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In this paper we give a short overview of the research conducted, initiated, and supervised by Klaus Neumann from the early sixties up to present. Of course, we do not claim exhaustiveness of our review. The major themes of research can be clustered into the three main areas sketched in Sections 2 to 4: In any of those fields, Klaus Neumann has significantly influenced the development of OR in Germany and beyond. From the very beginning, his research has combined solid mathematical foundation and applicability of theoretical results. The relevance of his achievements to the treatment of real-world problems has been reflected in many applied research and development projects. A selection of the projects that have been carried out in cooperation with different industrial partners is sketched in Section 5.

Until very recently, it has been believed that banks are exposed to two main types of risks: credit risk (the counterparty failure risk) and market risk (the risk of loss due to changes in market indicators, such as interest rates and exchange rates), in the order of importance. The remaining financial risks have been put in the category of risks, operational risk being one of them. Recent developments in the financial industry have shown that the importance of operational risk has been largely under-estimated. Newly defined capital requirements set by the Basel Committee for Banking Supervision in 2004, require financial institutions to estimate the capital charge to cover their operational losses [].

Nearly everybody can tell us what a really is. Most of those who teach or study (a) mathematics, (b) mathematical economics, (c) econometrics, or (d) operations research are able to define the term — verbally or by means of equations and/or inequalities. But only very few of them are able or willing to draw, on a piece of paper or in a paper to be published, a surface in ℝ that contains a saddle point.

Das vorherrschende Paradigma der Ablaufplanung ist nach wie vor geprägt durch den klassischen Optimierungsansatz. Es werden diskrete (kombinatorische) Optimierungsprobleme betrachtet, die eine Zielfunktion unter Beachtung bestimmter Präzedenzbeziehungen und ggf. weiterer problemspezifischer Restriktionen optimieren. Dabei sind in den letzten Jahren erhebliche Fortschritte in der Entwicklung leistungsfähiger Lösungsalgorithmen erzielt worden (vgl. z. B. ).

We consider a substantial generalization of a problem proposed by MacKinnon (2003). Within the setting of Bayesian Markovian decision processes we derive for the maximal expected -stage reward for a random initial state an integral recursion and an algorithmic recursion. From the former we obtain results about the dependence of on several parameters while the latter serves the same purpose, but also yields a numerical solution. An optimal policy is given in the form of an optimal stopping time. The model with a random initial state is dealt with by an appropriate choice of the state space.

In this paper we present a general concept for the formulation of the dual program which is based on generalized convexity. This is done in a purely algebraic way where no topological assumptions are made. Moreover all proofs are presented in an extreme simple way. A complete presentation of this subject can be found in the book of D. Pallaschke and S. Rolewicz [].

Airlines typically divide a pool of identical seats into several booking classes that represent e.g. different discount levels with differentiated sale conditions and restrictions. Assuming perfect market segmentation, mixing discount and higher-fare passengers in the same aircraft compartment offers the airline the potential of gaining revenue from seats that would otherwise fly empty. If too many seats are sold at a discount price, however, the airline company would loose full-fare passengers. If too many seats are protected for higher-fare demand, the flight would depart with vacant seats. Seat inventory control deals with the optimal allocation of capacity to these different classes of demand, forming a substantial part of a revenue management system.

„Der Sinn aller betrieblichen Betätigung besteht darin, Güter materieller Art zu produzieren oder Güter immaterieller Art bereitzustellen. Güter materieller Art bezeichnen wir als Sachgüter oder auch als Sachleistungen, Güter immaterieller Art als Dienste oder Dienstleistungen“ ().

When scheduling its audit-staff, the management of an auditing firm encompasses a number of decisions. These may be grouped into several categories which differ markedly in terms of organizational echelon involved, length of the planning horizon and the planning periods, degree of aggregation of the audit tasks, degree of detail of the required information, and decision objective. However, traditional audit-staff scheduling models (, , , , , , , , ) are single-level models which try to construct a direct assignment of auditors to tasks and periods. To facilitate algorithmic treatment, all these models are more or less gross simplifications of practical planning situations.

Due to factors such as the high variability of raw materials, intermediate and final products, fluctuating prices, and variable processing times and yields, production planning for sausages is generally a challenging task. One of the most distinctive factors to consider in fresh food production planning is shelf life. Shelf life restrictions directly influence wastage, out-of-stock rates and inventory levels. The shelf life of a product is defined as the time in which the food product will remain safe, be certain to retain the desired sensory, chemical, physical, and microbiological characteristics as well as comply with any label declaration of nutritional data (, according to the London Institute of Food Science and Technology Guidelines, 1993). The possibility to offer a higher shelf life than its competitors constitutes a pivotal competitive advantage for fresh food producers, making the provision of shelf life functions crucial for modern production planning systems.