Iterative matheuristic for the biomedical sample transportation problem

This paper proposes an iterative matheuristic for solving the biomedical sample transportation problem (BSTP), which is a routing problem with multiple and interdependent visits in the context of healthcare services. In this problem, the biomedical samples are collected from individuals at a set of healthcare or specimen collection centers and must be transported to designated laboratories to be analyzed. The perishable nature of the specimens forces to visit the collection centers more than once a day to ensure that the time from the moment they are drawn to the arrival at the laboratory do not exceed the samples lifespan. Also, a visit to one center imposes (1) a limit on the duration of the route that transports its samples to the laboratory, and (2) a limit on the latest time at which the same center must be visited again, creating an interdependency between visits, routes and the decision concerning the centers’ opening times. This paper first proposes a mathematical formulation to model the BSTP. Since this formulation is not able to solve medium or large sized instances efficiently, it also proposes an iterative matheuristic, which includes two main steps. The first step produces an approximated solution to the BSTP by a decomposition approach that splits the problem into a series of smaller subproblems that are solved by the proposed mathematical formulation. In the second step, two fix-&-optimize strategies are used with the mathematical formulation to perform a local search around the solutions produced by the decomposition method. The matheuristic has demonstrated its efficiency solving a rich set of real-life instances corresponding to the needs of several regions in the province of Quebec, Canada, in a fraction of the time required to solve the exact mathematical formulation.