A production inventory model with fuzzy random demand and with flexibility and reliability considerations

The classical inventory control models assume that items are produced by perfectly reliable production process with a fixed set-up cost. While the reliability of the production process cannot be increased without a price, its set-up cost can be reduced with investment in flexibility improvement. In this paper, a production inventory model with flexibility and reliability (of production process) consideration is developed in an imprecise and uncertain mixed environment. The aim of this paper is to introduce demand as a fuzzy random variable in an imperfect production process. Here, the set-up cost and the reliability of the production process along with the production period are the decision variables. Due to fuzzy-randomness of the demand, expected average profit of the model is a fuzzy quantity and its graded mean integration value (GMIV) is optimized using unconstraint signomial geometric programming to determine optimal decision for the decision maker (DM). A numerical example has been considered to illustrate the model.

[1]  Debjani Chakraborty,et al.  A single-period inventory model with fuzzy random variable demand , 2005, Math. Comput. Model..

[2]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[3]  Liang-Yuh Ouyang,et al.  Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand , 2006, Eur. J. Oper. Res..

[4]  R. A. Cuninghame-Green,et al.  Applied geometric programming , 1976 .

[5]  Manoranjan Maiti,et al.  Production policy for damageable items with variable cost function in an imperfect production process via genetic algorithm , 2005, Math. Comput. Model..

[6]  Liangjian Hu,et al.  The variance and covariance of fuzzy random variables and their applications , 2001, Fuzzy Sets Syst..

[7]  Manoranjan Maiti,et al.  Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions , 2004, Comput. Oper. Res..

[8]  Kit-Nam Francis Leung,et al.  A generalized geometric-programming solution to "An economic production quantity model with flexibility and reliability considerations" , 2007, Eur. J. Oper. Res..

[9]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[10]  Tapan Kumar Roy,et al.  A fuzzy EPQ model with flexibility and reliability consideration and demand dependent unit production cost under a space constraint: A fuzzy geometric programming approach , 2006, Appl. Math. Comput..

[11]  Sumer C. Aggarwal.  A review of current inventory theory and its applications , 1974 .

[12]  T. M. Whitin,et al.  An Optimal Final Inventory Model , 1961 .

[13]  Debjani Chakraborty,et al.  An inventory model for single-period products with reordering opportunities under fuzzy demand , 2007, Comput. Math. Appl..

[14]  Clarence Zener,et al.  Geometric Programming : Theory and Application , 1967 .

[15]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[16]  María Angeles Gil,et al.  The λ-average value and the fuzzy expectation of a fuzzy random variable , 1998, Fuzzy Sets Syst..

[17]  Paul van Beek,et al.  OR contributions to flexibility improvement in production/inventory systems , 1987 .

[18]  S. H. Chen,et al.  GRADED MEAN INTEGRATION REPRESENTATION OF GENERALIZED FUZZY NUMBER , 1999 .

[19]  Debjani Chakraborty,et al.  A Single-Period Inventory Problem with Resalable Returns: A Fuzzy Stochastic Approach , 2007 .

[20]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[21]  Elwood Spencer Buffa,et al.  Modern production/ operations management , 1961 .

[22]  T. Cheng.  An economic production quantity model with flexibility and reliability considerations , 1989 .

[23]  Debjani Chakraborty,et al.  Continuous review inventory model in mixed fuzzy and stochastic environment , 2007, Appl. Math. Comput..

[24]  K Frransis Lueng.  A GENERALIZED GEOMETRIC PROGRAMMING SOLUTION TO AN ECONOMIC PRODUCTION QUANTITY MODEL WITH FLEXIBILITY AND RELIABILITY CONSIDERATIONS , 2007 .

[25]  C. R. Bector,et al.  Fuzzy Mathematical Programming and Fuzzy Matrix Games , 2005 .

[26]  Yun Kyong Kim,et al.  Integrals of fuzzy-number-valued functions , 1997, Fuzzy Sets Syst..