A generalized model management system for mathematical programming

Reviewer: William Fennell Smyth

This clearly written paper first proposes a conceptual framework, called a Model Management System (MMS), for the description, storage, manipulation, display, and solution of models, especially mathematical models, of real world systems. It then describes a prototype MMS called GXMP (Generalized eXperimental Math Programming system). GXMP has been implemented to handle some of the MMS functions for some mathematical programming models, particularly those solvable using Linear Programming (LP) techniques. The author argues persuasively that an MMS should satisfy the following objectives: (1)it should handle models and their conceptual components as database management systems (DBMS) handle data; (2)it should be independent of particular solution algorithms; (3)it should support multiple user views of models (from manager to model-builder); (4)it should provide (expert system) support for building, integrating, and understanding models. To support these objectives, the author proposes the representation of a model by a model abstraction consisting of objects, procedures, and rules. This is another generalization of the abstract data type. To facilitate processing related to objective (4), all three components of the model abstraction would be described in the first-order predicate calculus. GXMP, which the author describes as “a first pass” at building an MMS, is described in terms of the following six components: (1) databases of model parameters, equations, procedures, and abstractions, plus a metadatabase covering these four types of model object; (2)a modeling language for expressing LP constraints and objective functions; (3)a model translator to translate LP equations into sparse matrix form; (4)a model solver to generate subroutine calls appropriate to the model; (5)a solution reporter to control user-friendly display of the model solution; and (6)a menu dialog. Although GXMP is, as the author points out, in many respects far from achieving a full MMS, it does nevertheless provide support for the view that the comprehensive approach provided by an MMS is valuable in practice. In particular, there is evidence that the use of the model abstraction, the DBMS, and the modeling language could yield immediate, positive benefits. What is not so clear is the extent to which GXMP, the prototype, can feasibly be extended to satisfy objectives (1)–(4); nor does the author provide specific information about the processing overheads required for GXMP. The author lists a number of areas for further research and development of GXMP, and he points out that in many cases, the appropriate course to follow is simply unknown. Developments such as the extension from LP to the mathematical programming techniques, or the introduction of a graphical rather than equational view of the model, or the introduction of inference mechanisms would raise questions for which there are at present simply no answers. The author perhaps places more faith in AI and systems technology than is really justified [1,2], and does not perhaps place enough emphasis on the enormous processing overheads that would result from extensions of GXMP. All in all, I would have been more comfortable if the adverb “potentially” had been inserted in the paper's conclusion that “the model abstraction concept is a valuable tool for generalizing model management.” It does not seem likely that an MMS much beyond the existing prototype in complexity can be achieved without the introduction of significant new techniques, such as massive parallelism [3].