Multiple Service Home Health Care Routing and Scheduling Problem: A Mathematical Model

A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand

Integration routing and scheduling for multiple home health care centers using a multi-objective cooperation evolutionary algorithm with stochastic simulation

This chapter investigates a vehicle routing problem with synchronization requirements for the services provided to customers. The problem finds an application in the home health care branch, where staff members of health care agencies have to be routed and services at patients’ homes have to be scheduled. The latter can involve simultaneous services, where two staff members have to serve one patient jointly, and services with given precedence, where two service operations have to be provided to a patient within a given time distance. This paper presents a Benders’ decomposition method for solving this problem exactly.

In the home healthcare routing and scheduling problem (HHCRSP), nurses are allocated to a variety of services demanded by clients during a planning horizon. The properties of this problem resemble vehicle routing and nurse scheduling. To propose an efficient solution, the authors consider various issues such as multi-depot, travelling time, time windows, synchronisation, the qualification levels, and other features of nurses and clients. In addition, the continuity of care and work overload should not be ignored in this perspective. First, the authors developed a model in which the continuity of care is redefined by considering connected (synchronous) jobs and the work overload is formulated considering nurse-to-patient staffing ratio. Second, a two-stage solution approach based on a cluster-assign algorithm and variable neighbourhood search (VNS) and variable neighbourhood descent (VND) algorithms are tested on a series of large-scale instances. Computational results present the relations and trade-offs among the aforementioned issues.

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O(n3). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O(n4). We demonstrate that with careful implementation it is possible, in most cases, to maintain the O(n3) complexity or, in a few cases, increase the time complexity to O(n3 log n). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics.

This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems. These algorithms exploit the two-faceted decision structure inherent to this problem class: First, assigning demands to vehicles and, second, routing each vehicle through its assigned demand stops. We describe the application of cyclic transfers to vehicle routing and scheduling problems. Then we determine the worst-case performance of these algorithms for several classes of vehicle routing and scheduling problems. Next, we develop computationally efficient methods for finding negative cost cyclic transfers. Finally, we present computational results for three diverse vehicle routing and scheduling problems, which collectively incorporate a variety of constraint and objective function structures. Our results show that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important vehicle routing and scheduling problems. Most importantly, they represent a novel approach to solution improvement which holds promise in many vehicle routing and scheduling problem domains.

The chapter by Teodor Crainic in this book discusses the long haul truck routing problem. Some of the key differences between the long haul truck routing problem and the vehicle routing problems considered in this chapter are as follows: 1. In the long haul truck routing problem, the routes can extend over several days whereas, in the vehicle routing problem described herein, the routes are of one-day duration. 2. In the long haul truck routing problem, the locations can be scattered over a wide region, even the entire United States, whereas in the vehicle routing problems considered herein, the locations requiring service are packed in a small region.

Home health care routing and scheduling problems: a literature review

Home health care nurse routing and scheduling problem considering ergonomic risk factors

SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.

Dynamic routing-scheduling problem for home health care considering caregiver-patient compatibility

This data corresponds to a set of 60 instances for the Home Health Care Routing and Scheduling Problem. The instances are split in three groups : Small, Medium and Large. All the important informations are reported in the "Read Me" file.

Solving large-scale vehicle routing problems with complex additional constraints such as the problem of combined vehicle routing and break scheduling is very difficult. Even large-scale vehicle routing problems with time windows without additional constraints can only be solved to optimality for problems with tight time windows and a structure which allows only few possible solutions (Pisinger and Ropke, 2007). Therefore, heuristics and metaheuristics are mainly applied to solve these problems (Funke et al., 2005). In the following the restricted dynamic programming (DP) heuristic developed by Kok et al. (2010) is presented and utilized for solving the problem of combined vehicle routing and break scheduling both from a centralized and from a distributed decision making perspective.KeywordsRest PeriodVehicle Route ProblemVehicle RouteDriving TimeTotal Travel DistanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A bi-criteria heuristic for the vehicle routing problem with time windows

In many countries, truck drivers are obliged by law to take a break or a rest regularly. In the European Union, for example, this is governed by Regulation (EC) No. 561/2006. It states that, after 4.5 hours of driving a truck, it is prohibited to continue driving until a 45-minute break is taken. After accumulating a driving time of 9 hours, a rest of 11 hours is mandatory. These are only two rules of a considerably longer list of break rules set out in this regulation, and it is only one of many regulations there are worldwide. Such breaks and rests have to be planned into the work schedules of the drivers. In general, the task of a dispatcher is to find routes and schedules for the truck drivers such that every customer is served in time. With the regulations on drivers’ working hours, both the routing and the scheduling parts of the task become more challenging. In this thesis, we study several optimization problems that arise in the context of drivers’ working hours. One is known as the truck driver scheduling problem. Here, a sequence of customers is given, and the task is to find a schedule for a driver such that every customer is visited within one of the customer’s time windows and the applicable break rules are complied with. Depending on the regarded break rules, we get different variants of the truck driver scheduling problem. Little is known about the complexity of the individual problem variants. One of the two focal points of this thesis is to present polynomial-time algorithms for different variants of the problem, for which polynomial-time algorithms are not yet known. With this, we can falsify the NP-hardness conjecture of Xu et al. (2003) for an important special case of their considered problem variant. But this thesis is not only about scheduling, it is also about routing. This constitutes the second focal point of this thesis. We present an integrated approach for the vehicle routing and truck driver scheduling problem. Here, a route refers to the order in which the customers are visited. However, the meaning of route is twofold. In another studied problem, the truck driver scheduling and routing problem, it means the sequence of road segments that the driver takes to drive from one customer to the other. In this problem, we take into account that, before taking a break, truck drivers need to head for a rest area or at least a spot where their vehicle can be parked. We even consider the time-dependent scenario in which driving times on road segments vary over the day due to rush hours. Both an exact approach and a heuristic for this problem are presented, and both are evaluated on a recent road network instance of Germany. It turns out that the heuristic is at least two orders of magnitude faster but still hardly worse than the exact approach. Our main motivation is the application in practice. It is our aim – and this is especially true for the second focal point – to provide helpful algorithms that may find their way into software products for dispatchers, like the described approach for the vehicle routing and truck driver scheduling problem is already integrated into the vehicle route planning tools of a commercial provider of logistics optimization software.