On the Capacity of a Process with Batch Processing and Setup times

While batch processes are ubiquitous across industries, there is little understanding of the determination of the capacity (i.e., the maximum long-term output rate) of such processes. In this paper, we consider processes with collaboration (activities may require multiple resources simultaneously) and multitasking (the same resource may be needed for multiple activities), and characterize the capacity of an arbitrary deterministic, single-product process with batch processing and (activity) setup times. Such a process can be viewed as an "intermittent" process in which production occurs in discrete quantities; specifically, in multiples of the batch size. To obtain a corresponding "smooth" process, we use the most natural transformation that eliminates batching and setups, and simply prorates the processing and setup time per flow unit. The main result of our analysis is that capacity remains unaffected in this transformation. Then, using recent developments in the literature on process capacity, the capacity of the transformed process can be obtained by computing the fractional chromatic number of an associated graph - this latter problem can be formulated as a linear program