Performance bounds for flexible systems requiring setups

Many organizations use product variety as one possible strategy for increasing their competitiveness. They have installed flexible manufacturing systems because these systems offer a powerful means for accommodating production and assembly of a variety of products. However, increased product variety comes at a cost. For instance, if the resource requires to be set up each time it switches to operate on a new product, the resulting delays and costs could negate the intended benefits of increased product variety. Analyzing these flexible resources for optimal design and operation is therefore very important. To address such issues, we model a flexible resource, serving multiple products, using a queueing model – more precisely, a polling model. In this model, a single server attends to multiple service centers (queues) at which requests arrive and queue up for service, performing a setup at a polled queue only if that queue is nonempty. This is the state dependent (SD) polling model. Exact analysis of the SD polling model is inherently very complex. This paper presents a very efficient procedure to compute a hierarchy of successively improving bounds on the values of performance measures obtained from the SD polling model with the exact solution as its limit. This procedure can be applied to quickly estimate performance measures for large SD polling models previously deemed analytically intractable.