In this paper we study the following problem, which we call the weighted routing problem. Let be given a graphG = (V, E) with non-negative edge weightsw e ∈ ℝ+ and letN,N ≥ 1, be a list of node sets. The weighted routing problem consists in finding mutually disjoint edge setsS 1,...,S N such that, for eachk ∈ {1, ...,N}, the subgraph (V(S k),S k) contains an [s, t]-path for alls, t ∈ T k and the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We describe our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to switchbox routing problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances.

The problem of contingent claim valuation in a market with a higher interest rate for borrowing than for lending is discussed. We give results which cover especially the European call and put options. The method used is based on transforming the problem to suitable auxiliary markets with only one interest rate for borrowing and lending and is adapted from a paper of Cvitanic and Karatzas (1992) where the authors study constrained portfolio problems.

In this paper we formulate an inverse shortest path problem as a special linear programming problem. A column generation scheme is developed that is able to keep most columns of the LP model implicit and to generate necessary columns by shortest path algorithms. This method can get an optimal solution in finitely many steps. Some numerical results are reported to show that the algorithm has a good performance.

Multistage Bayesian decision procedures in statistical quality control are known from attribute sampling. In this paper they are introduced in a more general framework occuring in lot-control by using the theory of Bayesian sequentially planned decision procedures. We show that under sufficiency and transitivity assumptions and monotonicity properties concerning the distribution and cost set-up these Bayes-procedures have (z, c −,c +)-structure which, on one hand, generalizes results of K.-H. Waldmann and, on the other hand, reduces computational effort significantly. Finally, examples taken from attribute sampling and life testing for an outgoing lot are presented.

The paper is devoted to two real problems that generate a cooperative game model with a so-calledk-convex characteristic function when certain conditions are fulfilled. Both a bankruptcy problem and an information trading problem are modelled as a cooperative game by constructing the corresponding bankruptcy game as well as the information market game. Firstly, it is established that the bankruptcy game is ak-convexn-person game where 1 ≤k ≤n − 2 if and only if the estate is sufficient to meet the claims of creditors in any (n − k)-person coalition. Secondly, it is shown that thek-convexity property for the information market game is equivalent to the nonexistence of profits with respect to a restricted class of submarkets.

We consider two person zero-sum games with lack of information on one side given bym matrices of dimensionm×m. We suppose the matrices to have the following “symmetric” structure:a ij s =a ij +cδ i s ,c>0, whereδ i s =1 ifi=s andδ i s =0 otherwise. Under certain additional assumptions we give the explicit solution for finite repetitions of these games. These solutions are expressed in terms of multinomial distributions. We give the probabilisitc arguments which explain the obtained form of solutions. Applying the Central Limit Theorem we get the description of limiting behavior of value closely connected with the recent results of De Meyer [1989], [1993].

We consider two-person zero-sum games of stopping: two players sequentially observe a stochastic process with infinite time horizon. Player I selects a stopping time and player II picks the distribution of the process. The pay-off is given by the expected value of the stopped process. Results of Irle (1990) on existence of value and equivalence of randomization for such games with finite time horizon, where the set of strategies for player II is dominated in the measure-theoretical sense, are extended to the infinite time case. Furthermore we treat such games when the set of strategies for player II is not dominated. A counterexample shows that even in the finite time case such games may not have a value. Then a sufficient condition for the existence of value is given which applies to prophet-type games.

This paper proposes an unconstrained dual approach and an efficient algorithm for solving Karmarkar-type linear programming problems. Conventional barrier functions are incorporated as a perturbation term in the derivation of the associated duality theory. An optimal solution of the original linear program can be obtained by solving a sequence of unconstrained concave programs, or be approximated by solving one such dual program with a sufficiently small perturbation parameter. A globally convergent curved-search algorithm with a quadratic rate of convergence is designed for this purpose. Based on our testing results, we find that the computational procedure is very efficient and can be a viable approach for solving linear programming problems.

We investigate a cooperative game with two types of players envolved: Every player of the first type owns a unit size bin, and every player of the second type owns an item of size at most one. The value of a coalition of players is defined to be the maximum overall size of packed items over all packings of the items owned by the coalition into the bins owned by the coalition. We prove that fore=1/3 this cooperative bin packing game ise-balanced in the taxation model of Faigle and Kern (1993).