Factores del éxito de la MDD desde la perspectiva del fabricante

Fikar and Hirsch (2017) is the only survey that specifically addresses home-health care rou- ting and scheduling problems. They categorized papers in the literature into two groups ; papers that studied single period and those that considered multi-period problems. Within each category, they discussed different objectives, constraints and solution methodologies. Moreover, Castillo-Salazar et al. (2016) provided a literature review on workforce scheduling and routing problems (WSRP) and shortly discussed some characteristics of home-health care problems as an example of WSRP. In the following, we review some of the most significant papers in home-health care routing and scheduling.

Eveborn et al. (2006) focused on staff scheduling in the public home-health system in Sweden. They formulated the problem as a set partitioning model and repetitively used a matching algorithm to assign visiting schedules to staff. In generating staff routes, they considered many constraints including time windows constraints, qualification of caregivers for assigned visits, and planned breaks for staff members.

Akjiratikarl et al. (2007) proposed a particle swarm algorithm for the scheduling of caregivers in the United Kingdom, where local authorities are responsible for providing home care services. In this problem, they aimed to minimize the total traveled distance providing that constraints on time windows and working hours must be satisfied.

Trautsamwieser et al. (2011) addressed a daily home care scheduling in the case of natural disasters. They formulated the problem as an MIP model minimizing the weighted sum of driving and waiting times, and the dissatisfaction levels of clients and nurses. The proposed model is only capable of solving small-sized instances. Therefore, they devised a variable neighbourhood search algorithm for larger instances. They evaluated the proposed algorithms

on data sets from Austrian Red Cross.

Hiermann et al. (2015) studied a multimodal home-healthcare scheduling problem in an Austrian home-health care provider. In this problem, “multimodal” refers to different trans- portation modes that caregivers can use to travel. The objective was to assign caregivers to patients and find efficient routes for them while addressing caregivers and patients prefe- rences. They proposed a two-step method where, in the first step, a constraint programming algorithm finds initial solutions and, in the second-step, four metaheuristic algorithms im- prove the solutions.

Mankowska et al. (2014) addressed a daily home-health care routing and scheduling problem with interdependent services. In home-health care context, interdependent services refer to services that caregivers must provide to patients simultaneously or with some time lags. They also took into account individual service requirements of patients, qualifications of nurses. They proposed an MIP model to minimize the sum of total traveled distance, and total tardiness in serving patients. They also proposed some constructive, local search, and variable neighborhood search heuristics to find solutions for large instances.

Bowers et al. (2015) studied routing and scheduling of midwives to visit mothers at homes. They emphasized that the continuity of case by the same midwife ensures a better relationship between mothers and health staff. They applied a variant of a multiple traveling salesman algorithm incorporating staff and mother preferences.

Braekers et al. (2016) studied a home care routing and scheduling problem considering many practical details such as skills, working regulations and overtime for nurses, travel costs depending on the transportation mode, hard time windows, and patients’ preferences on nurses and visit times. They proposed a bi-objective MIP model to minimize operational costs and maximize the service level simultaneously. For solving large instances, they also devised a metaheuristic algorithm that applies a large neighborhood search algorithm in a multi-directional local search structure.

Some authors treated home-health care routing and scheduling as a vehicle routing problem (VRP) and formulated the problem in a VRP setting (Bredström and Rönnqvist 2008, Ras- mussen et al. 2012, Mısır et al. 2015). Bredström and Rönnqvist (2008) studied a vehicle routing and scheduling problem with temporal precedence and synchronization constraints. The temporal constraint means that, for some customers, more than one visit is required and there must be a precedence order with time lags between them. They considered the application of this problem in the home-health care context and proposed an MIP and a heuristic solution algorithm.

Rasmussen et al. (2012) considered a home care scheduling problem with temporal, and soft preference constraints as a generalization of vehicle routing problem with time windows. They formulated the problem as a set partitioning problem and proposed a branch-and-price algorithm. In the proposed algorithm, temporal constraints are enforced within the branching procedure. Considering the soft preference constraints, they also introduced a visit clustering approach and showed that it decreases run time significantly.

Mısır et al. (2015) evaluated the performance of generalized heuristics in solving routing and rostering problem. They considered a home-health care routing and scheduling problem as one of the relevant problems in this category. In this problem, they emphasized on the patients preferences to nurses and vice versa. They also considered task synchronization for serving some patients and referred to it as “connected activities”. All constraints that they considered in this problem are soft constraints.

Some researchers extended the home-health care routing and scheduling by considering the weekly planning of visits (Nickel et al. 2012, Shao et al. 2012, Bard et al. 2014a,b, Traut- samwieser and Hirsch 2014, Cappanera and Scutellà 2015). Nickel et al. (2012) addressed a home-health care planning and scheduling in Germany. In the planning horizon, they decide on the visiting periods for patients during a week. In the scheduling horizon, they fix the staff routes and schedules. They also took into account the fact that operational decisions must be consistent as much as possible with the master schedule already fixed for a me- dium term. In this work, the objective function minimizes the weighted sum of the number of unscheduled patients, the patient-nurse loyalty penalty, caregivers’ overtimes, and the to- tal traveled distance. They proposed metaheuristic algorithms that were combined with a constraint programming model.

Shao et al. (2012) studied home-care planning, scheduling, and routing problem where a number of multi-skilled therapists visits patients over a week. The objective was to find weekly schedules for therapists such that the travel and administrative costs were minimized. They formulated the problem as an MIP model and because of its failure they devised a greedy randomized adaptive search procedure (GRASP) algorithm that generates tours for therapists in parallel. Bard et al. (2014a) studied the same problem and stated that the parallel GRASP developed by Shao et al. (2012) failed in instances with tight constraints. They addressed this issue by devising a GRASP algorithm that generates tours sequentially. Bard et al. (2014b) took a step forward and developed a branch-and-price-and-cut algorithm for the same problem. Their algorithm finds near optimal solutions for instances with up to 162 visits and 5 therapists.

duling problem considering working regulations such as breaks, maximum daily working time, and weekly rest times. They developed an MIP model. Then they reformulated it to a mas- ter problem and subproblems framework and applied a branch-and-price solution algorithm. They showed that the proposed branch-and-price algorithm is capable of solving instances with 45 patients, and 203 visits in the week.

Cappanera and Scutellà (2015) proposed an MIP model for simultaneously 1) assigning ap- propriately skilled operators to patients, 2) scheduling of visits, and 3) routing of operators. They aimed to optimize two balancing objective functions for palliative and terminal pa- tients. The first objective function maximizes the minimum utilization factors of operators, while the second one minimizes the maximum utilization of operators.

Papers cited above studied static home-health care routing and scheduling problems. As an exception, Bennett and Erera (2011) considered a home-health care routing and scheduling where patients arrive dynamically and nurses must visit them several times a week over a predetermined number of weeks. Appointment times for each visit must be selected from a list of available options. Visits must repeat at the same date and times during the service duration. They proposed a rolling horizon myopic planning approach to maximize the number of served patients in a special case that a single nurse serves all patients.

Yuan et al. (2015) is the only paper in the literature that studied home-health care routing and scheduling with stochastic service times. They proposed a two-stage stochastic programming model and then reformulated it to a set partitioning model and applied column generation and branch-and-price solution algorithms. They reported computational results for instances with up to 50 patients.