International Journal of Industrial Engineering, 21(1), 1-17, 2014 ISSN 1943-670X  INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING DEVELOPING A ROBUST PROGRAMMING APPROACH FOR THE RESPONSIVE LOGISTICS NETWORK DESIGN UNDER UNCERTAINITY Reza Babazadeh , Fariborz Jolai, Jafar Razmi, Mir Saman Pishvaee Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran Iran, Islamic Republic Of Operational and disruption risks derived from the environment have forced firms to design responsive supply chain networks. This paper presents a multi-stage multi-product robust optimization model for responsive supply chain network design (SCND) under operational and disruption risks. First, a deterministic mixed-integer linear programming (MILP) model is developed considering different transportation modes, outsourcing, flexibility and cross-docking options. Then, the robust counterpart of the presented model is developed to deal with the inherent uncertainty of input parameters. The proposed deterministic and robust models are assessed under both operational and disruption risks. Computational results show the superiority of the proposed robust model in managing risks with a reasonable increase in the total costs compared to deterministic model. Keywords: Robust Optimization, Responsive Supply Chain Network Design, Operational & Disruption Risks. 1. INTRODUCTION Facility location is one of the most important decisions in the supply chain network design (SCND) problem and plays a crucial role in the overall performance of the supply chain. Generally, the SCND problem includes determining the numbers, locations and capacities of facilities, as well as the amount of shipments between them (Amiri, 2006). Nowadays, time and cost are common gauges used to assess the performance of the supply chains and both are minimized, as they are treated simultaneously. The delivery time criterion is considered to be an individual objective that leads to a bi-objective problem. Minimizing delivery time and cost objectives in the form of a bi-objective problem are in conflict with each other (Pishvaee and Torabi, 2010). That is, quick delivery implies high amount of costs. The time minimization objective, however, can be integrated in cost objective when it is expressed in terms of monetary value. Increased environmental changes in the competitive markets force manufacturing companies to be more flexible and improve their responsiveness (Gunasekaran and Kobu, 2007). Some components, such as direct shipments from the supply centres to customers and decisions on opening or closing facilities (plants, distribution centres and etc.) for the forward seasons (Rajabalipour et al., 2013), utilizing different transportation modes can improve the flexibility of an SCN. Cross-docking is a logistics function in which products are shipped directly from the origin to the destination, without being stored in warehouses or distribution centres (Choy et al., 2012). Utilizing cross-dock centres as an intermediary stage between supply centres and customer zones leads to significant advantages for the manufacturing and service industries (Bachlaus et al., 2008). In recent decades, some companies, including Wal-Mart used cross-docks in different sites to achieve competitive advantages in distribution activities. Although inventory holding is not attractive, especially in lean production systems, it could play a significant role in dealing with supply and demand uncertainty (You and Grossmann, 2008). In today’s world, the increased diversity of customer needs prevents manufacturing and service industries from making fast changes, unless it is done through outsourcing. Outsourcing is performed for many reasons, such as saving on costs, focus on core business, quality improvement, knowledge, reduced time to market, enhance capacity for innovation and risk management (Kang et al. 2012). Some of companies, like Gina and Zara Tricot, which use the outsourcing approach, have a massive advantage (Choudhury and Holmgren, 2011). Many previously presented models consider fixed capacities for all facilities, whereas determining capacity of facilities is often difficult in practice (Wang et al., 2009). Therefore, capacity level of facilities should be determined as a decision variable in mathematical programming models. Since opening and closing of facilities are strategic and time- consuming decisions (Pishvaee et al., 2009), an SCN should be designed in the way that could be sustained under operational and disruption risks. Chopra and Sodhi (2004) and Chopra et al. (2005) mentioned that the organizations should consider uncertainty issues with its various forms in supply chain management to deal with their destructive and burdensome effects on supply chain. Exploring various sources proves that most presented works in the SCND area assume that input parameters, such as demands, are deterministic (see Melo et al., 2009; Klibi et al. 2010). Although some studies have considered the SCND under tentative conditions, most of them used the concept of stochastic and chance constrained programming methods (Alonso-Ayuso et al., 2003; Santoso et al., 2005; Listes and Dekker, 2005; Salema et al., 2007) . The major drawbacks