Optimization Models

Majority of the supply chain literature consists of multi-echelon inventory control models. A multi-echelon system is one in which there are multiple levels in the supply chain. The research on this front has a long history. A comprehensive review of these models can be found in Vollman et al. [#!Vollman!#]. These methods generally deal with operational or tactical/operational levels. Multi-echelon inventory models have been successfully implemented in industry. Cohen et al. [#!COHEN90!#] describe OPTIMIZER: IBM's Multi-Echelon Inventory System for Managing Service Logistics. They develop efficient algorithms and data structures to achieve large scale systems integration. Ettl et al. [#!ettl96!#] consider a supply network model to generate base stock levels at each store so as to minimize the overall inventory capital and guarantee the customer service requirements.

The other major focus area of supply chain optimization models is to determine the location of production, warehousing, and sourcing facilities, and the paths the products take through them. These methods provide models mostly for strategic and strategic/tactical levels. One of the earliest works in this area was in 1974 by Geoffrion and Graves [#!GEOFF74!#]. They introduce a multi-commodity logistics network design model for optimizing finished product flows from plants to distribution facilities to the final customers. They describe a mixed integer programming model for determining the location of distribution facilities and a solution technique based on Bender's decomposition. A modeling framework to provide a comprehensive model of a production-distribution system is described in system [#!Breit87!#] this is used to decide what products to produce, where and how to produce them, which markets to pursue and what resources to use. Parts of this project were successfully implemented in the General Motors.

Cohen and Lee [#!COHEN88!#,#!COHEN89!#] consider global manufacturing and distribution networks and formulate mixed integer optimization programs. Lee and Billington [#!LEE95!#] validate these models by applying it to analyze the global manufacturing strategies of Hewlett-Packard. Arntzen et al. [#!arntzen95!#] provide a comprehensive deterministic model for supply chain management called Global Supply Chain Model (GSCM), to determine optimal manufacturing and distribution strategies. GSCM minimizes cost or weighted cumulative production and distribution times or both subject to meeting estimated demand and restrictions on local content, offset trade, and joint capacity for multiple products, echelons, and time periods. GSCM is a large mixed integer linear program that incorporates a global, multi-product bill of materials for supply chains with arbitrary echelon structure. GSCM offers a very general approach to modeling supply chains and is applicable to virtually any firm that is involved in multi-stage, multi-product manufacturing. A successful implementation of this model was done at the Digital Equipment Corporation. Raghavan and Viswanadham [#!rpilag!#] formulate a non-linear programming model for sequencing and capacity planning of integrated supply chains and solve using Lagrangian relaxation. Most of these models are deterministic and static in nature. Because of their large scale they are often difficult to solve to optimality.