Scheduling multiple yard cranes in two adjacent container blocks with position-dependent processing times

This paper studies the management of three yard cranes in two adjacent container blocks in line, where cranes can move from one block to the other. Comparing with existing literature, the new multi-yard-crane scheduling problem incorporates different constraints together: (i) three yard cranes are deployed simultaneously in two adjacent blocks, (ii) non-crossing and inter-crane interference constraints of yard cranes are considered, (iii) the processing time of each container depends on its real-time location, i.e., position-dependent processing times. For the problem, a 0-1 mixed integer programming (MIP) model is constructed to minimize the total flow time to reduce the total container storage time in container yards, which helps to save container yard resources and increase production efficiency. The proposed model can be solved optimally by CPLEX for small-size instances. As the concerned problem is NP-hard, a fast heuristic and an improved genetic algorithm are devised to produce near-optimal solutions for large-size instances. Numerical experiments validate the developed MIP model and demonstrate the efficiency of the proposed algorithms.