Impact of partial product outsourcing, transportation mode selection, and single-assignment requirements on the design of a multi-stage supply chain network

In this paper, we propose a novel mixed-integer linear programming model for a comprehensive multi-stage supply chain network design problem. Our model integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, and distribution of multiple products through the network. The aim is to identify the network configuration with least total cost subject to side constraints related to resource availability, technological conditions, and required customer service level. In addition to in-house production, end products may also be purchased from external sources and consolidated in warehouses. Therefore, our model identifies the best mix between in-house production and product outsourcing. To measure the impact of this strategy, we further present two additional formulations for alternative network design approaches that do not include partial product outsourcing. Several classes of valid inequalities tailored to the problems at hand are also proposed. We test our models on randomly generated instances and analyze the trade-offs achieved by integrating partial outsourcing into the design of a supply chain network against a pure in-house manufacturing strategy, and the extent to which it may not be economically attractive to provide full demand coverage.