Efficient matheuristics to solve a rich production-routing problem

We present a rich production-routing problem having limited production and storage capacities at the plant, limited storage capacity at the clients, a heterogeneous fleet subjected to a maximum riding time, and allowing for back-orders to meet unfulfilled demands at penalty cost. As the problem scales quickly with the number of customers, periods, products, and vehicles, three hybrid two-level decomposition approaches using a top-down strategy were devised. The top tier determines the production and inventory levels, and the distribution of goods via CPLEX, that is, it makes tactical decisions, while the bottom tier heuristically routes a heterogeneous fleet in each period, that is, it makes operational decisions. The proposed methods rely on an iterated local search framework that combines tailored perturbation schemes prioritizing either tactical or operational decisions, or both. The main new feature of the algorithms is the adoption of an implicit cost that estimates the delivery routing costs when making production, holding, and transportation decisions. This implicit cost serves as an important guide to obtain improved solutions. The algorithms were tested over an extensive set of instances, and the results demonstrated that all methods overcome CPLEX by obtaining more, better, and faster solutions with much less computational effort. The devised heuristic, which prioritizes operational-level decisions during the perturbation phase, attained the best overall results.