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Variable very large neighbourhood algorithms for truck sequencing at transshipment terminals

This paper considers a scheduling problem motivated by transshipment terminals. Trucks delivering or picking up items at the terminal have to be sequenced. Here, inventory constraints must be considered, that is the current inventory level implied by initial inventory level, total pick up quantity up to this moment and total delivery quantity up to this moment must not be negative and must not exceed the inventory’s capacity. Several objective functions common in scheduling theory are considered, namely minimisation of maximum lateness, total weighted completion time, total weighted tardiness or weighted number of tardy trucks. We employ a local search strategy using a representation scheme where each individual corresponds to at least one and potentially to an exponential number of feasible solutions. Several neighbourhoods are proposed and embedded in a variable neighbourhood search algorithm. The decryption of an individual to an optimal corresponding solution is accomplished by customised polynomial time algorithms. Finally, we prove efficiency of the neighbourhood search algorithm by means of a computational study.