This research extends the work in the field of logistic network design problems by introducing a new mixed integer linear programming model to solve an integrated location, production and distribution planning problem in a multi-plant, multi-item, multi-retailer, intermodal transportation and single period logistic environment. Moreover, the non full coverage of customer demands is also considered. The non full coverage allows to model situations on which organizations can opt for outsourcing. Nowadays, many public and private organizations are using outsourcing as a way to improve their effectiveness and efficiency. Despite being commonly related with services, outsourcing can be used as an alternative way for production, as well. The integrated location, production and distribution planning problem considered in this research involves a set of suppliers that are eligible to provide raw materials for manufacturing a set of finished products on a non predetermined set of plants. For each potential site to locate plants, modular capacities are considered. Production capacities not only imposes upper bounds on the total production but also on the amount of production per product.The fixed set-up and operational costs for plants are capacity dependent whereas the production costs are quantity dependent. Once manufactured, products can be delivered either directly to customers or to warehouses, where they are stored and then send to customers. Therefore, plants and distribution centers can store finished products. Plus, total and per product storage capacities are considered. For warehouses, location and storage capacities choices, as well as fixed set-up and operational costs are also considered. Delivery takes place using intermodal transportation. Thus, more than one mode of transportation can be selected for delivering items (raw materials and manufactured products). Each mode of transportation incurs a fixed cost and a variable cost, which is in turn dependent on the distance and on the item, namely its quantity. Additionally, a minimum level of service is defined for both plants and distribution centers. This minimum level of service obliges that once operating facilities (plants and distribution centers) have to fulfill, which can mean produce or store, a certain percentage of their total capacity. For plants, the minimum level of service is related with production capacities whereas for distribution centers is related with storage capacities. It is assumed that demands are given and fixed. To cover the demand distribution centers can also be be supplied with finished products coming from external suppliers. However, the amount of outsourced products cannot exceed a pre-defined percentage of the total demand. Outsourced products have a penalty cost assigned to, which is product dependent. The objective is to select suppliers, to determine the location and size of plants and distribution centers, and to find the optimal production and distribution plan so as to minimize the total incurred cost. A mathematical mixed integer programming formulation of the problem is provided. Moreover, we propose some valid inequalities to strengthen the LP relaxation of the problem. To evaluate the model as well as the proposed valid inequalities a set randomly instances were generated and tested with CPLEX 12.3. Computational results will be presented and analyzed.

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Logistics, Supply chain network Design, Intermodal transportation, Mixed Integer Linear Programming