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.

Efficient Deployment of Mobile Detectors for Security Applications

We present a real-world problem that arises in security threat detection applications. The problem consists of deploying mobile detectors on moving units that follow predefined routes. Examples of such units are buses, coaches, and trolleys. Due to a limited budget not all available units can be equipped with a detector. The goal is to equip a subset of units such that the utility of the resulting coverage is maximized. Existing methods for detector deployment are designed to place detectors in fixed locations and are therefore not applicable to the problem considered here. We formulate the planning problem as a binary linear program and present a coverage heuristic for generating effective deployments in short CPU time. The heuristic has theoretical performance guarantees for important special cases of the problem. The effectiveness of the coverage heuristic is demonstrated in a computational analysis based on 28 instances that we derived from real-world data.

A note on the selection of priority rules in software packages for project management

Various software packages for project management include a procedure for resource-constrained scheduling. In several packages, the user can influence this procedure by selecting a priority rule. However, the resource-allocation methods that are implemented in the procedures are proprietary information; therefore, the question of how the priority-rule selection impacts the performance of the procedures arises. We experimentally evaluate the resource-allocation methods of eight recent software packages using the 600 instances of the PSPLIB J120 test set. The results of our analysis indicate that applying the default rule tends to outperform a randomly selected rule, whereas applying two randomly selected rules tends to outperform the default rule. Applying a small set of more than two rules further improves the project durations considerably. However, a large number of rules must be applied to obtain the best possible project durations.