W.K. Klein Haneveld

Crop succession requirements in agricultural production planning

A method is proposed to write crop succession requirements as linear constraints in an LP-based model for agricultural production planning. Crop succession information is given in the form of a set of inadmissible successions of crops. The decision variables represent the areas where a certain admissible sequence of crops is cultivated. The number of decision variables may be reduced by forming suitable combinations of crop sequences. For this purpose, an algorithm is presented. Also, multi-year linear programming models for farm production planning containing crop succession constraints are considered. It is shown that, under some regularity conditions, a stationary cropping plan is an optimal solution of such a model. Finally, it is discussed how to determine, given a collection of inadmissible sequences, crop sequences which are inadmissible but do not contain inadmissible subsequences. The length of the longest of these sequences determines the length of the crop sequences taken into account in the model.

A construction method in parametric programming

We consider a linear programming problem, with two parameters in the objective function, and present an algorithm for finding the decomposition of the parameter space into maximal polyhedral areas in which particular basic solutions are optimal. Special attention is paid to fill up areas of degenerate solutions.

Convex Approximations for Totally Unimodular Integer Recourse Models: A Uniform Error Bound

We consider a class of convex approximations for totally unimodular (TU) integer recourse models and derive a uniform error bound by exploiting properties of the total variation of the probability density functions involved. For simple integer recourse models this error bound is tight and improves the existing one by a factor 2, whereas for TU integer recourse models this is the first nontrivial error bound available. The bound ensures that the performance of the approximations is good as long as the total variations of the densities of all random variables in the model are small enough.

Optimizing existing railway timetables by means of stochastic programming

We present some models to find the best allocation of a limited amount of so-called running time supplements (extra minutes added to a timetable to reduce delays) on a railway line. By the best allocation, we mean the solution under which the sum of expected delays is minimal. Instead of trying to invent a completely new timetable, our aim is to finely adjust an already existing and well-functioning one. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, following Vromans [9]. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We include a case study that we managed to solve about 180 times faster than it was solved in [9]. By comparing our solution with other, seemingly intuitive solutions, we show that finding the best allocation is not obvious, and implementing it in practice promises a significant improvement in the punctuality of trains. A technique to estimate the model parameters from empirical data and an approximating deterministic problem are also presented, along with some practical ideas that are meant to enhance the applicability of our models.

A two-stage model for a day-ahead paratransit planning problem

Abstract We consider a dynamic planning problem for the transport of elderly and disabled people. In particular, we focus on a decision to take one day ahead: which requests should be served with own vehicles, and which requests should be subcontracted to taxis? We call this problem the Day-ahead Paratransit Planning problem (DaPP). The model developed for DaPP is a non-standard two-stage integer recourse model from stochastic programming. Both stages consist of two parts: requests are first clustered into routes, and these routes are in turn assigned to vehicles (own vehicles and taxis). To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets.