Perspectives on Operations Research

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.

Es ist für mich eine ehrenvolle Aufgabe, einen Beitrag für dieses Buch einzubringen. Gleichzeitig ist es ein herzliches Dankeschön für Herrn Prof. Klaus Neumann für seine wissenschaftlichen Arbeiten, deren Ergebnisse ich sehr gern nutze, und für seine Unterstützung und sein stetes Interesse an der Entwicklung unserer Forschungsgruppe. Ich verbinde dies mit alien guten Wünschen für einen gesunden Ruhestand der Familie Neumann, der - dessen bin ich mir sicher - öfter auch in einen Unruhestand ausarten wird.

Nearly everybody can tell us what a saddle 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 saddle point— 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 ℝ³ 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. Brucker, 2001).

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 N-stage reward d _n for a random initial state an integral recursion and an algorithmic recursion. From the former we obtain results about the dependence of d _N 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 [14].

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“ (Gutenberg 1951, S. 1).

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 (Balachandran and Zoltners 1981, Chan and Dodin 1986, Gardner et al. 1990, Dodin and Chan 1991, Drexl 1991, Dodin and Elimam 1997, Dodin et al. 1998, Brucker and Schumacher 1999, Rolland et al. 2005) 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 (Kilcast and Subramanian, 2000, 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.

Im Gutenberg-Produktionsmodell werden drei Anpassungsformen an alternative Beschäftigungen (Produktquantitäten) unterschieden: die zeitliche, die intensi-tätsmäßige und die quantitative Anpassung (vgl. Gutenberg, 1983). Zeitliche Anpassung bedeutet, dass bei konstanter Anzahl der eingesetzten Potenzialfakto-ren eines Typs (Aggregate) und konstanter Intensität (Produktionsgeschwindig-keit) die Einsatzzeit der Aggregate an die zu erzeugende Produktquantität angepasst wird. Intensitätsmäßige Anpassung liegt vor, wenn bei fester Anzahl der eingesetzten Aggregate gleichen Typs und gegebener Einsatzzeit die Intensität der Potenzialfaktoren in Abhängigkeit der Produktquantität variiert wird. Von quantitativer Anpassung wird schließlich gesprochen, wenn bei vorgegebener Intensität und Einsatzzeit die Anzahl der eingesetzten Aggregate variiert wird (vgl. z. B. Fandel, 1996). Es handelt sich dabei urn kurzfristige Anpassungsformen, da die Anpassung an alternative Produktquantitäten auf der Basis der zur Verfügung stehenden Potenzialfaktoren erfolgt, d. h. diese Anpassungsformen beziehen sich ausschließlich auf im Betrieb vorhandene Aggregate und sind daher sofort realisierbar (vgl. Bloech et al., 2001). Die zeitliche, intensitätsmäßige und quantitative Anpassung bestimmen die Leistungsabgaben der vorhandenen Potenzialfaktoren und damit sowohl die resultierenden Faktorverbräuche als auch die damit verbunden Kosten. In der betrieblichen Praxis werden diese Anpassungsformen i. d. R. kombiniert. Es stellt sich somit das Problem, die drei Anpassungsformen derart zu gestalten, dass die gewünschte (vorgegebene) Produktquantität effizient erzeugt wird.

Since the advent of just-in-time driven production planning and control at the Toyota manufacturing plants, the just-in-time paradigm has considered wide-spread consideration within production and operations management (cf., e.g., Schniederjans [22] and Cheng and Podolski [5]). While it was first employed for the high-volume-production of goods only, later there has been considerable research in the area of low-volume, make-to-order manufacturing (cf., e.g., Baker and Scudder [2], Neumann et al. [18], and Rachamadugu [21]). Agrawal et al. [1] considered a practical scheduling problem at Westinghouse ESG, where a number of customer-specific products have to be assembled subject to technological precedence and capacity constraints. The authors developed a MIP-formulation and — in the face of the NP-hardness of the problem — a ‘lead time evaluation and scheduling algorithm’ with acronym LETSA.

