We address a single machine scheduling problem arising in a last mile delivery setting for a food company. The same problem finds obvious applications also in the context of internal manufacturing logistics. A set of food orders are placed by the customers and are to be fulfilled by the company. Each order comprises a delivery point and an ideal delivery time An order is considered on time if it is delivered within a certain given time interval around the ideal delivery time. All food is prepared in a single production facility (restaurant) and immediately carried to the customers by a single courier, who may dispatch one or two different orders in a single trip. Since late deliveries correspond to canceled orders and an economic loss for the company, it is of interest to schedule orders so that the number of late orders is minimized. We model the resulting decision problem as a special single machine scheduling problem and propose different mixed integer programs to solve it. Their performance is assessed through a computational study on a set of test instances derived by our real-world application.
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