An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem

• The first study of a mixed no-idle flowshop where some machines have the no-idle constraint and others are regular machines.
• We present formulas to calculate the makespan of a sequence efficiently.
• We propose a MILP formulation and we introduce a set of formulas to accelerate the calculation of the insertion neighborhood.
• A modified Iterated Greedy method (IG) is presented with improved initialization, destruction and reconstruction operators.
• IG tested against 7 algorithms with a large benchmark. State-of-the-art results obtained both for mixed no-idle and full no-idle flowshops.

In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.