Joint optimization of product service system configuration and delivery with learning-based valid cut selection and a tailored heuristic

Most previous work on product service system configuration aims to meet the functionality need or ensure a cost-effective delivery separately, overlooking the mutual impact between the configuration and delivery procedures. In contrast to that, we jointly optimize the configuration scheme and the delivery plan to increase the customer satisfaction through a two-stage decision framework. However, this integration significantly heightens the model’s complexity due to the interdependence of the two stages. To address this challenge, we introduce an exact algorithm for finding globally optimal solutions, as well as an efficient two-stage heuristic aiming at enhancing the efficiency. The exact algorithm is built upon the branch-and-bound algorithm which, however, becomes less efficient as the problem size increases. To counteract this, we devise a series of valid cuts to boost the convergence. Additionally, recognizing that the optimal bundle of valid cuts may vary depending on the specific case, we adopt artificial intelligence techniques to adaptively select valid cuts. This can lessen unnecessary search efforts when tackling new cases and further enhance the computational performance. Despite this, efficiently handling large-scale cases in real-world applications remains a challenge. To mitigate this, we customize an efficient two-stage heuristic to assure a practical applicability. In the first stage, an effective local search is used to identify an appropriate configuration scheme, which then serves as a hyperparameter for the second stage, inspired by the machine learning. The second stage focuses on optimizing the delivery plan. To obtain this plan, we dedicate a modified adaptive large neighborhood search algorithm, equipped with tailored operators and selection methods to enrich search capabilities. Furthermore, a feasibility protection procedure is specialized to rectify the infeasible solutions and secure the diversity of the solution pool simultaneously. Our numerical experiments underscore the importance of the two-stage optimization framework, demonstrate the effectiveness of adaptive valid cut selection, and highlight the superiority of our heuristic in handling complex optimization tasks.