Optimal run lengths in deteriorating production processes in random fuzzy environments

This paper presents a random fuzzy economic manufacturing quantity (EMQ) model in a deteriorating process. It is assumed that the setup cost and the average holding cost are characterized as fuzzy variables and the elapsed time until shift is a random fuzzy variable. As a function of these parameters, the average total cost is also a random fuzzy variable, and the unimodality of its expected value is studied. To obtain the optimal run length and the minimum average cost, simultaneous perturbation stochastic approximation (SPSA) algorithm based on random fuzzy simulation is provided. Random fuzzy EMQ models with fuzzy deterioration, fuzzy linear deterioration and fuzzy exponential deterioration are presented, respectively. These models can be solved by the proposed algorithm. Numerical examples are presented in the end.

[1]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[2]  Baoding Liu,et al.  Toward Fuzzy Optimization without Mathematical Ambiguity , 2002, Fuzzy Optim. Decis. Mak..

[3]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

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

[5]  D. Dubois,et al.  The mean value of a fuzzy number , 1987 .

[6]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[7]  Chung-Chi Hsieh,et al.  Joint determination of production run length and number of standbys in a deteriorating production process , 2005, Eur. J. Oper. Res..

[8]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[9]  Chih-Hsiung Wang,et al.  Fast approach to the optimal production/PM policy , 2000 .

[10]  Chih-Hsiung Wang.  Integrated production and product inspection policy for a deteriorating production system , 2005 .

[11]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[12]  Meir J. Rosenblatt,et al.  Simultaneous determination of production cycle and inspection schedules in a production system , 1987 .

[13]  Caroline M. Eastman,et al.  Review: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

[14]  L. M. D. C. Ibáñez,et al.  A subjective approach for ranking fuzzy numbers , 1989 .

[15]  Jiuping Xu,et al.  World Journal of Modelling and Simulation , 2005 .

[16]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[17]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[18]  C. H. Kim,et al.  An optimal production run length in deteriorating production processes , 1999 .

[19]  Soo Y. Chang,et al.  Optimal production run length and inspection schedules in a deteriorating production process , 2001 .

[20]  Tadashi Dohi,et al.  Optimal control of preventive maintenance schedule and safety stocks in an unreliable manufacturing environment , 2001 .

[21]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[22]  J. Spall.  Implementation of the simultaneous perturbation algorithm for stochastic optimization , 1998 .

[23]  María Angeles Gil,et al.  Fuzzy random variables , 2001, Inf. Sci..

[24]  J. Spall.  A Stochastic Approximation Technique for Generating Maximum Likelihood Parameter Estimates , 1987, 1987 American Control Conference.

[25]  Meir J. Rosenblatt,et al.  A Production and Maintenance Planning Model with Restoration Cost Dependent on Detection Delay , 1989 .

[26]  Evan L. Porteus.  Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction , 1986, Oper. Res..

[27]  James C. Spall,et al.  AN OVERVIEW OF THE SIMULTANEOUS PERTURBATION METHOD FOR EFFICIENT OPTIMIZATION , 1998 .

[28]  Huibert Kwakernaak,et al.  Fuzzy random variables--II. Algorithms and examples for the discrete case , 1979, Inf. Sci..

[29]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .