Catálogo de publicaciones - libros

We present a one-sector growth model with finitely many households who differ from each other with respect to their endowments, their preferences, and the type of capital supplied to firms. There is monopolistic competition on the capital market and perfect competition on all other markets. We show that there exists a unique stationary equilibrium and that all households have strictly positive wealth in this equilibrium. We study how the stationary equilibrium depends on the time-preference rates of the households and on the elasticity of substitution between different types of capital. We also analyze the stability of the stationary equilibrium.

This paper examines open source software development in a competitive environment. The quality of open source software improves over time based upon contributions by firms and users. A firm’s decision to contribute is interesting because it also augments competitors’ software quality in future periods subject to compatibility considerations with their existing software. A differential game model is developed to understand why firms are increasingly involved in open source software development by determining the optimal contributions and software quality over time. We obtain a closed-loop Nash equilibrium solution. Examples are given to derive insights from this model.

A firm's new product development clockspeed is determined by the frequency of new product introductions to the marketplace. Using a simple analytic model, we derive an optimal firm NPD clockspeed that is driven by several external market and internal organizational related factors. Specifically, we analyze the impact of dynamic sales/demand curves and dynamic net revenues on the optimal pace of new product introductions.

Maintenance of a machine and its replacements by newer ones in the course of a predetermined planning horizon with fixed intermediate dates for potential replacement opportunities is considered. Using the Kamien-Schwartz optimal control model for maintenance, allowance for ceasing of production until installation of a new machine is studied with respect to regeneration points.

We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking into account congestion-responsive traffic assignment and adaptive traffic control. We observe dynamic traffic patterns which significantly depend on the respective network topology. Synchronization is only one interesting example and implies the emergence of green waves. In this connection, we will discuss adaptive strategies of traffic light control which can considerably improve throughputs and travel times, using self-organization principles based on local interactions between vehicles and traffic lights. Similar adaptive control principles can be applied to other queueing networks such as production systems. In fact, we suggest to turn push operation of traffic systems into pull operation: By removing vehicles as fast as possible from the network, queuing effects can be most efficiently avoided. The proposed control concept can utilize the cheap sensor technologies available in the future and leads to reasonable operation modes. It is flexible, adaptive, robust, and decentralized rather than based on precalculated signal plans and a vulnerable traffic control center.

We consider a problem of optimal production control of a single reliable machine. Demand is described as a discrete-time stochastic process. The objective is to minimize linear inventory/backlog costs over a finite time horizon. Using the necessary conditions of optimality, which are expressed in terms of co-state dynamics, we develop an optimal control policy. The policy is parameterized and its parameters are calculated from a computational procedure. Numerical examples show the convergence or divergence of the policy when the expected demand is greater or smaller than the production capacity. A non-stationary case is also presented.

We consider a control problem introduced by Cho, Abad and Parlar (1993) which “incorporates a dynamic maintenance problem into a production control model”. For a quadratic production cost function we present a detailed numerical study of optimal control policies for different final times. The maintenance control is either composed by bang-bang and singular arcs or is purely bang-bang. In the case of a linear production cost, we show that both production and maintenance control are purely bang-bang. A recently developed second order sufficiency test is applied to prove optimality of the computed controls. This test enables us to calculate sensitivity derivatives of switching times with respect to perturbation parameters in the system. Furthermore, numerical results are presented in the case where a state constraint on the number of good items is added to the control problem.

The reliability index is a useful indicator to compute the failure probability. If is the performance of interest and if is a Normal random variable, the failure probability is computed by and is the reliability index. When is a nonlinear function of normal random variables (, …, ), then the preceding formula can be generalized, with some approximation. One uses a nice property of the reliability index, to be the shortest distance of the origin to the failure region. This method introduced by B.M. Ayyub, provides an analytic alternative to the Monte Carlo method.

In this paper we present an extension of a direct solution method, originally due to Leitmann (1967) for single-player games on a finite time interval, to a class of infinite horizon -player games in which the state equation is affine in the strategies of the players. Our method, based on a coordinate transformation method, gives sufficient conditions for an open-loop Nash equilibrium. An example is presented to illustrate the utility of our results.