Lagrange relaxation decomposition for synchronized production and transportation planning with flexible vehicles

Effective management of interfaces between procurement, supply, production and distribution as a whole towards higher efficiency of supply chain is an important issue in a global manufacturing environment, where coordination of production and distribution particularly synchronization of production and transportation planning becomes an important savings in operational costs. A synchronized production and transportation planning for a production distribution network is discussed in this paper. In the production-distribution network, transportation business is subcontracted to professional transportation enterprise (PTE), e.g. 3PL in a vehicle-rent way. The problem addressed tries to determine not only the synchronized schedule of production and transportation (when and in what quantity each product is produced and for alignment with the shipment), but also the number of vehicles required towards minimum total costs of production set-up, inventory, transportation and rent costs in vehicles over the planning horizon. A non-linear 0-1 mixed integer programming is developed and a Lagrange relaxation decomposition method is proposed.