This paper studied an integrated logistics network design problem that optimizes supplierlocations and their assignments to terminal facilities, expedited shipment configurations andinventory management strategies in an uncertain environment. We first formulated elementarymodels for certain special case problems and discuss their model properties and solution methods.Built on these developments, we proposed a mathematical programming model that minimizesthe sum of supplier set-up costs, expected shipment costs for both regular and expeditedservices, and expected inventory holding cost under stochastic demand rates and transportationlead times for a general network logistics system throughout the planning horizon. Due to theconsideration of interdependent operational components including inventory management andshipment expedition, the proposed model is of high non-linearities and involve complex discretestructures. After studying problem element properties, we developed a customized solution approachbased on the Lagrangian relaxation technique that can solve the model efficiently andaccurately. This approach has been tested on a number of instances on three logistics networksof different scales, and their results uniformly showed that this approach can solve a realisticproblem instance to its exact optimum or a near-optimum solution in a short time. We presentedextensive experimental results to draw managerial insights into how problem settings andkey parameter values affect the optimal design results, including cost component magnitudes,transportation configurations, inventory management strategies and network layouts. We notedthat under the optimal design, utilizing expedited shipment services actually does not incurtoo much extra cost overall while guaranteeing service reliability. We also found under theintegrated design, all planning and operational components complement each other in the optimalway, and thus it is important and necessary to consider all the planning and operationaldecisions all together in a holistic design framework.
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