A Multiobjective Multi-Item Inventory Control Problem in Fuzzy-Rough Environment Using Soft Computing Techniques

The optimal production and advertising policies for an inventory control system of multi-item multiobjective problem under a single management are formulated as an optimal control problem with resource constraints under inflation and discounting in fuzzy rough (Fu-Ro) environment. The objectives and constraints in Fu-Ro are made deterministic using fuzzy rough expected values method (EVM). Here, the production and advertisement rates are unknown and considered as control (decision) variables. The production, advertisement, and demand rates are functions of time t. Maximization of the total proceed from perfect and imperfect units and minimization of the total cost consisting of production, holding, and advertisement costs are formulated as optimal control problems and solved directly using multiobjective genetic algorithm (MOGA). In another method for solution, membership functions of the objectives are derived and the multi-objective problems are transformed to a single objective by the convex combination of the membership functions and then the problem is solved by generalized reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the system.

[1]  Baoding Liu.  Toward uncertain finance theory , 2013 .

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

[3]  Tapan Kumar Roy,et al.  A three-layer supply chain integrated production-inventory model under permissible delay in payments in uncertain environments , 2013 .

[4]  Danny I. Cho,et al.  Analysis of optimal production and advertising policies , 1996, Int. J. Syst. Sci..

[5]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[6]  K. M. Ragsdell,et al.  The Generalized Reduced Gradient Method: A Reliable Tool for Optimal Design , 1977 .

[7]  S. T. A. Niaki,et al.  Multiproduct EPQ model with single machine, backordering and immediate rework process , 2011 .

[8]  Zaid T. Balkhi,et al.  A multi-item production lot size inventory model with cycle dependent parameters , 2009 .

[9]  R. Misra.  A note on optimal inventory management under inflation , 1979 .

[10]  J. Buzacott.  Economic Order Quantities with Inflation , 1975 .

[11]  H. Wee,et al.  An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation , 2007 .

[12]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[13]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

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

[15]  D. Khan,et al.  Theory and methodology for the JELS model in one-vendor, multi-customer situations when costs are fuzzy and lot sizes deterministic , 2013 .

[16]  C. K. Sivashankari,et al.  Production inventory model with reworking of imperfect production, scrap and shortages , 2014 .

[17]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[18]  Hui-Ming Wee,et al.  Erratum to "An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation": [Int. J. Product. Econ. 106(2), 493-505] , 2007 .

[19]  Tapan Kumar Roy,et al.  Multi-objective imperfect production inventory model in fuzzy rough environment via genetic algorithm , 2013 .

[20]  Jiuping Xu,et al.  A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem , 2010, Inf. Sci..

[21]  Huey-Ming Lee,et al.  Economic production quantity for fuzzy demand quantity, and fuzzy production quantity , 1998, Eur. J. Oper. Res..

[22]  C. Krishnamoorthi,et al.  An EPQ model for imperfect production systems with rework and incorporating a multi-delivery policy , 2013 .

[23]  Jiuping Xu,et al.  A class of rough multiple objective programming and its application to solid transportation problem , 2012, Inf. Sci..

[24]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[25]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

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

[27]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[28]  Barun Das,et al.  A fuzzy simulation via contractive mapping genetic algorithm approach to an imprecise production inventory model under volume flexibility , 2013, J. Simulation.

[29]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[30]  Jiuping Xu,et al.  A class of fuzzy rough expected value multi-objective decision making model and its application to inventory problems , 2008, Comput. Math. Appl..

[31]  D. Dubois,et al.  Twofold fuzzy sets and rough sets—Some issues in knowledge representation , 1987 .

[32]  T. Datta,et al.  Demand promotion by upgradation under stock-dependent demand situation – a model , 1998 .

[33]  Manoranjan Maiti,et al.  Numerical Approach of Multi-Objective Optimal Control Problem in Imprecise Environment , 2005, Fuzzy Optim. Decis. Mak..