The vehicle routing problem

Personnel scheduling: A literature review

Task allocation is an important aspect of many multi-robot systems. The features and complexity of multi-robot task allocation (MRTA) problems are dictated by the requirements of the particular domain under consideration. These problems can range from those involving instantaneous distribution of simple, independent tasks among members of a homogenous team, to those requiring the time-extended scheduling of complex interrelated multi-step tasks for members of a heterogenous team related by several constraints. The existing widely used taxonomy for task allocation in multi-robot systems was designed for problems with independent tasks and does not deal with problems with interrelated utilities and constraints. While that taxonomy was a ground-breaking contribution to the MRTA literature, a survey of recent work in MRTA reveals that it is no longer a sufficient taxonomy, due to the increasing importance of interrelated utilities and constraints in realistic MRTA problems under consideration. Thus, in this paper, we present a new, comprehensive taxonomy, iTax, that explicitly takes into consideration the issues of interrelated utilities and constraints. Our taxonomy maps categories of MRTA problems to existing mathematical models from combinatorial optimization and operations research, and hence draws important parallels between robotics and these fields.

A comprehensive taxonomy for multi-robot task allocation

Home health care routing and scheduling

This paper presents a model for the daily planning of health care services carried out at patients’ homes by staff members of a home care company. The planning takes into account individual service requirements of the patients, individual qualifications of the staff and possible interdependencies between different service operations. Interdependencies of services can include, for example, a temporal separation of two services as is required if drugs have to be administered a certain time before providing a meal. Other services like handling a disabled patient may require two staff members working together at a patient’s home. The time preferences of patients are included in terms of given time windows. In this paper, we propose a planning approach for the described problem, which can be used for optimizing economical and service oriented measures of performance. A mathematical model formulation is proposed together with a powerful heuristic based on a sophisticated solution representation.

The home health care routing and scheduling problem with interdependent services.

https://orbit.dtu.dk/files/4530526/2010_11.pdf

The Home Care Crew Scheduling Problem:: Preference-Based Visit Clustering and Temporal Dependencies

In the Home Care Crew Scheduling Problem (HCCSP) a staff of caretakers has to be assigned a number of tasks, such that the total number of assigned tasks is maximised. The tasks have different locations and positions in time, and travelling time and time windows must be respected. The challenge when assigning tasks to caretakers lies in the existence of several soft constraints and indeed also in timewise constraints connecting the tasks. Preferably all of these constraints are satisfied, however for different reasons, this is not always possible. We call a solution to the problem home care optimal, if it satisfies all soft constraints. The problem originates from the scheduling of tasks in the home care sector and has many similarities with the well-studied Vehicle Routing Problem with Time Windows (VRPTW) and the Crew Scheduling Problem with Time Windows (CSPTW). Former approaches to solving the HCCSP involve the use of heuristic methods. In this thesis, we will show that by using an exact algorithm as the basis and then modifying this intelligently, it is possible to generate home care optimal solutions which are in general better than the solutions found by the use of heuristics. The thesis constitutes a proof-of-concept and only focuses on the efficiency of the algorithm to some extent. The developed exact algorithm is based on a branch-and-price approach using column generation. The algorithm is tested on real-life problem instances supplied by the Danish company Zealand Care and we obtain solutions that are near to home care optimal in most cases. The problem is decomposed into a master and a subproblem. We model a very general precedence constraint that captures all timewise constraints from real-life, and we handle precedence constraints in the branching, which we have not seen elsewhere in the literature. We devise an exact label setting algorithm for solving the Elementary Shortest Path Problem with Resource Constraints (ESPPRC) subproblem. Solving the subproblem constitutes a substantial impact on the overall running time of the branch-and-price algorithm. To counteract this, intelligent reductions of the ESPPRC networks are introduced. When reducing the ESPPRC networks, the number of unassigned tasks may increase, hence the branch-and-price algorithm is extended to handle tasks that are unassigned as a consequence of the reductions of the ESPPRC networks.
 The reductions in the ESPPRC networks and the changes to the branchand-price algorithm result in improvements of both the quality of the solutions, many of which are close to being home care optimal, and the overall efficiency of the algorithm.

The Home Care Crew Scheduling Problem

The present paper addresses the problem of allocating check-in counters to check-in groups (single flight or common-use areas) in airports. The problem is formulated as an integer programming problem and takes airline preferences, the distribution of queues in the terminal areas, and the distribution of baggage inflow to the take-away belts into consideration. A case study demonstrates the successful implementation of the model in an optimization tool developed at Copenhagen Airport (CPH). The optimization tool has helped CPH improve the distribution of queues and baggage inflow in the terminals for international departures and led to a better utilization of the existing check-in counters, enabling CPH to both reduce and postpone the investments in additional check-in counters.

Tor Fog Justesen

Papers

The Home Care Crew Scheduling Problem:: Preference-Based Visit Clustering and Temporal Dependencies

The Home Care Crew Scheduling Problem

Allocation of Ground Handling Resources at Copenhagen Airport

Aircraft Stand Allocation with Associated Resource Scheduling