Optimal planning in large multi-site production networks

This contribution describes a general mixed-integer linear programming model based on a time-indexed formulation covering the relevant features required for the complete supply chain management of a multi-site production network. While the actual application is taken from the chemical industry, the model provides a starting point for many applications in the chemical process industry, food or consumer goods industry. In many real world problems certain features just need to be eliminated from this general model in order to describe a current situation. The model combines aspects related to production, distribution and marketing and involves production sites (plants) and sales points. Besides standard features of lot sizing problems (raw materials, production, inventories, demands) further aspects, e.g., different time scales attached to production and distribution, the use of periods with different lengths, the modeling of batch and campaign production need to be considered. There are also new conceptual aspects in this paper, e.g., how to define the capacity of a multi-site, multi-product production network, or how to approach complex planning problems. We give a complete description of features ready for implementation, and the experience we have with the current implementation in our company. A long-term implication of this contribution might be that it will initiate further research efforts aiming to derive special cuts improving the formulation.