Mathematical Methods of Operations Research 

About: Mathematical Methods of Operations Research is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Optimization problem & Markov chain. It has an ISSN identifier of 1432-2994. Over the lifetime, 1436 publications have been published receiving 28820 citations. The journal is also known as: ZOR. Mathematical methods of operations research (1996) & Mathematical methods of operations research (Heidelberg. Print).

Modelling of extremal events in insurance and finance

Abstract: Extremal events play an increasingly important role in stochastic modelling in insurance and finance. Over many years, probabilists and statisticians have developed techniques for the description, analysis and prediction of such events. In the present paper, we review the relevant theory which may also be used in the wider context of Operation Research. Various applications from the field of insurance and finance are discussed. Via an extensive list of references, the reader is guided towards further material related to the above problem areas.

Biconvex sets and optimization with biconvex functions: a survey and extensions

Abstract: The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function \(f:X\times Y\to{\mathbb{R}}\) is called biconvex, if f(x,y) is convex in y for fixed x∈X, and f(x,y) is convex in x for fixed y∈Y. This paper presents a survey of existing results concerning the theory of biconvex sets and biconvex functions and gives some extensions. In particular, we focus on biconvex minimization problems and survey methods and algorithms for the constrained as well as for the unconstrained case. Furthermore, we state new theoretical results for the maximum of a biconvex function over biconvex sets.

Steepest descent methods for multicriteria optimization

Abstract: We propose a steepest descent method for unconstrained multicriteria optimization and a “feasible descent direction” method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuously differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuously differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto optimality. Both methods do not scalarize the original vector optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the Steepest descent method and Zoutendijk's method of feasible directions, respectively.

A review of multi-component maintenance models with economic dependence

Abstract: In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice.

Covering Models and Optimization Techniques for Emergency Response Facility Location and Planning: A Review

Abstract: With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.