Scheduling of e-commerce packaging machines: blocking machines and their impact on the performance-waste tradeoff

To streamline their fulfillment processes, many e-commerce retailers today use automated packaging machines for their outbound parcels. An important performance-waste tradeoff is associated with these machines: To reduce packaging waste when handling different sized goods, packaging machines should be able to handle different carton sizes. However, more carton sizes lead to a more involved scheduling process, so that the throughput performance deteriorates (and vice versa). To investigate this tradeoff, this paper develops scheduling procedures for a specific type of packaging machine, called blocking machines. These packaging machines provide multiple back-to-back packaging devices, each continuously processing a dedicated carton size, but blocking each other whenever incoming goods are not properly ordered according to carton sizes on the infeed conveyor. To reduce the resulting throughput loss, we derive various scheduling problems for optimizing the inflow of goods, provide a thorough analysis of the computational complexity, and derive an exact dynamic programming approach that is polynomial in the number of orders to be packed. This allows us to solve even large real-world instances to proven optimality with which we can analyze the performance-waste tradeoff of blocking machines.