Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms...

This article is a survey about recent developments in the area of test sets of families of linear integer programs. Test sets are finite subsets of the integer lattice that allow to improve any given feasible non-optimal point of an integer program by one element in the set. There are various...

The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even...

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are...

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear...

We consider the problem of estimating optima of integer programs { max <Emphasis Type="Bold">cx | A <Emphasis Type="Bold">x≤<Emphasis Type="Bold">b,<Emphasis Type="Bold">0≤<Emphasis Type="Bold">x≤<Emphasis Type="Bold">1, <Emphasis Type="Bold">x− integral} where <Emphasis Type="Bold">b<Emphasis Type="Bold">0, <Emphasis Type="Bold">c≥<Emphasis Type="Bold">0 are rational vectors and A is an arbitrary rational m×n matrix. Using randomized rounding we find an efficiently verifiable sufficient condition for optima of such...</emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis></emphasis>

We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the...

We consider the design of line plans in public transport at a minimal total cost. Both, linear and nonlinear integer programming are adequate and intuitive modeling approaches for this problem. We present a heuristic variable fixing procedure which builds on problem knowledge from both...

The coupled task problem is to schedule jobs on a single machine where each job consists of two subtasks and where the second subtask has to be started after a given time interval with respect to the first one. The problem has several applications and is NP-hard. In this paper we present a...