k-server problems with bulk requests: an application to tool switching in manufacturing

The classical k-server problem has been widely used to model two-level memory systems (e.g., paging and caching). The problem is to plan the movements of k mobile servers on the vertices of a graph under an on-line sequence of requests. We generalize this model in order to process a sequence of bulk requests and formulate, in this way, a valid model for the usual two-level tooling configuration in automated production systems. A slight adaptation of the so-called Partitioning Algorithm provides an on-line algorithm for this more general case, preserving basically the same competitive properties as the classical model. This approach yields a new tool management procedure in manufacturing which outperforms in its quality the usual methods that are based on heuristics for the traveling salesman problem.