Anders Høeg Dohn

The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies

In the Home Care Crew Scheduling Problem a staff of home carers has to be assigned a number of visits to patients’ homes, such that the overall service level is maximised. The problem is a generalisation of the vehicle routing problem with time windows. Required travel time between visits and time windows of the visits must be respected. The challenge when assigning visits to home carers lies in the existence of soft preference constraints and in temporal dependencies between the start times of visits.

The manpower allocation problem with time windows and job-teaming constraints: A branch-and-price approach

The Manpower Allocation Problem with Time Windows, Job-Teaming Constraints and a limited number of teams (m-MAPTWTC) is a crew scheduling problem faced in several different contexts in the industry. The number of teams is predetermined and hence the objective is to create a schedule that will maximize utilization by leaving as few tasks uncompleted as possible. The schedule must respect working hours of the teams, transportation time between locations, and skill requirements and time windows of the tasks. Furthermore, some tasks are completed by multiple cooperating teams. Cooperating teams must initiate work simultaneously and hence this must be maintained in the schedule. The problem is solved using column generation and Branch-and-Bound. Optimal solutions are found in 11 of 12 test instances originating from real-life problems. The paper illustrates a way to exploit the close relations between scheduling and vehicle routing problems. The formulation as a routing problem gives a methodological benefit, leading to optimal solutions. A constraint on synchronization is imposed and successfully dealt with in the branching scheme.

The vehicle routing problem with time windows and temporal dependencies

In this article, we formulate the vehicle routing problem with time windows and temporal dependencies. The problem is an extension of the well studied vehicle routing problem with time windows. In addition to the usual constraints, a scheduled time of one visit may restrain the scheduling options of other visits. Special cases of temporal dependencies are synchronization and precedence constraints. Two compact formulations of the problem are introduced and the Dantzig–Wolfe decompositions of these formulations are presented to allow for a column generation-based solution approach. Temporal dependencies are modeled by generalized precedence constraints. Four different master problem formulations are proposed and it is shown that the formulations can be ranked according to the tightness with which they describe the solution space. A tailored time window branching is used to enforce feasibility on the relaxed master problems. Finally, a computational study is performed to quantitatively reveal strengths and weaknesses of the proposed formulations. It is concluded that, depending on the problem at hand, the best performance is achieved either by relaxing the generalized precedence constraints in the master problem, or by using a time-indexed model, where generalized precedence constraints are added as cuts when they become severely violated.

Optimising the Slab Yard Planning and Crane Scheduling Problem using a two-stage heuristic

In this paper, we present the Slab Yard Planning and Crane Scheduling Problem. The problem has its origin in steel production facilities with a large throughput. A slab yard is used as a buffer for slabs that are needed in the upcoming production. Slabs are transported by cranes and the problem considered here is concerned with the generation of schedules for these cranes. The problem is decomposed and modeled in two parts, namely a planning problem and a scheduling problem. In the planning problem, a set of crane operations is created to take the yard from its current state to a desired goal state. In the scheduling problem, an exact schedule for the cranes is generated, where each operation is assigned to a crane and is given a specific time of initiation. For both models, a thorough description of the modeling details is given along with a specification of objective criteria. Preliminary tests are run on a generic setup with simulated data. The test results are very promising. The production delays are reduced significantly in the new solutions compared with the corresponding delays observed in a simulation of manual planning.

A Column Generation-Based Heuristic for Rostering with Work Patterns

This paper addresses the Ground Crew Rostering Problem with Work Patterns, an important manpower planning problem arising in the ground operations of airline companies. We present a cutting stock-based integer programming formulation of the problem and describe a powerful heuristic decomposition approach, which utilizes column generation and variable fixing, to construct efficient rosters for a six-month time horizon. The time horizon is divided into smaller blocks, where overlaps between the blocks ensure continuity. The proposed methodology is able to circumvent one step of the conventional roster construction process by generating rosters directly based on the estimated workload. We demonstrate that this approach has the additional advantage of being able to easily incorporate robustness in the roster. Computational results on real-life instances confirm the efficiency of the approach.

Branch-and-price for staff rostering: An efficient implementation using generic programming and nested column generation

We present a novel generic programming implementation of a column-generation algorithm for the generalized staff rostering problem. The problem is represented as a generalized set partitioning model, which is able to capture commonly occurring problem characteristics given in the literature. Columns of the set partitioning problem are generated dynamically by solving a pricing subproblem, and constraint branching in a branch-and-bound framework is used to enforce integrality. The pricing problem is formulated as a novel three-stage nested shortest path problem with resource constraints that exploits the inherent problem structure. A very efficient implementation of this pricing problem is achieved by using generic programming principles in which careful use of the C++ pre-processor allows the generator to be customized for the target problem at compile-time. As well as decreasing run times, this new approach creates a more flexible modeling framework that is well suited to handling the variety of problems found in staff rostering. Comparison with a more-standard run-time customization approach shows that speedups of around a factor of 20 are achieved using our new approach. The adaption to a new problem is simple and the implementation is automatically adjusted internally according to the new definition. We present results for three practical rostering problems. The approach captures all features of each problem and is able to provide high-quality solutions in less than 15minutes. In two of the three instances, the optimal solution is found within this time frame.