A simulated annealing approach to minimize the maximum lateness on uniform parallel machines

This paper considers the uniform parallel machine scheduling problem which is to minimize the maximum lateness. This problem is equivalent to the uniform parallel machine scheduling problem, which is to minimize the maximal completion time of n jobs whose release times are zero, processing times depend on the speed of the machine to which they are assigned, and their delivery times are different. This problem is NP-hard, even if the machines' speeds are identical and all the delivery times equal to zero. We propose a simulated annealing algorithm, named LPDT-SA, to obtain solutions with high quality for large-sized problems. A heuristic algorithm LPDT is built to generate initial solutions. An effective method for solution representation is designed, which is efficient to realize the swap and insertion neighborhood, and simultaneously avoid some obvious inferior solutions, therefore the efficiency of the proposed simulated annealing algorithm is improved. A large set of instances are generated randomly to test the solution quality of LPDT-SA and assess its runtime. The results and analysis of experiments are reported and discussed.