Fuzzy models for single-period inventory problem

  • Authors:

  • Lushu Li;S. N. Kabadi;K. P. K. Nair

  • Affiliations:

  • Faculty of Administration, University of New Brunswick, Fredericton, N.B., Canada E3B 5A3;Faculty of Administration, University of New Brunswick, Fredericton, N.B., Canada E3B 5A3;Faculty of Administration, University of New Brunswick, Fredericton, N.B., Canada E3B 5A3

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2002

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Abstract

In this paper, we consider the single-period inventory problem in the presence of uncertainties. Two types of uncertainties, one arising from randomness which can be incorporated through a probability distribution and the other from fuzziness which can be characterized by fuzzy numbers, are considered. We develop two models, in one the demand is probabilistic while the cost components are fuzzy and in the other the costs are deterministic but the demand is fuzzy. In each, the objective is maximization of profit which is fuzzy and optimization is achieved through fuzzy ordering of fuzzy numbers with respect to their total integral values. We show that the first model reduces to the classical newsboy problem, and therefore an optimal solution is easily available. In second model, we show that the objective function is concave and hence present a characterization of the optimal solution, from which one can readily compute an optimal solution. Besides discussion of the models, a relevant extension is outlined.