Abstract
It is argued that any non-trivial real world problems involve multiple objectives. The simplistic approach of combining objectives in linear form can generate highly misleading and biased results, and is poor operational research practice. Such biases are illustrated by means of a simple example, and it is demonstrated that two simple approaches based on goal programming and piecewise linear value functions can largely resolve these problems. These methods require careful attention to problem structuring but are easily implemented by use of standard linear programming (LP) packages.
Highlights
Two of the four themes in [2] are the closely related issues of linear programming (LP) and game theory
The original goal programming (GP) model was an early extension of LP, and is generally discussed in introductory texts on OR/MS, so that most readers would probably consider this approach to be very well known
We have argued firstly that good practice in any linear programming modelling should include identification of the inevitable multiplicity of objectives
Summary
Two of the four themes in [2] are the closely related issues of linear programming (LP) and game theory. Winston [13] recognizes a “seven-step model-building process” consisting of (1) Formulate the problem; (2) Observe the system; (3) Formulate a mathematical model of the problem ( this step may be challenged by those from the “soft OR” school); (4) Verify the model and use the model for prediction; (5) Select a suitable alternative (in which Winston explicitly recognizes that there may be more than one objective); (6) Present the results and conclusions of the study to the organization; and (7) Implement and evaluate recommendations Such an OR process inevitably acknowledges careful problem structuring as an essential part of OR (e.g. Winston’s steps 1–3), and to the recognition of “objectives” in the plural. Public sector applications (especially in a developing world context) inevitably have to deal with conflicts between economic, social and environmental goals as well as between the interests of different stakeholder groups These multiple goals are seldom directly commensurate, and as we shall illustrate cannot generally be aggregated in simple additive fashion.
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