A MILP-based approach to address the production and distribution planning of large industrial gas supply chains

This paper focuses on addressing the Production Routing Problem (PRP) of industrial gas supply chains (SC). The work introduces a Mixed-Integer Linear Programming (MILP) based approach to effectively tackle this challenging problem. The proposed framework aims to increase company profits by optimizing both production and distribution activities simultaneously. For the distribution part, a route generation algorithm is employed to initially generate a set of feasible routes, ensuring that only routes with practical significance are considered. Subsequently, the mathematical model is developed considering only the set of routes generated. The formulation includes decisions associated with plants production levels, plant selection to supply the different consumers, clients to be visited per trip and day, quantity to be delivered and routes to be used. As part of the problem, it is considered that trucks can make several trips per day, as well as trips of several days. To take into account the last feature, the approach accounts for the explicit effect of the lead time on production and distribution decisions. In this way, the work allows for different delivery times for customers included in the same route, according to their inventories and usage levels. The model considers fleet unavailability until they return to the plants after finishing a trip. Finally, two case studies, one motivating and the other industrial size, are presented and solved. The results obtained demonstrate the effectiveness of the proposed approach to solve the case studies in reasonable CPU times.