Unternehmensforschung

Gegeben seien endliche MengenX, Y undZ ⊂ X × Y, Z x ={y¦(x,y)∈ Z},Z y ={x¦(x,y)∈ Z}. Man nenntA ⊂ X (bzw.B ⊂ Y)zuordenbar, wenn es eine Injektionρ:A → Y (bzw.ψ: B →X) mitρ(x) ∈ Z x (bzw.ψ(y) ∈ Z y ) gibt, und (A, B) mit #A=#B > 0 einZuordnungspaar, wenn eine Bijektionf:A →B mitf(x)∈Z x ∩ B (bzw.f −1 (y)∈ Z y ∩ A) existiert. Die Bijektionf heißtZuordnungsplan fürA, B. In der vorliegenden Arbeit werden Fragen nach der Existenz von optimal zuordenbaren Mengen und optimalen Zuordnungspaaren behandelt, wenn man auf den MengenX undY Ordnungen vorgibt, wobei auch Nebenbedingungen berücksichtigt werden. In manchen Fällen lassen sich anhand der Beweise Zuordnungspläne oder ihre Berechnungsvorschrift explizit angeben. Zum Schluß werden die Aussagen an konkreten, dem Bereich der Wirtschaftswissenschaften entnommenen Beispielen erläutert.

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm. The portfolio optimization is done using the first two moments of the predictive discrete asset return distribution. For illustration purposes we apply our method to empirical stock market data where daily asset log-returns are assumed to follow an orthogonal MGARCH process with t-distributed perturbations. Our results are compared with other portfolios suggested by popular optimization strategies.

In this paper we formulate a mathematical programming model for solving a class of manpower scheduling problems. The objective is to assign working schedules to a fixed number of employees in order to meet the workforce demand, assumed to be constant over the planning period. Necessary and sufficient conditions of existence of the solution are stated, heuristic methods are presented and the results of computational experiences are reported.

An attempt is made here to implicate the technical problem of power cables into programming language. Economic use of power cables demand consideration of various cost-factors, both of technical and commercial character. The problem is mathematically solved to derive the condition for minimum of costs or — in other words — for optimum use of a cable. Graphical exhibits clearly demarcate the optimum use of cables under changes in cost-factors. The problem simultaneously tries to differentiate between the criterions of „technical maximum“ and „economic optimum“.

In this paper we address the problem of estimating the mean derivative when the entity containing the parameter has jumps. The methods considered are finite differences, infinitesimal perturbation analysis and the likelihood ratio score function. We calculate the difference between the differentiated mean and the mean derivative. In case of finite differences, we compute the stepsize in the simulation that asymptotically minimizes the mean square error. We also show that the two latter methods, infinitesimal perturbation analysis and likelihood ratio score function, are mathematically equivalent.

Service operations involving an intermediate store are modelled using an extended definition of the system state which is a conventional definition of state supplemented with an indicator of the live capacity in the store. Additional to the parameters of mean service rate and mean arrival rate, a mean discharge rate of the store is introduced and the steady state probabilities are calculated in terms of these three quantities. Both finite source and infinite source cases are considered under the assumption of exponential distributions. The models permit production comparisons for systems with and for systems without storage devices.

This paper considers the problem of minimizing a convex differentiable function subject to convex differentiable constraints. Necessary and sufficient conditions (not requiring any constraints qualification) for a point to be an optimal solution are given in terms of a parametric linear program. Dual characterization theorems are then derived, which generalizes the classical results ofKuhn-Tucker andJohn.

Zur Prognose über das Anwachsen von Verbraucheranzahlen (Fernsprechteilnehmer, Verbraucher von Konsumgütern usw.) wird vielfach mit Erfolg ein Wachstumsmodell benutzt, das sich durch die sogenannte „logistische Kurve“, d. h. eine durch den Tangens hyperbolicus ausdrückbare Funktion darstellen läßt. Im folgenden wird ein „Wachstumsnetz“ angegeben, in dem sich die Kurven dieser Klasse nach ihrer Normierung (Sättigungswert bei 100%) zu Geraden strecken. So erhält man ein (in der Handhabung dem bekannten Wahrscheinlichkeitsnetz vergleichbares) Prognosehilfsmittel, dessen Gebrauch erläutert wird. Insbesondere ist das Wachstumsnetz geeignet, systematische zeitliche Änderungen der Wachstumsgesetzmäßigkeiten erkennen zu lassen und besser fundierte Approximationen zu liefern, als sie bisher mit graphischen oder numerischen Mitteln erreicht wurden. Ein besonderer Vorteil des Wachstumsnetzes liegt darin, daß es ein einfaches Kriterium dafür liefert, ob ein beobachteter Wachstumsprozeß ganz oder zeitweise einer logistischen Kurve folgt und deshalb eine entsprechende Prognose sinnvoll ist.

Facility layout problems involve the location of facilities in a planar arrangement such that facilities that are strongly connected to one another are close to each other and facilities that are not connected may be far from one another. Pairs of facilities that have a negative connection should be far from one another. Most solution procedures assume that the optimal arrangement is bounded and thus do not incorporate constraints on the location of facilities. However, especially when some of the coefficients are negative, it is possible that the optimal configuration is unbounded. In this paper we investigate whether the solution to the facility layout problem is bounded or not. The main Theorem is a necessary and sufficient condition for boundedness. Sufficient conditions that prove boundedness or unboundedness are also given.