Flexible Manufacturing System Design

The Context

One of the most important issues facing industry today is the effective use of the new flexible manufacturing systems in the modern machining factory. The recent growth in the development of such systems, where machines are adjusted automatically by computer to produce different parts, has created new design-for-efficiency issues in industrial engineering.

The Problem

Many production plants operate machines each of which utilizes a series of tools in order to carry out some manufacturing process. These tools are located in equally spaced pockets on a circular magazine which can be rotated either clockwise or anticlockwise. When a particular tool is required by the machine, the magazine is rotated until such a tool (there may be identical tools in various pockets) is opposite the (unique) loader arm. The arm removes the tool, places it in the machine and places the present tool that is in the machine (if any) in the pocket just emptied. The machine then carries out some procedure using the new tool. While this is taking place the magazine is rotated to position the next required tool opposite the arm. A given strict sequence of operations is to be repeated indefinitely, each successive one requiring the machine to employ exactly one tool, which is in a different pocket from that required by the previous operation. However any one type of tool may be stored in more than one pocket, and certain pockets may be empty. The duration times for the operations are known constant d, and the time to rotate the magazine radians is md. A rotation, but not a swap, can take place while a tool is being used. A rotation takes longer than some, but not all, operations.

This leads to the objective of specifying which pocket is to house each tool just before each operation so as to minimize the total elapsed completion time (the makespan) of one complete sequence of operations.

The Role of Discrete Mathematics

The above problem has been formulated as an integer programming model that can be solved, for practical industrial numerical instances, by commercially available software. The constraint matrix for any numerical instance of the model can be generated using the mathematical formulation system MGG. This can be used as input into the SCICONIC mathematical programming system, which solves the integer programming model by branch and bound enumeration. The solutions produced led, on average, to a saving of 25% of overall machine centre time, compared to those previously used in industry.

The Benefits of Further Research

It is likely that certain tools will be sufficiently large to overlap neighboring pockets. Thus it is desirable that modifications are made to a solution to leave gaps (empty pockets) to accommodate fat tools. Other design problems are also of considerable interest to manufacturing engineers:

(i)

For given magazine hardware, what sets of operational sequences can be achieved in a given time?

(ii)

For a given set of operational sequences, how many pockets and which tool duplications are required to achieve the possible minimum makespan?

For More Information

For an introduction to flexible manufacturing systems, see:
R. G. Askin and C. R. Standridge, Modeling and Analysis of Manufacturing Systems, Wiley, 1993.

For further discussion on the specific problem mentioned here, see:
L. R. Foulds and J. M. Wilson, ``Formulation and Solution of Problems of Tool Positioning on a Single Machine Centre'', International Journal of Production Research 31 (1993) 2479-2485.

Fri Feb 2 13:46:33 CST 1996