# Process Flexibility Revisited: Graph Expander and Food-From-The-Heart

#### by Professor Chung-Piaw, Teo

Institution: Sungkyunkwan University Korea
Date: Fri 5th August 2005
Time: 1:05 PM
Location: Room 213, Richard Berry Building, Dept of Mathematics and Statistics, University of Melbourne.

Abstract: The notion of Process Flexibility has been used in many situations to
achieve higher service levels, shorter response times, etc without
requiring additional capacity investments. In this paper, motivated by a bread delivery problem faced by a charity organization (Food From The
Heart Program) in Singapore, we revisit the issue of process flexibility in a
delivery planning setting. In particular, we study how process flexibility
structure should be designed to allow the system to better cope with
fluctuating supply/demand, and to match supply with demand in a more
effective manner.

We show that the process flexibility problem is intimately connected to
the graph expansion problem, a well-studied subject in computer science and mathematics where there have been significant recent breakthroughs. The well-accepted belief that a simple chaining strategy (flexibility
structure with small number of links) can perform nearly as well as a
fully flexible structure,'' is merely a result of the fact that certain sparse
graphs can achieve nearly the same expansion as a complete graph. This
connection allows us to prove a mathematically precise statement
concerning the existence of flexibility structure with small number of links, but with close to the capability of a fully flexibile system. We also generalize the notion of graph expansion to allow us to handle the case where supply/demand are non-identical.

We use the bread delivery problem to motivate a few other issues not
commonly addressed in the process flexibility literature. In particular,
we examine the issue of unequal supply and demand, and dynamic supply-demand assignment decision (in real time, as information is released), for any given process flexibility structure. We propose a simple heuristic to construct flexibility structure in this case. We demonstrate the effectiveness of this approach using a set of real data taken from the