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One of the main points of criticism on academic research in operations research (management science ) is that there is too much emphasis on the mathematical aspects of the discipline. In particular, the mathematical models that lend themselves to rigorous mathematical analysis are often rough simplifications of the actual decision problems that need to be solved in practice. Moreover, advanced mathematical solution methods may lead to overkill, since sometimes acceptable solutions may already be found by relatively simple ad hoc methods. In this address, we argue that although these observations may be true, this does not necessarily mean that mathematically oriented research is not useful in solving practical decision problems. We believe that the criticism ignores both the role of academic research within the discipline as well as the fact that certain recent successful applications of operations research owe much to mathematically oriented research. We illustrate the usefulness of this type of research by discussing research projects in container logistics and public transport scheduling.Rede, in verkorte vorm uitgesproken op vrijdag 20 september 2002 bij de aanvaarding van het ambt van bijzonder hoogleraar aan de Faculteit der Economische Wetenschappen, vanwege de Vereniging Trustfonds Erasmus Universiteit Rotterdam, met als leeropdracht Mathematische Besliskunde, in het bijzonder Toepassingen in Transport en Logistiek

Calculation of Stability Radii for Combinatorial Optimization Problems

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min-max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to the tolerance approach to sensitivity analysis

An Algorithm for Single-item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs

We consider the Capacitated Economic Lot Size problem with piecewise linear production costs and general holding costs, which is an NP-hard problem but solvable in pseudo-polynomial time. A straightforward dynamic programming approach to this problem results in an [TeX: $O(n^2 \\bar{c} \\bar{d} )$] algorithm, where [TeX: $n$] is the number of periods, and [TeX: $\\bar d$ and $\\bar c$] are the average demand and the average production capacity over the $n$ periods, respectively. However, we present a dynamic programming procedure with complexity [TeX: $O(n^2 \\bar{q} \\bar{d} )$], where [TeX: $\\bar q$] is the average number of pieces of the production cost functions. In particular, this means that problems in which the production functions consist of a fixed set-up cost plus a linear variable cost are solved in [TeX: $O(n^2 \\bar{d})$] time. Hence, the running time of our algorithm is only linearly dependent on the magnitude of the data. This result also holds if extensions such as backlogging and start-up costs are considered. Moreover, computational experiments indicate that the algorithm is capable of solving quite large problem instances within a reasonable amount of time. For example, the average time needed to solve test instances with 96 periods, 8 pieces in every production function and average demand of 100 units, is approximately 40 seconds on a SUN SPARC 5 workstation

The two-dimensional cutting stock problem within the roller blind production process

In this paper we consider a two-dimensional cutting stock problem encountered at a large manufacturer of window covering products. The problem occurs in the production process of made-to-measure roller blinds. We develop a solution method that takes into account the characteristics of the specific problem. In particular, we deal with the fact that fabrics may contain small defects that should end up with the waste. Comparison to previous practice shows significant waste reductions

Effective algorithms for integrated scheduling of handling equipment at automated container terminals

In this paper we consider the problem of integrated scheduling of various types of handling equipment at an automated container terminal, where the objective is to minimize the makespan of the schedule. We present a Branch & Bound algorithm that uses various combinatorial lower bounds. Computational experiments show that this algorithm is able to produce optimal or near optimal schedules for instances of practical size in a reasonable time. We also develop a Beam Search heuristic that can be used to tackle very large problem instances. Our experiments show that for such instances the heuristic obtains close to optimal solutions in a reasonable time

Effective algorithms for integrated scheduling of handling equipment at automated container terminals

In this paper we consider the problem of integrated scheduling of various types of handling equipment at an automated container terminal, where the objective is to minimize the makespan of the schedule. We present a Branch & Bound algorithm that uses various combinatorial lower bounds. Computational experiments show that this algorithm is able to produce optimal or near optimal schedules for instances of practical size in a reasonable time. We also develop a Beam Search heuristic that can be used to tackle very large problem instances. Our experiments show that for such instances the heuristic obtains close to optimal solutions in a reasonable time

Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems

NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist, by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models

A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we perform a sensitivity analysis on our main assumption that the travel times of the trips are known exactly a certain amount of time before actual operation. We provide extensive computational results on some real-world data instances of a large public transport company in the Netherlands. Due to the complexity of the vehicle and crew scheduling problem, we solve only small and medium-sized instances with such a dynamic approach. We show that the results are good in the case of a single depot. However, in the multiple-depot case, the dynamic approach does not perform so well. We investigate why this is the case and conclude that the fact that the instance has to be split in several smaller ones, has a negative effect on the performance

A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is tight, this is in contrast to the optimality property of the economic order quantity (EOQ) model, where setup cost and holding cost are perfectly balanced. Furthermore, we show that this property can be used for the design of a new heuristic and that the result may be useful in worst case analysis

A Note on "Stability of the Constant Cost Dynamic Lot Size Model" by K. Richter

In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution