A multistage optimisation algorithm for the large vehicle routing problem with time windows and synchronised visits

Abstract

We propose a multistage algorithm for the Vehicle Routing Problem with Time Windows and Synchronised Visits, which is capable of solving large problem instances arising in Home Health Care applications. The algorithm is based on a Constraint Programming formulation of the daily Home Care Scheduling and Routing Problem. It contains visits with hard time windows and pairwise synchronisation to be staffed by carers who have different skills and work custom shift patterns with contractual breaks. In a computational study, we first experiment with a benchmark set from the literature for the Vehicle Routing Problem with Time Windows and Synchronised Visits. Our algorithm reproduced the majority of the best-known solutions, and strictly improved results for several other instances. Most importantly, we demonstrate that the algorithm can effectively solve real scheduling instances obtained from a UK home care provider. Their size significantly surpass similar scheduling problems considered in the literature. The multistage algorithm solved each of these instances in a matter of minutes, and outperformed human planners, scheduling more visits and significantly reducing total travel time.

An exact solution method for home health care scheduling with synchronized services

“…However, the difference between the two service start times cannot exceed the threshold . Note that the assumption that each patient requiring synchronized services can request at most two medical services is in line with observations in real HHC operations (Polnik et al, 2020) and studies on synchronized services in the literature. For example, a patient may need a routine checkup and a targeted treatment at the same time.…”

“…For example, given an instance, if the ratio is very high, more constraints about synchronized services will be imposed, which renders the problem difficult to solve. Based on the realistic situation of synchronized services in HHC (see, e.g., Frifita & Masmoudi, 2020; Polnik et al, 2020), we set the ratio of patients requiring synchronized services within the range of ϑ ∈ {10%, 20%, …, 60%}.…”

“…However, Larsen (2012) pointed out that an HHC institution usually encounters a situation where some patients simultaneously require multiple services, which is referred to as synchronized services in the literature. Although about 10%–20% of the patients require synchronized services in real HHC (Polnik et al, 2020), only a few studies have considered HHCRSP with synchronized services. The addition of the synchronized service requirement makes the problem extremely hard to solve.…”

Hybrid Heuristic for Vehicle Routing Problem with Time Windows and Compatibility Constraints in Home Healthcare System

“…Putting compatibility in the objective function, Ait Haddadene et al [6] minimize total travel time as well as non-preferences between caretakers and patients to maximize compatibility while adding synchronization constraints, as some patients may need multiple services at the same time. Polnik et al [7], also with synchronized visits to a home, construct a heuristic to solve the problem where each stop has only one task that might need multiple caretakers. Considering compatibility in the constraints, Yu et al [8] minimize maximum traveling time with the vehicle allowed to visit only compatible nodes.…”

“…Constraints ( 6) are the compatibility constraints to guarantee that only a caretaker compatible with the patient will travel and take care of that patient. Constraints (7) and ( 8) are the subtour elimination constraint together with capacity constraints. Constraints (9) will activate when caretaker k travels from patient i to patient j (x k ij = 1).…”