We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.
Supply chain management is increasingly being recognized as the integration of key business processes across the supply chain. For example, Hammer argues that now that companies have implemented processes within the firm, they need to integrate them between firms: Streamlining cross-company processes is the next great frontier for reducing costs, enhancing… (More)
Network flow problems with non-convex piecewise linear cost structures arise in many application areas, most notably in freight transportation and supply chain management. In the present paper, we consider mixed-integer programming (MIP) formulations of a generic multi-commodity network flow problem with piecewise linear costs. The formulations we study are… (More)
The demand management process is concerned with balancing the customers' requirements with the capabilities of the supply chain. This includes forecasting demand and synchronizing it with production, procurement, and distribution capabilities. A good demand management process can enable a company to be more proactive to anticipated demand, and more reactive… (More)
Departement d'informatique et de recherche op6rationnelle and Centre de recherche sur les transports Universit6 de Montreal Abstract We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost… (More)
INVENTORY CONSIDERATIONS IN NETWORK DESIGN Optimization is accepted by logisticians as the appropriate approach to network design. While network design is used to make decisions regarding many aspects of logistics networks, one set of important decisions relates to the number, location, and size of warehouses in the network. Managers must also determine the… (More)
We develop integer programming formulations and solution methods for addressing operational issues in merge-in-transit distribution systems. The models account for various complex problem features including the integration of inventory and transportation decisions , the dynamic and multimodal components of the application, and the non-convex piecewise… (More)