This study considers the production of chemotherapy drugs for cancer treatment. An important factor determining the quality of service of chemotherapy treatment is the time the patient must wait to receive his or her injection of the chemotherapy drug. Chemotherapy production and delivery are modeled as a production scheduling problem combined with a vehicle routing problem. The scheduling problem is a three-stage hybrid flow shop scheduling problem, and the routing problem is a variant of the multi-trip vehicle routing problem with due dates. The objective function is the minimization of the total time delay for chemotherapy treatment. To solve this problem, we propose several heuristic algorithms to provide quality solutions within reasonable computation times. Computational experiments are used to compare the performance of the heuristics applied to real data-based random instances.