Optimal buffer allocation in a production line operating under IB, EB, and CONWIP policies

We consider a production line consisting of several machines in series with finite intermediate buffers. The machines have geometrically distributed processing times. We address the problem of determining the optimal buffer sizes to maximize the average profit of the line subject to a minimum average throughput constraint, under three operating policies. The average profit is defined as the weighted average throughput of the line minus the sum of the weighted average WIP plus total buffer capacity. The considered policies are: installation buffer (IB), echelon buffer (EB), and CONWIP. IB is the traditional policy under which a machine can store the parts that it produces only in its immediate downstream buffer. Under EB, it can store them in any of its downstream buffers. CONWIP is a special case of EB where the capacities of all buffers, except the last one, are zero. To find the optimal buffer allocation for each policy, we use a two-step gradient algorithm, where the average profit for given buffer sizes is estimated using decomposition-based approximation. Numerical results show that the optimal EB policy outperforms the optimal IB and CONWIP policies.