Logistic operations in a hospital: a multi-item inventory distribution problem with heterogeneous fleet

Abstract

A multi-item inventory distribution problem motivated by a practical case study occurring in the logistic operations of a hospital is considered. There, a single warehouse supplies several nursing wards. The distribution of medical products is done by two different teams of workers using a heterogeneous fleet, that is, the available vehicles have different capacities and different structures required to be used in specific nursing wards. The goal is to define a weekly distribution plan of medical products ensuring a balanced workload of both working teams and satisfying all the required constraints (inventory capacities, safety stock levels, vehicle capacities, etc.) that minimizes the total number of visits to locations. A mixed integer formulation is presented and several improvements are discussed. This is a NP-hard problem hardly solved to optimality within a reasonable amount of time, and more so for real size instances, with hundreds to few thousand of products. To circumvent this issue, a matheuristic is proposed to solve the problem. Finally, computational tests are reported and discussed.