Annals of Operations Research

, Volume 38, Issue 1, pp 1–16 | Cite as

A problem identification taxonomy for classification and automated formulation of multiple objective linear programming models

  • Ajay K. Aggarwal
  • Edward R. Clayton
  • Terry R. Rakes
  • Joanna R. Baker


This paper presents a knowledge-based Decision Support System (DSS) for classification, formulation and solution of multiple objective linear programming problems. The authors propose a generic taxonomy which is used to classify commonly encountered types of linear programming problems. Classification of the problem, vis-à-vis the proposed taxonomy, is based on the interaction with the user to determine the attributes which best describe the context or setting of the problem. A total of twenty-four problem types are included in the taxonomy. Following classification, a problem type-specific rule base is invoked to assist the user in constraint formulation. A product blending linear programming problem is used to demonstrate this component of the system since these types of problems typically include more varied constraints, including ratio as well as additive types. A second rule base is invoked for formulation of the multiple criteria objective function, model solution and sensitivity analysis. An initial goal prioritization scheme is obtained by use of the Analytical Hierarchy Process [17]; the optimal goal ordering is obtained by interaction with the user in the form of pairwise attribute value tradeoffs. The system developed is intended for use by the OR-naive user who is more familiar with the content of a problem than he/she is with the mathematical tools needed to formulate and solve such models. The system is a model management tool designed to interpret user inputs and translate those inputs into a solvable multiple objective LP. This interface alleviates the technical burdens of content specification and solution. The approach expands previous formulation tools, such as those based on natural language processing [8], to a broader range of problem types in a multiple criteria environment. The system was implemented on a personal computer using VP-Expert, BASIC and LINDO, and is demonstrated on a multiple objective blending problem. The ability of the approach to accurately classify LP problems was tested on thirty-six subjects. Results suggest that correct classification of problems was more likely to occur when the system was used.


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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1992

Authors and Affiliations

  • Ajay K. Aggarwal
    • 1
  • Edward R. Clayton
    • 2
  • Terry R. Rakes
    • 2
  • Joanna R. Baker
    • 2
  1. 1.Department of Management ScienceMillsaps CollegeJacksonUSA
  2. 2.Department of Management ScienceVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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