Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 12 (2017), 179 -- 192

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


François Dubeau

Abstract. Mixture problems are basic but important problems in Operations Research. In this paper we consider variants of the basic linear mixture problem and indicate mathematical links between them.

2010 Mathematics Subject Classification: 90C05; 90C08; 90C29; 90C31.
Keywords: Mixture problem; linear program; bi-criteria; Pareto set; linear-fractional program; geometric transformation.

Full text


  1. A.~Charnes and W.W.~Cooper, Programming with linear fractional functionals, Naval Research Logistics Quarterly, 9(1962), 181-186. MR0152370. Zbl 0127.36901.

  2. G.B.~Dantzig. Linear Programming and Extensions, Princeton Press, Princeton, New Jersey, USA, 1963. MR0201189. Zbl 0108.33103.

  3. G.B.~Dantzig, The diet problem, Interfaces, 20(1990), 43-47.

  4. F.~Dubeau, P.-O.~Julien, and C.~Pomar, Étude de cas : un porcin dans un environnement sain, INFOR, 46(2008), 199-217.

  5. F.~Dubeau and A.~Kadri, Computation and visualization of the Pareto set in the criterion space for the bicriteria linear programming problem, International Journal of Mathematics and Computation, 15(2)(2012), 1-15. MR2877371. Zbl 0127.36901.

  6. F.~Dubeau, M.E.~Ntigura Habingabwa, On best mixture problems in metallurgy: a case study, Mathematical Problems in Engineering, Volume 2017(2017), Article ID 2742540, 11 pages.

  7. S.G.~Garille and S.I.~Gass, Stigler's diet problem revisited, Operations Research, 49(2001), 1-13.

  8. É.~Joannopoulos, F.~Dubeau, J.-P.~Dussault and C.~Pomar, Chapter 18 Diet problems, in Handbook of Operations Research in Agriculture and the Agri-Food Industry, L.M.~Plà~Aragonés (ed.), International Series in Operations Research & Management Science, Vol. 224(2015), 397-417.

  9. L.M.~Lancaster, The evolution of the diet model in managing food systems, Interfaces, 22(1992), 59-68.

  10. L.M.~Lancaster, The history of the application of mathematical programming to menu planning, European Journal of Operational Research, 57(1992), 339-347.

  11. R.E.~Steuer, Multiple Criteria Optimization, Wiley, New York, USA, 1986. MR0836977. Zbl 0663.90085.

  12. G.J.~Stigler, The cost of subsistance, Journal of Farm Economics, 27(1945), 303-314.

François Dubeau
Département de mathématiques, Université de Sherbrooke,
2500 Boulevard de l'Université,
Sherbrooke (QC), Canada, J1K2R1.