Mathematics in the Supply Chain

Abstract

Mathematical models and methods have been established in various fields of applications in recent years. These include transport and traffic (see for instance the Oberwolfach workshop on “Traffic and Transport Optimization” in 1999), production planning (see Handbooks in Operations Research and Management Science, the volume on “Logistics of Production and Inventory” Graves, Rinnooy Kan and Zipkin (eds.), North-Holland, 1993), communication networks (see “Handbook of Discrete and Combinatorial Mathematics” Rosen (ed.), or “Handbook in Operations Research and Management Science” the volume on “Network Models” Ball, Magnanti, Monma and Nemhauser (eds.)) and financial engineering (“Options, Futures, and Other Derivatives” by J. Hull). The success of mathematical methods does not only rely on progress in computer technology, but in a fundamental way it relies on the improvement of the underlying mathematical models, methods and associated algorithmic developments. In recent years new challenges from industry and business have arisen. Modern problems contain more and more structures whose origins lie in various disciplines of mathematics, including graphs and networks, optimization, control and stochastic processes. A prominent field in which such problems arise is supply chain management. Supply chain management is typically defined as: A set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores so that merchandise is produced and distributed in the right quantities, to the right locations, and at the right time, in order to minimize systemwide costs while satisfying service level requirements. The idea of the workshop was to bring people from mathematics who have successfully applied mathematical methods for the solution of practical problems together with people who are in touch with the real-world problems that constitute supply chain management. To motivate and initiate interactions between the two groups, the mathematicians presented their applied methods and explained the situations in which they are effective as well as the underlying theory. These methods and concepts cover a wide spectrum, ranging from integer programming and dynamic programming methods through approximation algorithms to stochastic optimization methods. Similarly, supply chain management experts explained their problems, pointed out where current methods will help and where further developments are necessary. The scope of these problems is quite impressive. It includes distribution problems that integrate warehousing and transportation, inventory management models, the integration of procurement and manufacturing activities with demand planning processes and pricing and auction models that are used to improve business-to-consumer and business-to-business interactions. In this way we hope that the workshop provided a forum for open discussions about interesting new mathematical problems that are of central importance to supply chain management. The workshop itself was organized as follows. We had a series of plenary talks from world leading experts in mathematics and in supply chain management about the current state-of-the-art in these fields. We completed the program by having a series of shorter talks where people reported on their chosen models and solution methods for these models. In particular we invited and encouraged young people to participate in the workshop. They used the chance to gain as well as to present insights into new developments in applied mathematics and supply chain management. The interconnection of the two disciplines showed to provide a great source for new, interesting research projects in the future. The Oberwolfach workshop on “Mathematics in the Supply Chain” turned out to be of great interest for both experts in mathematics and experts in supply chain management. The meeting offered a platform for mathematicians to become acquainted with an important future-oriented field of applications. Vice versa, it offered a platform for supply chain management people to learn more about current mathematical models and methods potentially useful in solving further problems. We are very happy that we had the opportunity to organize such an interdisciplinary workshop at Oberwolfach.