Cost minimizing planning of container inspection and repair in multiple facilities

A problem of optimal mid-term or long-term planning of inspection and repair of freight containers in multiple facilities is introduced and investigated. The containers are of different types and quality levels, which define their repair costs and workforce requirements. The objective function includes the total holding, inspection, repair, transportation and rejection costs. We propose a deterministic, time-dependent, integer linear min-cost multi-commodity network-flow formulation. The problem is shown to be polynomially solvable if there is a single facility, a single time period and all the containers are repairable and have to be repaired. It is shown to be NP-hard for three important special cases. The computational results of our experiments on randomly generated instances based on real data show that instances of sizes 3 facilities, 4 container types and up to 9 container quality levels can be solved with CPLEX in 5 minutes on a conventional PC, even for 30 periods, with an optimality gap of less than 3%. This is sufficient for medium-term or weekly planning or for short-term recovery planning. However, there are instances of the same magnitude, but with 360 periods of a considerably longer planning horizon, for which an optimality gap of 28% remained even after 10 hours of CPLEX computation.