Planning container inspection and repair: A case study

Abstract

The aim of this paper is to introduce a real-life problem of optimal planning of container inspection and repair on several facilities over several time periods assuring effective supply of empty containers indispensable for seamless global maritime transportation. The containers are of several types and quality levels. The objective is to minimize the total holding, inspection, repair, transportation and rejection costs. We formulate a deterministic min-cost multi-commodity network flow problem and prove NP-hardness for two special cases. Values of the rejection costs are determined such that no container is rejected in an optimal solution if there exists a feasible solution with no container rejected. An algorithmic mechanism is proposed to support a negotiation of periodic container demands between the container provider and the container users with the aim to reduce the overall costs. Computer experiments with instances obtained by random deviation from industrial data demonstrate that the majority of instances with up to 4 facilities, 4 container types, 7 quality levels, and 7, 14 or 30 time periods can be solved with an acceptable quality using an academic version of CPLEX in two hours on a standard PC.