Problem on the integration between production and delivery with parallel batching machines of generic job sizes and processing times

•A methodology based on the parallel-batching machine environment.•A polynomial constructive heuristics able to generate primal and dual bounds.•A worst-case scenario interpretation for the proposed heuristic.•Results evidence tight gaps for the objective function analyzed.•Heuristic results outperform mathematical model. In recent years the manufacturing industries are currently focused on adopting optimal hybrid mass/customized strategies. Working solely on customized production or mass production is not a desirable strategy for many manufacturers anymore. The rapid advances in technology, applications, and customers’ requirements are increasing the competitiveness and, therefore, productivity. Given this new scenario, the integration between production and delivery with parallel batching machines comes as an essential issue in logistics. Efficient integrated production and delivery operation is a critical factor for minimizing costs and increasing customer satisfaction. The particular case discussed in this paper consists of scheduling jobs of generic sizes and processing times on identical and parallel batching machines, aiming to maximize profits. The objective is to get a joint production and delivery schedule that maximizes total profits, focusing on attending consumers on time. We propose a mathematical formulation and show that the addition of a set of constraints improves the commercial solver performance. Additionally, we focus on the development and analys is of two fast polynomial methods. The first, RKP, aims to obtain relaxed solutions, while the last, CMFFDA, aims to obtain feasible solutions. Furthermore, computational experiments and sensitivity analysis with random instances of different sizes are conducted to evaluate the proposed methods and the integrated system. The results show tight gaps for the mathematical formulation and algorithms RKP and CMFFDA. The proposed algorithms present short computational times for small, moderate, and large size instances, an essential quality for daily operation.