s purchasing power and consumption levels through price regulation and hence to improve people’s living standards.     

Methodological comparison between DEA (data envelopment analysis) and DEA–DA (discriminant analysis) from the perspective of bankruptcy assessment

This study compares DEA (data envelopment analysis) with DEA–DA (discriminant analysis) in terms of bankruptcy assessment. Recently, many DEA researchers propose a use of DEA as a quick-and-easy tool to assess corporate bankruptcy. Meanwhile, other DEA researchers discuss a use of DEA–DA for bankruptcy-based financial analysis. The two groups are very different from the conventional use of DEA because we have long applied DEA to the measurement of operational performance, or productivity analysis. The two research groups open up a new application area (bankruptcy-based financial assessment) for DEA. This study discusses methodological strengths and weaknesses of DEA and DEA–DA from the perspective of corporate failure. The proposed comparative analysis has the three main criteria: (a) how to handle negative data in financial variables, (b) how to handle data imbalance between default and non-default firms, and (c) how to identify a failure process over time. This study finds that DEA is a managerial tool for the initial assessment of corporate failure and DEA is useful for busy corporate leaders and financial managers. In contrast, DEA–DA is useful for researchers and individuals who are interested in the detailed assessment of bankruptcy and its failure process in a time horizon.