The Production Routing Problem (PRP) in industrial gas supply chains is particularly challenging to solve, especially when dealing with real-world industrial cases. This paper presents a Mixed-Integer Linear Programming (MILP) approach, along with a solution strategy, to effectively address this problem. The proposed framework aims to minimize total operational costs by optimizing both production and distribution simultaneously. A route generation algorithm is used in the distribution phase to create a set of candidate routes for the solution. The formulation incorporates decisions related to production levels at plants, customer-plant allocation, the customers included in each trip, the day of visits, the routes used, and the quantities delivered. Since multi-day trips are considered, the model explicitly accounts for the impact of lead times on production and distribution decisions. Additionally, it considers fleet unavailability until vehicles return to the plants after completing a trip. The solution strategy involves sequential steps that progressively identify feasible solutions and seek to improve them throughout the process. Finally, to demonstrate the effectiveness of the proposed approach, both a motivating example and industrial-sized cases are presented and solved.
