Logistics and Transportation in Supply Chains

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SHIPMENT CONSOLIDATION (SCL) is the purposeful combination of several small loads, for dispatch together, as a single larger shipment. Although delay of order deliveries may incur a cost, SCL can lead to significant economies of scale in transportation, thus reducing the overall system cost. Service to the receiver of the goods need not be degraded, if attention is paid to the maximum holding time (length of the consolidation cycle). The shipper wishes to select an appropriate consolidation policy that determines the right moment to terminate the accumulation process and dispatch a load. Our new work aims to propose and study policies that are more general than the typical ones that are based solely upon the aggregate shipment weight and/or the maximum holding time. Our new models are capable of recording more information about the order-accumulation process (e.g. delays of individual orders), thus permitting consideration of policies dependent on such information. We will also improve the accuracy of our models by considering Markovian arrival processes that go beyond the typically-assumed Poisson distribution, and by incorporating potential correlations between the arrivals of consecutive orders and their weights. Continuing our recent success with the Matrix-Analytic method, we will develop efficient solution techniques to obtain accurate results. We will employ a more realistic cost structure: a delay penalty cost (customer disutility of waiting) that is strictly increasing in that waiting time. The ultimate goals are to identify the form of the optimal policy for the general case, and to construct efficient algorithms to determine the parameters of that optimal policy, for a consolidation process involving orders of multiple products whose transport costs and/or delay-penalty rates may differ.LOT-SIZING PROBLEMS seek to determine the timing and replenishment quantities, of a single item or of several items, to minimize total costs while meeting demand requirements. Demand, based on orders from customers, can be satisfied through the production and distribution when those items are grouped into families. The joint coordination via families recognizes the sharing of a resource in transportation (as in SCL) or in the manufacturing portion of the supply chain. Our research in the study of lot-sizing of several multi-product families is new in the production context. This work will also shed light on coordinated inventory control of products ordered from a common supplier. We will explore various strong reformulations for the multi-family lot-sizing problem, and test new heuristics to speed up solution times, maintaining solution quality. THE INVENTORY-ROUTING PROBLEM concerns both vehicle routing (the sequencing of customers in making deliveries by truck) and the management by the vendor of stocks for those customers whose products are being delivered. Our research allows, when advantageous, the development of indirect routes. These serve logically-grouped sets of customers that receive goods through a given cross-dock (CD). There can be as many customers on the routes as permitted by vehicle capacity. Both the inventory holding costs at customers and the pipeline stocks are considered. This theme extends, in a non-trivial way, the applicant’s previous publications on VMI (Vendor Managed Inventory) and cross-docking. We hope to obtain general, provably near-optimal results, and an efficient solution algorithm, for a system containing several CDs in which distinct products from multiple suppliers are delivered by a private fleet on routes to various customers. This work will represent one of the very first such models.