Q2. What are the future works mentioned in the paper "The home care crew scheduling problem: preference-based visit clustering and temporal dependencies" ?
The authors see a number of directions in which future work on this problem could go.
Q3. What is the reason why the generalised precedence constraints are relaxed?
The relatively simple expression (20) for the reduced costs of a column is one of the reasons why the generalised precedence constraints are relaxed.
Q4. What is the way to solve the Home Health Care Problem?
Bertels and Fahle (2006) use a combination of linear programming, constraint programming and metaheuristics for solving what they call the Home Health Care Problem.
Q5. What is the reason why the constraint branching strategy is called?
The authors will exploit the strong integer properties of the constraint matrix of the RMP to apply a so-called constraint branching strategy, see Ryan and Foster (1981).
Q6. What is the goal of the rescheduling?
The goal of the rescheduling is to provide a new, feasible plan very fast, i.e. within minutes, with as few alterations to the original plan as possible.
Q7. How can the authors model the temporal dependencies of visits?
These temporal dependencies can be modelled by introducing generalised precedence constraints of the formσi + pij ≤ σj ,where σi denotes the start time of visit i, and pij ∈ R quantifies the required gap.
Q8. What are the possible options for the visit?
Possible options are to: reduce the duration of the visit, extend the time window of the visit or extend the work shift of one of the caretakers.
Q9. What is the value of the time window for caretaker k?
For algorithmic reasons, the authors introduce artificial visits 0k and nk as the start visit respectively end visit for caretaker k ∈ K, and the authors define N k = C ∪ {0k, nk} as the set of all potential visits for caretaker k.
Q10. How many times did the visit clustering scheme decrease run times?
The tests have shown that by using clusters with only preferred visits, run times were significantly decreased, while there was only a loss of quality for few instances.
Q11. What are the constraints enforced in the branching?
All temporal dependencies are modelled as generalised precedence constraints, and these constraints are enforced through the branching.
Q12. What is the reason why the clustering is so sensible?
This is also sensible, as the clustering is preference-based and as such independent of types and numbers of temporal dependencies.
Q13. What is the generalised precedence constraint for a set of pairs of visits?
The set of pairs of visits (i, j) ∈ C×C for which a generalised precedence constraint exists is denoted P.As can be seen, this constraint simply implies that j starts minimum pij time units after i.
Q14. How many generalised precedence constraints are generated for each of these sets?
Sets A, B, and C, where the number of generalised precedence constraints approximately is, respectively, 10%, 20%, and 30% of the number of visits.
Q15. What is the way to deal with an uncovered visit?
Constraint adjustments are another way of dealing with an uncovered visit, so that it is possible to fit the visit into the schedule anyway.
Q16. Why is it possible to improve the solution in the branch-and-bound tree?
This is possible, because the authors reach the time out limit on some test runs, and therefore the returned solution is not necessarily optimal, but only the best solution in the branch-and-bound tree at time out.