• Article close
• Mathematical Methods of Operations Research close

This paper studies noncompact feasible sets of a semi-infinite optimization problem which are defined by finitely many equality constraints and infinitely many inequality constraints. The main result is the equivalence of the overall validity of the Extended Mangasarian Fromovitz Constraint Qualification with certain (topological) stability conditions. Furthermore, two perturbation theorems being of independent interest are presented.

In this paper, we study the problem of a variety of nonlinear threshold autoregressive model Xn+1=(Xn)+n+1(Zn+1) in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {n(i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.

An on-line portfolio selection strategy with transaction costs is presented. It ensures investors to achieve at least the same exponential growth rate of wealth as the best stock for a long term. This equipped with a new prediction method based on “cross rates” for price relative sequences yields a profitable algorithm, which has been tested on real data from the London Stock Exchange.

Die Haupt — Problemkreise der Unternehmensforschung, namlich Lagerhaltungsprobleme, Zuordnungs- oder Zuteilungsprobleme, Wartezeit — Probleme, Ersatzstellungs- und Wartungsprobleme, sowie Konkurrenz-probleme werden besprochen und ihre Losungsmoglichkeiten kurz skizziert. Dabei wird die Bedeutung elektronischer Datenverarbeitungsmaschinen zur Losung solcher Probleme besonders hervorgehoben.

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.

Counting and enumerating maximal and maximum independent sets are well-studied problems in graph theory. In this paper we introduce methods to count and enumerate maximal/maximum independent sets in threshold graphs and k-threshold graphs and improve former results for these problems. The results can be applied to combinatorial optimization problems, and in particular to different variations of the knapsack problem. As feasible solutions for instances of those problems correspond to independent sets in threshold graphs and k-threshold graphs, we obtain polynomial time results for special knapsack and multidimensional knapsack instances. Also, we show lower and upper bounds for the number of necessary bins in several bin packing problems.

Die Schweizerischen Bundesbahnen haben sich entschieden, kunftig fur die Bildung der Nahguterzuge in den dafur geeigneten Anlagen die Simultanformation mit dem Triangularschema anzuwenden und die Bauprojekte fur neue Rangierbahnhofe auf dieser Basis zu planen. Dieses Rangierverfahren besitzt grose Vorzuge, da man mit verhaltnismasig wenig Geleiseanlagen und Einzelmanovern auskommt. Allerdings ist der Bedarf an Geleisekapazitat und die Zahl der Ablaufe bei einem gegebenen Wagenaufkommen je nach Ablaufplan verschieden. Das hier beschriebene Verfahren erzeugt einen Ablaufplan, der die verfugbare Geleisekapazitat nicht uberbeansprucht und gleichzeitig die Anzahl der Ablaufe moglichst klein halt. Es handelt sich um ein heuristisches Verfahren, das im allgemeinen nur eine suboptimale Losung liefert, sich aber in der Praxis bereits gut bewahrt hat.