Unternehmensforschung

In this paper, we take an in-depth look at the complexity of a hitherto unexplored multiobjective minimum weight minimum stretch spanner problem; or in short multiobjective spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied minimum t-spanner problem. This multiobjective approach allows to find solutions that offer a viable compromise between cost and utility—a property that is usually neglected in singleobjective optimization. Thus, the MSp can be a powerful modeling tool when it comes to, e.g., the planning of transportation or communication networks. This holds especially in disaster management, where both responsiveness and practicality are crucial. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if $${\textbf{P}} \ne \textbf{NP}$$ , the set of extreme points cannot be computed in output-polynomial time, for instances with unit costs and arbitrary graphs. Furthermore, we consider the directed versions of the cases above.

Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation.

This paper studies a special class of min max problems in two sections. In Section I, a procedure is developed which gives the optimal solution of the problem. The Section II deals with ranking the solutions in increasing order of the value of the objective function.

In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multi-objective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multi-objective optimization problem. This approach can be used to reduce the dimensionality of the objective space as well as to discard certain unwanted solutions, especially the ‘extreme’ ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions.

It has long been recognised that situations in which some key resource or service is to be allocated among jobs or customers competing for it are often subject to a range of uncertainties. Key amongst these concern the reliability of service itself. When the service being delivered to a job is disrupted by some failure of the service mechanism, it is reasonable to suppose that effort may subsequently be required to restore that job to its position before the breakdown occurred. We develop optimal index policies for service allocation for a range of semi-Markovian models which capture this key feature in a range of ways.

Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation—i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay.

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer’s utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.

In this paper, we wish to introduce the idea of stochastic effects in optimal routing problems. This can be done by committing mistakes while making decisions. We will illustrate this idea by a classical puzzle: “The Wine Pouring Problem”.