Responsiveness is defined as the ability of a supply chain to respond rapidly to changes in demand, both in terms of volume and mix of products (Christopher, 2000). The ability of quick response enables supply chains to meet the customer demands for ever-shorter lead times, and to synchronize the supply to meet the peaks and troughs of demand (Sabath, 1998), which is of critical importance in nowadays time-based competition (Stalk, 1988). In the prevailing business environment, responsive supply chains have become not only the linchpin of companies to competitive success but also the key to survival (Fisher, 1997; Christopher, 2000, 2005). Uncertainties in demands are unavoidable due to the changing market conditions and customer expectations. In supply chains, inventory is the currency of service that helps deal with uncertainty and provides flexibility, though it can be costly (Chase and Aquilano, 1995; Bernard, 1999).
In this work, we consider the design of responsive supply chain with integration of inventory and safety stock under customer demand uncertainty. The supply chain has multi-site processing facilities and corresponds to a multi-echelon production network with both dedicated and multiproduct facilities. The major goal is to determine the processes that are to be integrated in the supply chain network, with their corresponding suppliers and customers, including transportation modes of the materials. The major considerations in the design are the supply chain responsiveness and profitability. Profitability is expressed in terms of net present value. The responsiveness accounts for transportation times, residence time, cyclic schedules in multiproduct plants, and inventory management. A quantitative characterization of responsiveness for supply chain networks is presented, which measures the expected response time or expected lead time to changes under uncertain demands with integration of inventory and safety stock level. This measure is incorporated into a multi-period mixed-integer non-linear programming (MINLP) model, which takes into account the selections of suppliers and manufacturing sites, process technology, production levels, scheduling and inventory level. The problem is formulated as a bi-criterion optimization model in which the objectives are to maximize the expected net present value and to minimize the expected lead time. This allows establishing trade-offs between the economics and responsiveness of the supply chain network. The multi-objective optimization problem is solved with ε-constraint method and it produces a Pareto-optimal curve, which reveals how the optimal net present value, and therefore the supply chain network structure, changes with different specifications of lead time. A hierarchical algorithm is also proposed for the solution of the resulting large-scale nonconvex MINLP model based on the decoupling of the different decision-making levels (strategic and operational) identified in our problem. The application of this model is illustrated through several example problems, including an example on styrene and related products. The modeling approach developed in this work and the results obtained show that the proposed approach yields useful insights regarding responsiveness of the supply chain systems.
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