The diet problem and DEA

Abstract

In this paper we relate the Diet Problem, formulated by Stigler in 1945, to the data envelopment analysis version of the profit maximization model.

Keywords:

• DEA
• diet problem
• profit maximization

Acknowledgements

We are grateful to William Cooper and two anonymous referees for their comments.

Notes

1 Although Stigler did not formulate the diet problem as an activity analysis problem—since activity analysis models were not developed at the time (as pointed out to us by William Cooper)—it has become ‘the classical illustration of linear programming’ (Gale, 1960, p 1).

2 Other forms of returns to scale may be imposed on the technology by adding restrictions to the intensity variables. See Färe and Grosskopf (2004).

3 Here, we formalize the problem in terms of inequalities rather than strict equalities.

4 We solve for the intensity variables as well in the profit maximization problem, however, they are not included in the objective function.

5 This is a standard transformation, see Baldani et al (1996).