Sparse flexibility structures: Design and application

Abstract

Flexibility is a widely applicable concept in many business areas to help a company to deal with the demanding task of matching supply and demand in uncertain situations, without incurring much cost. Many companies in manufacturing, transportation and service industries have adopted flexibility as a key competitive tool. Flexibility practices, properly incorporated, could increase service levels, decrease response times without enquiring additional capacity investment. The challenge is to effectively design a flexibility structure with a good performance, but with small implementation cost.We first introduce the concept of a??graph expandera??, which is widely used in graph theory, computer science and communication network design areas. We propose that a good flexibility structure possesses the properties of graph expander. Estimation on the performance of an expander flexibility structure is also proposed under the assumption of balanced and identical demands/supplies. We further examine the connections between the popular ``chaining" structures and our expander structures, and propose that a a??chaina?? is just the special case of an expander structure. The concept of a??expandera?? can be further utilized to build an index to calibrate structures in terms of flexibility. We then extend our analysis to a generalized unbalanced and non-identical demands/supplies case. Another approach called "constraint sampling" is applied to analyze the problem. The analysis also shows that a well designed sparse flexibility structure provides comparable performance to the full flexibility structure even when demands/supplies are unbalanced and non-identical.We propose two heuristics to design good sparse flexibility structures based on the a??graph expandera?? and a??constraint samplinga?? concept. Both heuristics are simple and effective. These heuristics can be applied to a broad range of applications, such as process flexibility, transshipment, and cutting stock problems. We use real data from the Food-From-The-Heart (FFTH) program to support our conclusion. The theoretical results developed in our study are applied to fix the problem of their food-delivery operational system and enhance the operational performance. The result shows that by adding a little flexibility to the original dedicated system using our approach, the daily wastage of FFTH program can be reduced from more than 15 kilograms to only 2.808 kilograms. This result strongly supports the merits of our theoretical analysis.