Heuristics for a flowshop scheduling problem with stepwise job objective function

In this work, we introduce the Flowshop Scheduling Problem with Delivery Dates and Cumulative Payoffs. This problem is a variation of the flowshop scheduling problem with job release dates that maximizes the total payoff with a stepwise job objective function. This paper contributes towards proposing a mathematical formulation for this new problem and an original constructive heuristic. Additionally, we develop a new benchmark of 300 hard instances which are available in a public repository together with the best primal and dual bounds. Extensive computational experiments were carried out taking into account classical constructive heuristics and hybrid local searches. Results show the merit of the FF heuristic when compared to other classical heuristics for flowshop scheduling problems. Additionally, we compare an Iterated Local Search (ILS), an Iterated Greedy Search (IGS), and a Biased Random-Key Genetic Algorithm (BRKGA), both customized for the studied problem, and a commercial mixed integer programming solver. The comparison between these methods showed that the BRKGA starting with a solution from FF heuristic is able to find the best solutions in a very short period of time. Iterated local search and the commercial solver presented significantly worse results than the aforementioned methods.