The concept of chaining, or in more general terms, sparse process structure, has been extremely influential in the process flexibility area, with many large automakers already making this the cornerstone of their business strategies to remain competitive in the industry. The effectiveness of the process strategy, using chains or other sparse structures, has been validated in numerous empirical studies. However, to the best of our knowledge, there have been relatively few concrete analytical results on the performance of such strategies, vis-a-vis the full flexibility system, especially when the system size is large or when the demand and supply are asymmetrical. This paper is an attempt to bridge this gap.We study the problem from two angles: (1) For the symmetrical system where the (mean) demand and plant capacity are balanced and identical, we utilize the concept of a generalized random walk to evaluate the asymptotic performance of the chaining structure in this environment. We show that a simple chaining structure performs surprisingly well for a variety of realistic demand distributions, even when the system size is large. (2) More generally, consider the linear optimization problemand A is a m × n matrix. When b is random, the process flexibility design problem reduces to choosing a small set of variables in S (typically |S| ∼ O(m)) so that E b (Z(b, S)) is as close to E b (Z(b, {1, . . . , n}) as possible. For the more general problem, we identify a class of conditions under which only a sparse flexible structure is needed so that the expected performance is already within optimality of the full flexibility system.Our approach provides a theoretical justification for the widely held maxim: In many practical situations, adding a small number of links to the process flexibility structure can significantly enhance the ability of the system to match (fixed) production capacity with (random) demand.

We examine how a flexible process structure might be designed to allow the production system to better cope with fluctuating supply and demand, and to match supply with demand in a more effective manner.We argue that good flexible process structures are essentially highly connected graphs, and use the concept of graph expansion (a measure of graph connectivity) to achieve various insights into this design problem.A number of design guidelines are well known in the literature. Principles such as "a long chain performs better than many short chains," and that one should "try to equalize the number of plants (resp. products), measured in total units of capacity (resp. mean demand), which each product (resp. plant) in the chain is directly connected to," can now be interpreted from this new angle as a development of different ways in which the underlying network can achieve a good expansion ratio. The same principle extends to other new design guidelines -trying to equalize the number of plants (measured in total number of units) assigned to each pair (or even triplet) of products, or vice versa, can also help the decision maker to arrive at a good process structure.We analyze the worst-case performance of the flexible design problem under a more general setting, which encompasses a large class of objective functions. We show that whenever demand and supply are balanced and symmetrical, the graph expander structure (a highly connected but sparse graph) is within ǫ optimality of the fully flexible system, for all demand scenarios, although it uses a far smaller number of links. Furthermore, the same graph expander structure works uniformly well for all objective functions in this class.Based on this insight, we develop a simple and easy-to-implement heuristic to design flexible process structure. Numerical results show that this heuristic performs well for a variety of numerical examples previously studied in the literature. We also use this idea on a set of real data obtained from a bread delivery system in Singapore, with the goal of minimizing the excess amounts of bread brought to each location.

One of the most effective ways to minimize supply/demand mismatch cost, with little increase in operational cost, is to deploy valuable resources in a flexible and timely manner to meet the realized demand. This notion of flexible processes has significantly changed the operations in many manufacturing and service companies. For example, flexible production system is now commonly used by automobile manufacturers, and work force cross-training system is by now a common practice in many service industries. However, there is a tradeoff between the level of flexibility available in the system and the associated complexity and operational cost. The challenge is to have the "right" level of flexibility to capture the bulk of the benefits from a full flexibility system, while controlling for the increase in implementation cost. This paper reviews the latest development on the subject of process flexibility in the past decade. In particular, we focus on the phenomenon, often observed in practice, that a slight increase in process flexibility can reap a significant amount of improvement in system performance. This review explores the issues in three perspectives: design, evaluation and applications. We also discuss how the process flexibility concept has been deployed in several manufacturing and service systems.

Sciences (INFORMS). It incorporates referee's comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document.

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