Last-Mile Delivery of Pharmaceutical Items to Heterogeneous Healthcare Centers with Random Travel Times and Unpunctuality Fees

This paper analyzes a real-life distribution problem that is related to a pharmaceutical supplier in Spain. Every day, a fleet of vehicles has to deliver the previously requested items to a large set of pharmacies. The distribution has to be conducted with (i) the total distance and time incurred by the entire fleet being reasonably low and (ii) the time of the delivery meeting the specified time windows or, if that is not possible and some delays occur, the total fee incurred by these unpunctualities being minimized. Unpunctuality fees depend upon how important is the customer for the distributor, and the size of the tardiness gap. To include even more realistic details, travel times are modeled as random variables, which also makes the problem more challenging to solve by employing traditional optimization methods. To solve this stochastic variant of the problem, a simheuristic algorithm is proposed and evaluated.