Cor A. J. Hurkens

Short Shop Schedules

We consider the open shop, job shop, and flow shop scheduling problems with integral processing times. We give polynomial-time algorithms to determine if an instance has a schedule of length at most 3, and show that deciding if there is a schedule of length at most 4 is 𝒩𝒫-complete. The latter result implies that, unless 𝒫 = 𝒩𝒫, there does not exist a polynomial-time approximation algorithm for any of these problems that constructs a schedule with length guaranteed to be strictly less than 5/4 times the optimal length. This work constitutes the first nontrivial theoretical evidence that shop scheduling problems are hard to solve even approximately.

Process Discovery Using Integer Linear Programming

The research domain of process discovery aims at constructing a process model (e.g. a Petri net) which is an abstract representation of an execution log. Such a model should (1) be able to reproduce the log under consideration and (2) be independent of the number of cases in the log. In this paper, we present a process discovery algorithm where we use concepts taken from the language-based theory of regions, a well-known Petri net research area. We identify a number of shortcomings of this theory from the process discovery perspective, and we provide solutions based on integer linear programming.

Makespan minimization for chemical batch processes using non-uniform time grids

We present a mixed-integer linear programming model for minimizing the makespan of batch processes occurring in the chemical industry. The formulation of the model is based on the starting and processing times of the batches without using an external uniform time grid. A special form for the objective function is chosen and additional redundant constraints are added in order to speed up the solution process. A comparison with the classical uniform time discretization model shows that in many cases the size of the new model as well as its solution time is smaller. Computational results on several instances are reported. The modular structure of the model allows a combination with other continuous-time models for batch processing problems.

Incorporating the strength of MIP modeling in schedule construction

Linear programming techniques can be used in constructing schedules but their application is not trivial. This in particular holds true if a trade-off has to be made between computation time and solution quality. However, it turns out that - when handled with care - mixed integer linear programs may provide effective tools. This is demonstrated in the successful approach to the benchmark constructed for the 2007 ROADEF computation challenge on scheduling problems furnished by France Telecom.

Lower Bounds for the Head-Body-Tail Problem on Parallel Machines: A Computational Study of the Multiprocessor Flow Shop

The multiprocessor flow-shop is the generalization of the flow-shop in which each machine is replaced by a set of identical machines. As finding a minimum-length schedule is NP-hard, we set out to find good lower and upper bounds. The lower bounds are based on relaxation of the capacities of all machine sets except one. This results in a parallel-machine scheduling problem with release dates and delivery times, for which we derive a number of lower bounds. We pay special attention to the time complexity of algorithms for computing these bounds. To obtain the upper bounds a constructive algorithm in subsequent stages is used. We present an experimental comparison of the various lower and upper bounds for the multiprocessor flow-shop problem.

Stable multi-skill workforce assignments

This paper analyzes stability in multi-skill workforce assignments of technicians and jobs. In our stability analysis, we extend the notion of blocking pairs as stated in the Marriage model of Gale-Shapley to the multi-skill workforce assignment. It is shown that finding stable assignments is NP-hard. A special case turns out to be solvable in polynomial time. For the general case, we give a characterization of the set of stable assignments by means of linear inequalities involving binary variables. We propose an integer programming (IP) model to construct optimal stable assignments with several objectives. In the computational results, we observe that it is easier to attain stability in instances with easy jobs and we consider a range of instances to show how fast the solution time increases. Open questions and further directions are discussed in the conclusion section.

Complexity and approximation of an area packing problem

Motivated by an application in mobile telecommunication systems, we investigate a packing problem in which items are specified in terms of area constraints. We establish strong

Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances

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