Home chemotherapy: Integrating the production and administration of drugs

We introduce an integrated production scheduling and vehicle routing problem originally motivated by the rising trend of home chemotherapy. Oncology departments of Belgian hospitals have a limited capacity to administer chemotherapy treatments on site. Also, patients in a stable condition often prefer to get their treatment at home to minimize its impact on their personal and professional life. The optimization of underlying logistical processes is complex. At the operational level, chemotherapy drugs must be produced in the hospital pharmacy and then administered to patients at home by qualified nurses before the drugs expire. The lifetime of the drug, i.e., the maximum period of time from the production start until the administration completion, is sometimes very short, depending on the treatment type. The problem we consider calls for the determination, for each patient, of the drug production start time and administration start time, as well as the assignment of these two tasks to a pharmacist and a nurse respectively.

Drugs may be produced by any of the available pharmacists which are considered to be homogeneous. The working duration of a pharmacist is the time elapsed between the production start time of the first drug and the completion time of the last drug. The allowed working duration of each pharmacist is limited but the start time of each working shift is a decision variable implicitly defined by the production schedule.

Drugs are administered by nurses that have a limited working duration. The administration of each drug must be scheduled within a time window that depends on the concerned patient and before the drug expires. This expiry aspect is crucial since it calls for the integration of the scheduling and the routing aspects of the problem. Multiple trips are allowed, i.e., each nurse may come back at the hospital during its journey to take drugs recently produced.

The objective of the problem is to minimize the total working time of pharmacists and nurses.

We address this problem heuristically using destroy-and-repair mechanisms and allowing infeasible solutions to be visited. The main challenge is that a small change in the production schedule or the administration schedule affects other decision variables in a cyclic fashion. Thus, the change in the objective function associated to a given move is difficult to evaluate efficiently. To circumvent this issue, we propose to iterate between the production and the routing subproblems, by imposing constraints on one of the subproblems depending on the incumbent solution of the other. Moves on the solution of one subproblem are thus evaluated seemingly independently from the other one. Then, occasionally, an exact procedure is called to determine the optimum schedule of the integrated incumbent solution given the task sequence of each pharmacist and of each nurse.