Fleet sizing of trucks for an inter-facility material handling system using closed queueing networks

Material handling systems (MHS) are integral to logistics functions by providing various supports such as handling, moving, and storing materials in manufacturing and service organisations. This study considers determining the optimal size of a homogeneous fleet of trucks to be outsourced (or subcontracted) from a third-party logistics provider to be used daily to cyclically transport different types of raw materials from designated storage yards to intermediate buffer locations to be fed as inputs to a production facility for processing. Within this context, the problem is modelled as a closed queueing network (CQN) combined with mixed-integer nonlinear programming (MINLP) to determine the optimal fleet size. This study proposes an analytical method based on sequential quadratic programming (SQP) methodology coupled with a mean value analysis (MVA) algorithm to solve this NP-Hard problem. Furthermore, a discrete event simulation (DES) model is developed to validate the optimisation of non-dominant solutions. The proposed analytical approach, along with the simulation, are implemented in a real case study of a steel manufacturing setup. Analytical model results are validated using the simulation results, which are proved to be very accurate, with deviations ranges within ±7%.