A Benders decomposition-based heuristic for a production and outbound distribution scheduling problem with strict delivery constraints

The problem addressed in this paper is from a chemotherapy production and delivery environment, where production and delivery are strongly connected problems. Independent jobs have to be prepared by pharmacy technicians working in parallel. These jobs represent pouches of injectable chemotherapy preparations. The production process corresponds to a classic parallel machine scheduling problem. Then, the jobs must be delivered to the patients by a given due date. Only one person ensures all the deliveries, making several trips between the pharmacy production unit and the patient locations. We model this step as a multi-trip traveling salesman problem, where only one salesman can make more than one trip. The objective to minimize is the maximum tardiness of delivery. In addition to the constraints that link the two problems, some constraints related to the chemical stability of chemotherapy drugs have to be taken into account: The time between the production starting time and the date the treatment is administered to the patient (here, the delivery time) cannot exceed the stability duration, as the drug may otherwise become dangerous or ineffective for the patient. Due to these constraints, the problem is more difficult to solve. The proposed resolution method in this paper is a Benders decomposition-based heuristic that makes it possible to find feasible solutions and lower bounds. The advantage of the Benders decomposition approach is that this method exploits the structure of the problem, which can be easily decomposed into two stages. Computational experiments are conducted, and a comparison with a direct exact resolution shows the efficiency of this approach.