This paper analyzes a realistic variant of the permutation flow-shop problem (PFSP) by considering a non-smooth objective function that takes into account not only the traditional makespan cost but also failure-risk costs due to uninterrupted operation of machines. After completing a literature review on the issue, the paper formulates an original mathemati- cal model to describe this new PFSP variant. Then, a Biased-Randomized Iterated Local Search (BRILS) algorithm is proposed as an efficient solving approach. An oriented (biased) random behavior is introduced in the well-known NEH heuristic to generate an initial solution. From this initial solution, the algorithm is able to generate a large number of alternative good solutions without requiring a complex setting of parameters. The relative simplicity of our approach is particularly useful in the presence of non-smooth objective functions, for which exact optimization methods may fail to reach their full potential. The gains of considering failure-risk costs during the exploration of the solution space are an- alyzed throughout a series of computational experiments. To promote reproducibility, these experiments are based on a set of traditional benchmark instances. Moreover, the performance of the proposed algorithm is compared against other state-of-the-art metaheuristic approaches, which have been conveniently adapted to consider failure-risk costs during the solving process. The proposed BRILS approach can be easily extended to other combinatorial optimization problems with similar non-smooth objective functions.

• Ferrer A., Guimarans D., Ramalhinho H.R. and Juan A.A. (2015), A BRILS Metaheuristic For Non-Smooth Flow-Shop Problems with Failure-Risk Costs, Expert Systems with Applications (accepted for publication) doi:10.1016/j.eswa.2015.09.011
• On the UPF web in Catalan and Spanish.

Distribution planning is crucial for most companies since goods are rarely produced and consumed at the same place. Distribution costs, in addition, can be an important component of the final cost of the products. In this paper, we study a VRP variant inspired on a real case of a large distribution company. In particular, we consider a VRP with a heterogeneous fleet of vehicles that are allowed to perform multiple trips. The problem also includes docking constraints in which some vehicles are unable to serve some particular customers, and a realistic objective function with vehicles’ fixed and distance-based costs and a cost per customer visited. We design a trajectory search heuristic called GILS-VND that combines Iterated Local Search (ILS), Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Descent (VND) procedures. This method obtains competitive solutions and improves the company solutions leading to significant savings in transportation costs.

Coelho V.N., Grasas A., Ramalhinho H., Coelho I.M., Souza M.J.F. (2015), An ILS-based Algorithm to Solve a Large-scale Real Heterogeneous Fleet VRP with Multi-trips and Docking Constraints, European Journal of Operational Research (accepted for publication September 2015) doi:10.1016/j.ejor.2015.09.047.

On the UPF web (in Catalan)