Scheduling algorithms for the lock scheduling problem

In the present contribution we will show that scheduling a lock having at least two identical chambers requires solving the identical parallel machine scheduling problem with unit processing times, release dates and sequence dependent setup times. The lock scheduling problem considers the order in which a number of ships should be transferred through a lock. A lock may have one or more parallel chambers of a different size, each requiring a certain amount of time to transfer any possible feasible set of ships, called a lockage, through the lock. A mathematical model and meta heuristic are proposed for solving this problem.