Simultaneous optimization of work and buffer space in unpaced production lines with random processing times

Much of the previous research on unpaced production lines with variable processing times has addressed either the issue of the allocation of work to the stations or the allocation of storage space to the buffers between stations. Our focus is instead on the simultaneous optimization of the workload allocation and the buffer allocation. We use a basic cost-based model that includes both revenue per unit of throughput and cost per unit of buffer space. Using both exponential and Erlang processing times, exact numerical results are obtained for the underlying Markov chain for cases where the number of states range up to over 2000 000. We investigate how the bowl phenomenon for workload allocation and the storage bowl phenomenon for buffer allocation interact when performing both allocations simultaneously. We also find counterexamples to a conjecture previously published in the literature that a balanced buffer allocation is optimal when the total number of buffer spaces is an integer multiple of the number of buffers.