We address the problem of designing a supply chain network with four layers comprising suppliers, plants, warehouses and customer zones. Strategic decisions include the location of new plants and warehouses, and the choice of their capacity levels from a finite set of available options. Tactical decisions involve the selection of suppliers, the procurement of raw materials, and planning the production and distribution of end products to meet customer demands. Different transportation modes are available for raw material and end product distribution. Each mode is associated with a minimum shipment quantity, a maximum transportation capacity and a variable cost. A further distinctive feature of our problem is that each customer zone must be served by a single facility (either a plant or a warehouse). Many companies strongly prefer single-sourcing deliveries as they make the management of the supply chain considerably simpler. Direct shipments from a plant to a customer zone are only permitted if at least a given quantity is distributed to the customer zone. Such a delivery scheme reduces transportation costs for large quantities. In addition, each raw material must be purchased from a single supplier by an operating plant. However, different raw materials may be procured from multiple suppliers by the same plant. This feature overcomes the disadvantages of singlesupplier dependency. Furthermore, a strategic choice between in-house manufacturing, product outsourcing and a combination of both is also to be made. Outsourced products are consolidated at warehouses. Although product outsourcing incurs higher costs than in-house manufacturing, this option may be attractive when the cost of establishing a new facility to process given end items is higher than the cost of purchasing the products from an external source. We propose a mixed-integer linear programming (MILP) formulation to identify the network configuration with minimum total cost. We also develop a second MILP formulation for the special situation in which all products delivered to customers must be in-house manufactured but customer demands do not have to be completely satisfied. In this case, a minimum customer service level is guaranteed. Valid additional inequalities are developed to enhance both formulations. A computational study is performed to assess the impact of various problem characteristics on the ability of state-of-the-art optimization software to solve problem instances within a reasonable time limit. Using a set of randomly generated instances, valuable insights are provided on the trade-offs achieved by considering product outsourcing against a pure in-house manufacturing strategy, and the extent to which it may not be economically attractive to meet all demand requirements.

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• Mathematics - Natural Sciences