Optimality aspects with assigning of Magistrates to Sessions and Teams of the Amsterdam Criminal Court

In the criminal court (Arrondissements rechtbank, sector strafrecht) of Amsterdam the assignment of magistrates (judges, officers, etc) to sessions needed to handle the cases presented, has become a problem last years mainly caused by the increase of so called mega-sessions. One complicating factor is that there are specialisations amongst the magistrates for sessions at different levels. Another one is that for some (severe) cases a team of three magistrates or judges are required (MK). The assignment takes a period of 4 weeks at a time in which each week up to 100 magistrates and 150 sessions have to be scheduled. The objective of this research is to develop an optimal decision support system for personnel [1] to work in teams with different functions, organised in different groups. With such a system, a scheduler could make assignments in a shorter time period, more reliable and at least with the same quality. In order to reach for an optimal mix of support and user friendliness against minimal construction time/costs, we used EXCEL (with Visual Basic) for the administration-input-report data representation orientated parts and FORTRAN for the combinatorial assignment parts. CPLEX was used to obtain optimal solutions. In general the problem described here can be characterized as a problem with a multiple conflicting objective function under overdetermined requirements with both qualitative and quantitative data [2]. The overall optimal assignment approach followed in this applied research is based on three main steps after the input of the relevant data, which is quite a problem in itself. Firstly, a so-called Availability Matrix is developed, which indicates which personnel can be assigned to which tasks, on an individual basis. In former presentations at PATAT conferences [3] the whole administrative system was explained in order to arrive at relevant, robust and reliable data. Database management is crucial here. Pre-processing and reduction rules were applied which reduced the solution space considerably without deleteting possible assignments. Next, in order to take into account the team assignments and the working conditions [4], a Combination Matrix is constructed indicating which tasks in the week the personnel can be assigned to. This assignment is still individually based. Finally, the Overall Schedule for the teams is constructed, giving a minimal difference between the total available working hours and the assigned ones: the objective function. The approach is demonstrated with a (small!) example in Tables 1..4, see Appendix. The general approach used is to generate a number of possible alternatives and pick the optimal one. In order to arrive always at a solution within a restricted time period we used a crash approach, a Greedy algorithm, a version of the Marriage Problem and an heuristic based on the Branch-And-Bound principle with integer linear programming [5]. The paradox here is that approaches easy to apply give in general solutions far from the optimal one. The more complex the approach the better the solution possibilities will be against a more time consuming character. Another question which is dealt with is the use of commercial available Integer-Linear-Programming packages in parts of the approach. The optimization part is still in a development stage, but a lot of experiments were executed and the results are promising. The administration part is already in use for some years.