An MILP-based heuristic for staff scheduling problems with acceptance levels

We present a real-world staff-assignment problem that was reported to us by a provider of an online workforce scheduling software. The problem consists of assigning employees to work shifts subject to a large variety of requirements related to work laws, work shift compatibility, workload balancing, and personal preferences of employees. A target value is given for each requirement, and all possible deviations from these values are associated with acceptance levels. The objective is to minimize the total number of deviations in ascending order of the acceptance levels. We present an exact lexicographic goal programming MILP formulation and an MILP-based heuristic. The heuristic consists of two phases: in the first phase a feasible schedule is built and in the second phase parts of the schedule are iteratively re-optimized by applying an exact MILP model. A major advantage of such MILP-based approaches is the flexibility to account for additional constraints or modified planning objectives, which is important as the requirements may vary depending on the company or planning period. The applicability of the heuristic is demonstrated for a test set derived from real-world data. Our computational results indicate that the heuristic is able to devise optimal solutions to non-trivial problem instances, and outperforms the exact lexicographic goal programming formulation on medium- and large-sized problem instances.

Efficient list-generation techniques for scheduling assessment centers

Human resources managers often conduct assessment centers to evaluate candidates for a job position. During an assessment center, the candidates perform a series of tasks. The tasks require one or two assessors (e.g., managers or psychologists) that observe and evaluate the candidates. If an exercise is designed as a role-play, an actor is required who plays, e.g., an unhappy customer with whom the candidate has to deal with. Besides performing the tasks, each candidate has a lunch break within a prescribed time window. Each candidate should be observed by approximately half the number of the assessors; however, an assessor may not observe a candidate if they personally know each other. The planning problem consists of determining (1) resource-feasible start times of all tasks and lunch breaks and (2) a feasible assignment of assessors to candidates, such that the assessment center duration is minimized. We present a list-scheduling heuristic that generates feasible schedules for such assessment centers. We propose several novel techniques to generate the respective task lists. Our computational results indicate that our approach is capable of devising optimal or near-optimal schedules for real-world instances within short CPU time.

A heuristic approach for scheduling assessment centers

Human resources managers often use assessment centers to evaluate candidates for a job position. During an assessment center, the candidates perform a series of exercises. The exercises require one or two assessors (e.g., managers or psychologists) that observe and evaluate the candidate. If an exercise is designed as a role-play, an actor is required as well which plays, e.g., an unhappy customer with whom the candidate has to deal with. Besides performing the exercises, the candidates have a lunch break within a prescribed time window. Each candidate should be observed by approximately half the number of the assessors. Moreover, an assessor cannot be assigned to a candidate if they personally know each other. The planning problem consists of determining (1) resource-feasible start times of all exercises and lunch breaks and (2) a feasible assignment of assessors to candidates, such that the assessment center duration is minimized. We propose a list-scheduling heuristic that generates feasible schedules for such assessment centers. We develop novel procedures for devising an appropriate scheduling list and for incorporating the problem-specific constraints. Our computational results indicate that our approach is capable of devising optimal or near-optimal solutions to real-world instances within short CPU time.

Future water quality monitoring--adapting tools to deal with mixtures of pollutants in water resource management.

Environmental quality monitoring of water resources is challenged with providing the basis for safeguarding the environment against adverse biological effects of anthropogenic chemical contamination from diffuse and point sources. While current regulatory efforts focus on monitoring and assessing a few legacy chemicals, many more anthropogenic chemicals can be detected simultaneously in our aquatic resources. However, exposure to chemical mixtures does not necessarily translate into adverse biological effects nor clearly shows whether mitigation measures are needed. Thus, the question which mixtures are present and which have associated combined effects becomes central for defining adequate monitoring and assessment strategies. Here we describe the vision of the international, EU-funded project SOLUTIONS, where three routes are explored to link the occurrence of chemical mixtures at specific sites to the assessment of adverse biological combination effects. First of all, multi-residue target and non-target screening techniques covering a broader range of anticipated chemicals co-occurring in the environment are being developed. By improving sensitivity and detection limits for known bioactive compounds of concern, new analytical chemistry data for multiple components can be obtained and used to characterise priority mixtures. This information on chemical occurrence will be used to predict mixture toxicity and to derive combined effect estimates suitable for advancing environmental quality standards. Secondly, bioanalytical tools will be explored to provide aggregate bioactivity measures integrating all components that produce common (adverse) outcomes even for mixtures of varying compositions. The ambition is to provide comprehensive arrays of effect-based tools and trait-based field observations that link multiple chemical exposures to various environmental protection goals more directly and to provide improved in situ observations for impact assessment of mixtures. Thirdly, effect-directed analysis (EDA) will be applied to identify major drivers of mixture toxicity. Refinements of EDA include the use of statistical approaches with monitoring information for guidance of experimental EDA studies. These three approaches will be explored using case studies at the Danube and Rhine river basins as well as rivers of the Iberian Peninsula. The synthesis of findings will be organised to provide guidance for future solution-oriented environmental monitoring and explore more systematic ways to assess mixture exposures and combination effects in future water quality monitoring.