Annals of Operations Research 93 (2000) 117–144 117
Efﬁcient algorithms for buffer space allocation
Stanley B. Gershwin
and James E. Schor
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
Analytics, Inc., 101 Rogers Street, Cambridge, MA 02142, USA
This paper describes efﬁcient algorithms for determining how buffer space should be
allocated in a ﬂow line. We analyze two problems: a primal problem, which minimizes total
buffer space subject to a production rate constraint; and a dual problem, which maximizes
production rate subject to a total buffer space constraint. The dual problem is solved by
means of a gradient method, and the primal problem is solved using the dual solution.
Numerical results are presented. Proﬁt optimization problems are natural generalizations of
the primal and dual problems, and we show how they can be solved using essentially the
1.1. Problem description
Production systems are often organized with machines or work centers connected
in series and separated by buffers. This arrangement is often called a ﬂow line,or
transfer line,orproduction line. A ﬁve-machine line is represented in ﬁgure 1, in which
the squares represent machines and the circles represent buffers. Material moves in the
direction of the arrows, from upstream inventory to the ﬁrst machine for an operation,
to the ﬁrst buffer where it waits for the second machine, to the second machine, etc.
Material ﬂow may be disrupted by machine failures or variable processing times.
Buffers are inserted between machines to limit the propagation of disruptions, and
this increases the average production rate of the line. Inclusion of buffers requires
additional capital investment and ﬂoor space, which may be expensive. Buffering
also increases in-process inventory. If the buffers are too large, the work-in-process
inventory and capital costs incurred will outweigh the beneﬁt of increased productivity.
If the buffers are too small, the machines will be underutilized or demand will not be
Often, the limitation on the amount of in-process inventory is not due to physical
constraints. Instead this limitation is a control policy, for example, a version of the
J.C. Baltzer AG, Science Publishers