A system with a certain amount of flexibility that enables it to adapt to uncertainties is known as a flexible system. Flexibility is an important concept in many aspects, not only in manufacturing but applicable to other fields including economics, various service industries and organization management. Flexibility is a significant competitive strength for companies, which empowers them to deal with various environmental uncertainties in a timely and cost-effective manner.

Process flexibility is reflected by a set of products that the system can produce without implementing major setups. It also helps to deploy resources in a flexible manner which will meet the realized demand with some operational costs and increase flexibility leading to an improvement in performan...[ Read more ]

A system with a certain amount of flexibility that enables it to adapt to uncertainties is known as a flexible system. Flexibility is an important concept in many aspects, not only in manufacturing but applicable to other fields including economics, various service industries and organization management. Flexibility is a significant competitive strength for companies, which empowers them to deal with various environmental uncertainties in a timely and cost-effective manner.

Process flexibility is reflected by a set of products that the system can produce without implementing major setups. It also helps to deploy resources in a flexible manner which will meet the realized demand with some operational costs and increase flexibility leading to an improvement in performance. Currently, the chaining concept proposed by Jordan and Graves (1995) is the most influential method used in flexible system design. Long chain and 3-chain are commonly used structures with 2 and 3 flexibility levels respectively in terms of the symmetrical systems. There are other systems of 3 flexibility levels that do not follow the chaining structure, for example, the Levi system.

We implement the study of the performance of limited-flexible systems at operational level. Normally, the performance is studied under the assumption that each order can be assigned one by one unit to different facilities. Under normal conditions, a two or three flexibility level is then adequate enough to achieve a performance level close to that of full-flexibility. However, in practice, orders may not be able to be split, which are termed discrete orders. This poses the question as to whether 2 or 3 degrees of flexibility is still acceptable. In general, with discrete orders, the satisfied demand would be less. We evaluate the performance gap for these systems between the continuous case and discrete case, which is the gap between design and implementation as well. We also measure how the gap would change with the number of demand types and the number of discrete orders. We propose one dynamic programming framework for long chain and formulate MIP for systems with 3 degrees of flexibility to obtain an optimum schedule under the discrete case.

In addition, we also measure the performance gap between limited-flexible systems and full-flexibility both under discrete case from two other aspects. First, we set the total completion time of a given job set as the objective to be minimized. Then we consider each job with a corresponding due date and to minimize the number of late jobs.

Finally, the design of the flexible system is studied with a new application. Process flexibility has been widely applied in many systems and the on-demand packaging system is one of them. Packing lines with cardboard of different width applied have different capabilities to handle different types of packing orders. We propose one framework to obtain the foremost packing line width design for on-demand packaging. Our objective is to decide the optimal width for cardboard used in each packing line in order to minimize waste of packing material. We measure the performance of the proposed model by comparing the cost with two other straightforward methods. We believe our framework will lead to a significant reduction of packing materials as well as a drop of shipping space leading to a corresponding decrease in transportation costs.

Keywords: Flexible system, Job scheduling, Packing line design