Statistica Neerlandica

Van Hoesel, Stan; Wagelmans, Albert

doi: 10.1111/j.1467-9574.2007.00363.xpmid: N/A

Kolen, Antoon

doi: 10.1111/j.1467-9574.2007.00357.xpmid: N/A

We describe a genetic algorithm for the partial constraint satisfaction problem. The typical elements of a genetic algorithm, selection, mutation and cross‐over, are filled in with combinatorial ideas. For instance, cross‐over of two solutions is performed by taking the one or two domain elements in the solutions of each of the variables as the complete domain of the variable. Then a branch‐and‐bound method is used for solving this small instance. When tested on a class of frequency assignment problems this genetic algorithm produced the best known solutions for all test problems. This feeds the idea that combinatorial ideas may well be useful in genetic algorithms.

Van Hoesel, Stan P. M.; Wagelmans, Albert P. M.

doi: 10.1111/j.1467-9574.2007.00347.xpmid: N/A

In this paper we consider the p‐coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p‐coverage problem which runs in O (pn logn) time, n being the number of clients.

Oosten, Maarten; Rutten, Jeroen H. G. C.; Spieksma, Frits C. R.

doi: 10.1111/j.1467-9574.2007.00350.xpmid: N/A

In this paper, we consider the problem of disconnecting a graph by removing as few vertices as possible, such that no component of the disconnected graph has more than a given number of vertices. We give applications of this problem, present a formulation for it, and describe some polyhedral results. Furthermore, we establish ties with other polytopes and show how these relations can be used to obtain facets of our polytope. Finally, we give some computational results.

Pijls, Wim

doi: 10.1111/j.1467-9574.2007.00348.xpmid: N/A

Shortest path problems occupy an important position in operations research as well as in artificial intelligence. In this paper we study shortest path algorithms that exploit heuristic estimates. The well‐known algorithms are put into one framework. Besides, we present an interesting application of binary numbers in the shortest path theory.

Brauner, N.; Crama, Y.; Grigoriev, A.; Van De Klundert, J.

doi: 10.1111/j.1467-9574.2007.00362.xpmid: N/A

High multiplicity scheduling problems arise naturally in contemporary production settings where manufacturers combine economies of scale with high product variety. Despite their frequent occurrence in practice, the complexity of high multiplicity problems – as opposed to classical, single multiplicity problems – is in many cases not well understood. In this paper, we discuss various concepts and results that enable a better understanding of the nature and complexity of high multiplicity scheduling problems. The paper extends the framework presented in ( (2005) Vol. 9, pp. 313–323) for single machine, non‐preemptive high multiplicity scheduling problems, to more general classes of problems.

Dorndorf, Ulrich; Jaehn, Florian; Lin, Chen; Ma, Hui; Pesch, Erwin

doi: 10.1111/j.1467-9574.2007.00361.xpmid: N/A

This paper introduces models of robustness in flight gate assignments at airports. We briefly repeat the general flight gate assignment problem and disruptions occurring in airline scheduling. Recovery strategies and robust scheduling are surveyed as the main methods in disruption management. We present a non‐robust flight gate assignment model and incorporate two approaches of robustness.

Koster, Arie M. C. A.; Zymolka, Adrian

doi: 10.1111/j.1467-9574.2007.00351.xpmid: N/A

With the introduction of optical switching technology in telecommunication networks, all‐optical connections, so‐called lightpaths, can be established. Lightpaths have to be assigned a wavelength in such a way that no two lightpaths sharing a fiber use the same wavelength. The wavelength of operation can only be exchanged by the deployment of a wavelength converter. In this paper, we study the minimum converter wavelength assignment problem. We develop three integer programming formulations to minimize the number of converters and study their properties. Where the first two formulations lack the power to provide non‐trivial lower bounds, tight lower bounds can be computed by solving the linear relaxation of the third formulation by delayed column generation. In fact, the lower bound equals the best known solution value for all realistic instances at our disposal. In a computational study, we compare different strategies to enhance the column generation algorithm.

Kuijpers, Bart H. M.; Schotman, Peter C.

doi: 10.1111/j.1467-9574.2007.00349.xpmid: N/A

Valuation of the prepayment option in Dutch mortgages is complicated. In the Netherlands, mortgagors are not allowed to prepay the full mortgage loan without a compensating penalty. Only a limited amount of the initial mortgage loan can be prepaid penalty‐free. We introduce a general model formulation for the valuation of limited callable mortgages, based on binomial trees. This model can be used for determining both the optimal prepayment strategy and the value of embedded prepayment options. For some mortgage types the prepayment option can be valued exactly, whereas other types require approximative methods for efficient valuation. The heuristic we propose here determines the prepayment option value efficiently and accurately for general mortgage types.

Lok, Reinder B.; Morales, Dolores Romero; Vermeulen, Dries

doi: 10.1111/j.1467-9574.2007.00356.xpmid: N/A

For the allocation of heterogeneous items, it is known that the buyers‐are‐substitutes condition is necessary and sufficient to ensure that a pricing equilibrium can yield the same allocation and payments as the VCG mechanism. Furthermore, concavity of the corresponding transferable utility TU‐game guarantees that this VCG outcome can also be achieved by an ascending price auction. We show that concavity, and hence the buyers‐are‐substitutes condition, holds for the TU‐game of the assignment problem with general capacities. Therefore, the VCG mechanism is supported by a pricing equilibrium which can also be achieved by an ascending auction. We also show that the buyers‐are‐substitutes condition, and hence concavity, does not hold anymore for very natural and straightforward extensions of this problem. This shows that the necessity of the substitutes property is a considerable restriction on the applicability of the VCG mechanism.