Martin J. Beckmann

A Paradox in Consumption Theory

Consider a consumer with a utility function of the form

THE SOFT SCIENCE OF PREDICTING TRAVELLER BEHAVIOUR

{\text{u = }}\sum\limits_{{\text{i = 1}}}^{\text{n}} {{{\text{a}}_{\text{i}}}\Phi \left( {{{\text{x}}_{\text{i}}}} \right)}

Lagerhaltung bei Unsicherheit

where xi are quantities consumed of good i, Φ is a common function which is monotonically increasing and concave, and the ai are attraction coefficients which measure the strength of the consumers’ preference for the good i. The utility function may be applied to all consumption activities. But it is often more meaningful to restrict oneself to subsets of related goods i. This requires the further assumption, however, that a budget has been set for the consumption of this subset of goods.

Some principles of efficient organizational design

SummaryThe purpose of this paper is to develop a theory of household purchasing decisions which are based on utility maximization and are responsive to product “attractions”. Attractions are defined and are introduced as parameters of the utility function. Alternative specifications are examined, in particular the case of a so-called linear expenditure system. Expenditure and market shares are derived as functions of these attractions. Next, relationships between advertising and attractions are considered. In this way a theoretical basis is found for various ad-hoc-formulae for the relationship between advertising and market share postulated in the marketing literature.ZusammenfassungZiel dieses Aufsatzes ist eine Theorie der Kaufentscheidungen zu entwickeln, die auf der Nutzenmaximierung basiert und zugleich „Produktattraktionen“ anspricht. Attraktionen werden definiert und als Parameter der Nutzenfunktion eingeführt. Alternative Spezifikationen werden untersucht, insbesondere der Fall eines sogenannten linearen Ausgabensystems. Ausgaben und Marktanteile werden als Funktion der Attraktionen abgeleitet. Weiter werden Beziehungen zwischen Werbung und Attraktionen betrachtet. Daraus ergibt sich eine theoretische Begründung für verschiedene ad-hoc-Formeln, die für die Beziehung zwischen Werbung und Marktanteil in der Marktliteratur postuliert worden sind.

Contract Length and Rank in Organizations

Predicting traffic generation and distribution is treated as a problem of economic demand. This demand is assumed to be generated by utility maximizing households and then aggregated. The prediction formulae obtained for the class of separable utility functions are compared with the gravity and entropy expressions. Some empirical results from the Detroit area are introduced as illustrations. In this case, the entropy approach does as well empirically as the utility approach. But the utility model identifies additional economic variables that are relevant. It also reveals the rather strong economic assumptions implied by the entropy and gravity approaches. Shortcomings of the present utility model based on separable utility functions are noted and discussed.

Bidding for Research Funds

J.M. KEYNES differentiated three motives for holding money which can be applied to inventory problems.

Optimal Gambling Strategies

ZusammenfassungDas Referat behandelt die grundsätzlich möglichen Ansätze zu einer Analyse optimaler sequentieller Entscheidungen beim Lagerhaltungsproblem bei Unsicherheit. DasArrow-Harris-Marschak-Modell wird entwickelt, und einige seiner Abwandlungen werden erwähnt. Das Problem der Bestimmung optimaler Lagerhaltungspolitiken wird analysiert. Methoden zur Kalkulation optimaler Verhaltungsregeln werden dargestellt unter besonderer Berücksichtigung des Wert-Iterations-Schemas der Dynamischen Programmierung. Dabei werden die Beziehungen zwischen Dynamischer Programmierung und stochastischen Gleichgewichtsmodellen herausgestellt. Der Gebrauch von Warteschlangenmodellen in der Lagerhaltungsanalyse wird erläutert. Schließlich werden einige Bemerkungen zum Mehrphasen-Lagerhaltungsproblem gemacht sowie zum verbundenen Lagerhaltungsproblem bei verschiedenen Gütern und zum statistischen Problem der gleichzeitigen sequentiellen Schätzung von Nachfrageverteilungen. Es wird erwähnt, daß der Rahmen eines individuellen Lagerhaltungsproblems unter Umständen ausgedehnt werden muß, damit weitere Entscheidungen, wie Instandhaltung, Ersatz, Verteilung usw. im Modell mitbehandelt werden können.SummaryThis paper discusses the basic approaches to optimal sequential ordering decisions in inventory control. TheArrow-Harris-Marschak model is developed and some of its modifications are mentioned. The problem of determining optimal inventory policies is analysed. Methods of calculating optimal policies are presented with special emphasis on the value iteration scheme of Dynamic Programming. The interrelations between Dynamic Programming and stochastic equilibrium models are exhibited. The use of queueing models in inventory analyses is illustrated. Some remarks are made on the multi-echelon inventory problem, on joint inventory problems for several commodities, and on the sequential estimation of demand distributions. It is pointed out that the framework of an individual inventory problem must sometimes be broadened to include such further decisions as maintenance, replacement, distribution etc.

Stochastic Models with Continuous Review

The efficiency of organizations and bureaucracies in both design and operation depends to some extent on internal and external factors Examples of the former include overstaffing, a top-heavy management structure, uneven distribution of the workload, and intersupervisory conflict. The latter includes variation in the market competition, communication breakdowns, and the effects of outside agents. Inefficiency is rarely deliberately incorporated within any structure : it most often develops as a result of overfast, haphazard or unnecessary growth, and can often be avoided or remedied. As societies develop, they depend increasingly upon organizational structures and it is thus the intention of this paper to examine some aspects of organizational efficiency by drawing on some of the basic principles of systems science