Labor costs become more and more important for a company’s success. This holds especially true for high-wage countries like Germany and for labor-intensive service industries like such as call centers or casinos. Efficient planning and allocation of personnel resources is therefore essential and quite a lot of models and methods for this so-called “workforce scheduling problem” have been developed thus far. Nevertheless, real problems are very different, complex, and specific. There exists no standard procedure to find optimal — or at least suboptimal — solutions (if the complexity of the problem is too great for exact algorithms). The formulation of the problem has to take into account the unique situation of a company and subsequently an appropriate solution method has to be adapted.

This paper is dedicated to Prof. Dr. Klaus Neumann on the occasion of his entrance into the retirement.

Production planning and inventory control is facing challenging risk management problems if it is confronted with uncertainties from both the demand and the process side. By analyzing the respective planning problems with methods of stochastic inventory control it is possible to gain remarkably deep insights into the way how optimal reorder and safety stock management responds to joint demand and yield risks. These insights can be exploited to assess and improve the simple type of risk management rules employed in MRP systems to cope with uncertainties in demand and production yield.

The hub & spoke network design problem is a strategic logistics planning problem with applications for airlines, telecommunication companies, computer networks, postal services, and trucking companies, for example. Basically, the problem in all these applications is that for a given set V = 1,... , n of nodes (airports, computers, post offices, depots, ...) goods must be transported between possibly every pair of nodes. Direct connections between every pair of nodes would result in n(n − 1) linkages which is impractically high and economically non-profitable. Consider, for instance, an airline that serves several airports worldwide. Offering nonstop flights between every pair of airports would require a huge amount of planes and crews and many empty seats on board could be observed for many connections. In such settings, it turns out to be reasonable to install one or more so-called hub locations where direct links are then available to hub nodes as indicated in figure 1 where nodes 3, 6, and 9 are assumed to be hubs. Transporting goods from, say, node 1 to node 11, can then be done via hubs 3 and 6.

In this paper we consider one-buyer, one-seller, finite horizon, multi-period inventory models in which the economic order quantity is integrated with the economic production quantity (EOQ-EPQ in short). We introduce the Stackelberg equilibrium framework in which the objective is to maximize the vendor’s total benefit subject to the minimum total cost that the buyer is willing to incur. Some existence results, optimality conditions and the optimal replenishment policy under the Stackelberg equilibrium concept are obtained and a numerical algorithm is presented to find the optimal replenishment policy in practice.

Die wenigsten Autofahrer werden einen Bezug zwischen Operations Research — oder kurz OR — und ihrem Navigationssystem herstellen. Genauso wenig denkt man beim Studium der Reiseroute, die man sich gerade im Internet errechnet hat, an Begriffe wie „Minimalgerüst“ und „kürzeste Wege“. Und was hat die pünktliche Auslieferung der bestellten Möbel mit dem Knoten-orientierten Tourenplanungsproblem zu tun?

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 other 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 [6].

Die Nutzwertanalyse und der Analytic Hierarchical Process (AHP) sind be-kannte, auch in der Praxis verwendete Verfahren zur Lösung von Mehrzielentscheidungen. Beide berücksichtigen die beschränkte Informationsverarbeitungs-kapazität bzw. die eingeschränkte Rationalität eines Entscheiders und entsprechen so dem Wunsch der Praktiker nach realistischeren und anwendbaren Entscheidungsunterstützungsmethoden. Wie empirisch nachgewiesen wurde, haben Menschen große Schwierigkeiten, Alternativen widerspruchsfrei anzuordnen, wenn mehr als zwei Ziele beachtet werden müssen, vgl. May [6, S. 9–13]. Entsprechend werden in der Nutzwertanalyse und dem AHP bei Vorliegen sehr vieler Ziele diese durch ein hierarchisch aufgebautes Zielsystem strukturiert, in dem schrittweise nur wenige, zumeist zwei oder drei Teilziele zu einem höheren Ziel aggregiert werden, vgl. Abbildung 1.