Optimal collection of medical specimens and delivery to central laboratory

Abstract

We propose an efficient algorithm to provide transportation routes and schedules to pick up medical specimens from clinics, physician’s offices, and hospitals and deliver them to a central laboratory quickly. This healthcare vehicle routing and scheduling problem differs from existing vehicle routing problems primarily in that, instead of minimizing driving time, the objective is to minimize the completion time, that is, the time from when the specimen is available for pickup until it is delivered to the central laboratory. We combine the routing problem with scheduling of vehicles and formulate a mixed integer linear program. We present a new algorithm to solve this optimization problem, called the Vehicle Routing and Scheduling Algorithm (VeRSA). VeRSA uses an indexing method inspired by scheduling methods to efficiently traverse a branch-and-bound tree associated with the mixed integer program. Instead of using a linear programming relaxation, as is common, we prove several propositions that lead to expressions that are fast to compute. We also prove a theoretical lower bound to provide some information on an optimality gap. Numerical results on three small and three large test problems demonstrate the high quality of solutions provided by VeRSA. The data in the large test problems are based on data provided by the University of Washington Medical Center (with modifications to protect confidentiality). The computational speed of VeRSA makes it applicable to real-time operational decisions when demand may be updated at any time due to cancellations or additional pickups. This model is applicable to other types of pickup and delivery systems where the waiting time of a package is important, such as perishable items.

Appendix

The data used in the test problems is included in this appendix. Tables 4 and 5 provide distance and time window data for the small test problem. Tables 6 and 7 provide distance and time window data for the large test problem.

Table 4 Distance matrix $(t_{i,j})$ for the small test problem $n=9$

Table 5 Time window $(e_i,d_i)$ for the small test problem $n=9$

Table 6 Distance matrix $(t_{i,j})$ for the large test problem $n=57$

Table 7 Time window $(e_i,d_i)$ for the large test problem $n=57$