his paper presents measures which quantify the notion of how well manufacturing systems,in which machines are assigned to participate in tasks, can absorb changes in the environment. Several measures are proposed and their properties discussed. This paper takes the viewpointthat such measuresare relativeto reference task-sets.
l. Introduction
This paper presents a framework for defining measures of flexibility in production systems. The measures we present quantify the notion of how well a machine or group of machines can absorb changes in a given manufacturing environment: changes in demand for products, changes in costs and prices, introduction of new parts or products, changes in tooling, changes in production efficiency, expansion of capacity, etc. The framework will be given in general terms, so that a user will be able to analyse specific situations within the general framework. Computation of our flexibility values is much like the situation of evaluating probabilities. The probabilist delimits for each new problem a sample space, a set of events, a measure on the events, relevant random variables, etc., and then proceeds to compute probabilities. Similarly, the analyst of an (automated) manufacturing system in our scheme will define task sets, machines or groups of machines for accomplishing the tasks, machine-task efficiency ratings, weights of importance for tasks, etc., in order to compute relevant flexibility values.Many authors have attempted to attain a qualitative understanding of flexibility in manufacturing systems. Several have classified flexibility into categories such as job and machine flexibility (Buzacott 1982), and eight types including routing, machine, expansion, etc. (Brown et al. 1984). Other authors have emphasized the importance of management, information and learning in the use of flexibility in manufacturing systems (Jaikumar 1984). The relationship between flexibility and productivity has also been studied (Gustavsson 1984, Buzacott and . Decision-theoretic approaches have been used to study a wide range of issues in flexibility and general decision making (Mandelbaum 1978 , 1989). General production frameworks which include operations, machines, tasks, etc., as basic elements, are presented by various authors (for example, Menipaz 1984, Chatterjee er al. 1984).Whereas most of the above authors have dealt with flexibility in general, or qualitative terms, others have attempted to quantify flexibility specifically for manufacturing systems. Some-authors have developed measures of flexibility based on counting of options for general routing and process centres . Measures of flexibility have been discussed with respect to environmental conditions and process requirements (Zelenovic 1982). The measures are taken to be design adequacy and the time needed for system transformation/adaptation, respectively. An Revision