Inventory groups and commodity flows : optimization in a capacitated multicommodity multiple supplier environment

Abstract

The multiple supplier inventory grouping problem concerns the minimization of total logistics cost for a firm that has many suppliers. Each supplier may provide multiple items, subject to capacity limitations. Logistics costs included are transportation, inventory holding, ordering, and purchasing (possibly with price discounts). The cost elements interact in complex ways resulting in multiple tradeoffs. The problem is complicated by the need to simultaneously optimize commodity flows, inventory groups, and group cycle times. It is of considerable interest to firms involved in transportation, distribution and manufacturing. The primary background areas are Inventory Grouping, Inbound Consolidation, and Freight Networks. The focus of Inventory Grouping is on finding the optimal inventory groups and associated cycle times for joint orders, in situations where holding costs and ordering costs interact and purchase orders have a header cost component. Inbound Consolidation is concerned with the integration of transportation costs and transshipment terminals into the inventory grouping framework. Finally, Freight Networks typically involve commodity flows with multiple sources and sinks. The model developed in this study may be viewed as a multicommodity freight network with side (complicating) constraints. The problem is formulated as a 0-1 linear integer programming model. Problem complexity grows exponentially with size, and a fast solution algorithm is necessary in order to solve large problems in reasonable time. The model is solved by a specialized method, based on subgradient optimization, that is developed in the dissertation, and also by a state-of-the-art commercial routine (OSL) developed by IBM. The specialized algorithm is able to solve problems in a small fraction of the time taken by OSL. For large problems, OSL's solution time, computer memory and storage requirements are exceedingly high, making it impractical for regular use. It is expected that the specialized algorithm will eventually be embedded in a decision support system for firms involved with transportation, distribution and manufacturing.