Catálogo de publicaciones - libros

In chemical engineering, pinch analysis holds a long tradition as a method for determining optimal target values for heat or mass exchanger networks by calculating an optimal alignment of available flows. A graphical representation of the time-material production relationship derived from the original pinch analysis can be used for aggregate production planning. This can deliver insights in the production planning problem as several production strategies can be compared. The approach is applied to a case study on bicycle coating.

Supply chain network are considered as solution for effectively meeting customer requirements such as low cost, high product variety, quality and shorter lead times. The success of a supply chain lies in good strategic and tactical planning and monitoring at the operational level. Strategic planning is long term planning and usually consists in selecting providers and distributors, location and capacity planning of manufacturing/servicing units, among others.

Scheduling a sports league requires to solve a hard combinatorial optimization problem. We consider a league of a set T of n teams supposed to play in a single round robin tournament (SRRT). Accordingly, each team i ∈ T has to play against each other team j ∈ T, j ≠ i , exactly one match. The tournament is partitioned into matchdays (MD) being periods where matches can be carried out. Each team i ∈ T shall play exactly once per MD. Hence, we have a compact structure resulting in an ordered set P of n −1 MDs.

In many practical applications of resource-constrained project scheduling a work content (e.g., in man months) is specified for each activity instead of a fixed duration and fixed resource requirements. In this case, the resource usages of the activities may vary over time. The problem then consists in determining the resource usage of each activity at each point in time such that precedence constraints, resource scarcity, and specific constraints on the evolution over time of resource usages are respected and the project duration is minimized. We present two priority-rule methods for this problem and report on results of an experimental performance analysis for instances with up to 200 activities.

Die Projektportfolioplanung stellt ein multikriterielles Entscheidungsproblem dar, das neben der Projektauswahl unter Berücksichtung von Projektabhängigkeiten und Synergieeffekten verschiedener Art auch die zeitliche Einplanung von Projekten umfasst. Dabei sollen auch die Begrenzungen für den Ressourcenverbrauch von erneuerbaren und nicht erneuerbaren Ressourcen beachtet werden. Um eine Entscheidungsunterstützung hierfür zu bieten, wird zunächst ein mathematisches Modell aufgestellt, um darauf folgend den Einsatz von Standardoptimierungssoftware wie auch von heuristischen Verfahren als Möglichkeit zum Umgang mit mehreren Zielfunktionen vorzustellen.

Es wird die Architektur eines entwickelten Multi-Agenten Systems (MAS) zur dezentralen Lösung des Decentral Resource Constrained Multi Projekt Scheduling Problem (DRCMPSP) vorgestellt. Die Systemarchitektur basiert auf Web-Services, welche die einfache Integration und somit auch Evaluation alternativer Koordinationsmechanismen von Agenten ermöglichen. Bei dem System handelt es sich um eine internetbasierte Anwendung, deren Funktionalität über einen Internetbrowser zur Verfügung gestellt wird (http://www.agentcopp.de). Auf diese Weise kann das MAS auch zukünftig von Systementwicklern und Wissenschaftlern in den von ihnen gewählten IT-Umgebungen benutzt und mit anderen Systemen unter identischen IT-Rahmenbedingungen verglichen werden. Ferner werden 80 Benchmarkprobleme und Lösungen für das DRCMPSP präsentiert. Mit dem Beitrag wird das Ziel verfolgt, das Benchmarking von Systemen für das DRCMPSP transparenter zu gestalten.

In the work a resource-constrained project scheduling problem (RCPSP) is considered. This classical NP-hard problem evokes interest from both theoretical and applied points of view. Thus we can divide effective (i.e. polynomial) approximation algorithms in two groups: fast heuristic algorithms for the whole problem and generalizations and algorithms with performance guarantee for particular cases. In first section we consider the statement of the problem and some generalizations. Along with renewable resources we consider consumable resources which can be stored to be used at any moment after the moment of allocation. A polynomial optimal algorithm for solving the problem with consumable resources only was suggested by Gimadi, Sevastianov and Zalyubovsky [2]. So we can consider polynomially solved relaxation of RCPSP. In this relaxation instead of each renewable resource we have consumable resource which is allocated at each moment of time in one and the same amount. Then we can use information about the solution of this relaxation for approximate solving the original problem in polynomial time (for example, the order of starting times can be used as a heuristic for serial scheduling scheme). Furthermore, the optimal value of relaxation gives the lower bound for the optimal value of the original problem.

The usual optimization criteria for Markov decision processes (e.g. total discounted reward or mean reward) can be quite insufficient to fully capture the various aspects for a decision maker. It may be preferable to select more sophisticated criteria that also reflect variability-risk features of the problem. To this end we focus attention on risk-sensitive optimality criteria (i.e. the case when expectation of the stream of rewards generated by the Markov processes evaluated by an exponential utility function is considered) and their connections with mean-variance optimality (i.e. the case when a suitable combination of the expected total reward and its variance, usually considered per transition, is selected as a reasonable optimality criterion). The research of risk-sensitive optimality criteria in Markov decision processes was initiated in the seminal paper by Howard and Matheson [6] and followed by many other researchers (see e.g. [1, 2, 3, 5, 4, 8, 9, 14]). In this note we consider a Markov decision chain X = X _n, n = 0,1, ... with finite state space $$ \mathcal{I} $$ = 1,2, ..., N and a finite set $$ \mathcal{A}_i $$ = 1,2, ..., K _i of possible decisions (actions) in state i ∈ $$ \mathcal{I} $$ . Supposing that in state i ∈ $$ \mathcal{I} $$ action k ∈ $$ \mathcal{A}_i $$ is selected, then state j is reached in the next transition with a given probability p _ ij ^ k and one-stage transition reward r _ij will be accrued to such transition.

In the Black-Scholes model optimal trading for maximizing expected power utility under proportional transaction costs can be described by three intervals B, NT, S : If the proportion of wealth invested in the stocks lies in B, NT, S , then buying, not trading and selling, respectively, are optimal. For a finite time horizon, the boundaries of these trading regions depend on time and on the terminal condition (liquidation or not). Following a stochastic control approach, one can derive parabolic variational inequalities whose solution is the value function of the problem. The boundaries of the active sets for the different inequalities then provide the boundaries of the trading regions. We use a duality based semi-smooth Newton method to derive an efficient algorithm to find the boundaries numerically.

Classical floating point random numbers fail simple tests when considered as rational numbers.