A production inventory model with fuzzy production and demand using fuzzy differential equation: An interval compared genetic algorithm approach

In this paper, a production inventory model, specially for a newly launched product, is developed incorporating fuzzy production rate in an imperfect production process. Produced defective units are repaired and are sold as fresh units. It is assumed that demand coefficients and lifetime of the product are also fuzzy in nature. To boost the demand, manufacturer offers a fixed price discount period at the beginning of each cycle. Demand also depends on unit selling price. As production rate and demand are fuzzy, the model is formulated using fuzzy differential equation and the corresponding inventory costs and components are calculated using fuzzy Riemann-integration. @a-cut of total profit from the planning horizon is obtained. A modified Genetic Algorithm (GA) with varying population size is used to optimize the profit function. Fuzzy preference ordering (FPO) on intervals is used to compare the intervals in determining fitness of a solution. This algorithm is named as Interval Compared Genetic Algorithm (ICGA). The present model is also solved using real coded GA (RCGA) and Multi-objective GA (MOGA). Another approach of interval comparison-order relations of intervals (ORI) for maximization problems is also used with all the above heuristics to solve the model and results are compared with those are obtained using FPO on intervals. Numerical examples are used to illustrate the model as well as to compare the efficiency of different approaches for solving the model.

[1]  Manoranjan Maiti,et al.  Fuzzy inventory model with two warehouses under possibility constraints , 2006, Fuzzy Sets Syst..

[2]  Manoranjan Maiti,et al.  Multi-item inventory model of breakable items with stock-dependent demand under stock and time dependent breakability rate , 2010, Comput. Ind. Eng..

[3]  Ashish Sharma,et al.  Inventory model for seasonal demand with option to change the market , 2010, Comput. Ind. Eng..

[4]  S. K. Goyal,et al.  An application of Genetic Algorithm in solving an inventory model with advance payment and interval valued inventory costs , 2009, Math. Comput. Model..

[5]  Przemyslaw Grzegorzewski,et al.  Nearest interval approximation of a fuzzy number , 2002, Fuzzy Sets Syst..

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

[7]  Yi-Chih Hsieh,et al.  Optimal ordering and pricing policy for an inventory system with trial periods , 2010 .

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

[9]  Hsien-Chung Wu,et al.  The fuzzy Riemann integral and its numerical integration , 2000, Fuzzy Sets Syst..

[10]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[11]  Sanat Kumar Mahato,et al.  Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization , 2006 .

[12]  Y. Chalco-Cano,et al.  Comparation between some approaches to solve fuzzy differential equations , 2009, Fuzzy Sets Syst..

[13]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[14]  Manas Kumar Maiti,et al.  A production inventory model with stock dependent demand incorporating learning and inflationary effect in a random planning horizon: A fuzzy genetic algorithm with varying population size approach , 2009, Comput. Ind. Eng..

[15]  Jong Yeoul Park,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

[16]  Atanu Sengupta,et al.  Fuzzy Preference Ordering of Intervals , 2009 .

[17]  Liang-Yuh Ouyang,et al.  An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit , 2009, Comput. Ind. Eng..

[18]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[19]  S. K. Goyal,et al.  Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payments , 2008, Eur. J. Oper. Res..

[20]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[21]  Hui-Ming Wee,et al.  A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment , 2009, Eur. J. Oper. Res..

[22]  P. Siarry,et al.  A genetic algorithm with real-value coding to optimize multimodal continuous functions , 2001 .

[23]  James J. Buckley,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

[24]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[25]  Tapan Kumar Pal,et al.  Fuzzy Preference Ordering of Interval Numbers in Decision Problems , 2009, Studies in Fuzziness and Soft Computing.

[26]  Manas Kumar Maiti,et al.  A fuzzy genetic algorithm with varying population size to solve an inventory model with credit-linked promotional demand in an imprecise planning horizon , 2011, Eur. J. Oper. Res..

[27]  Enver Yücesan,et al.  A fuzzy newsvendor approach to supply chain coordination , 2010, Eur. J. Oper. Res..

[28]  Dmitri Vorobiev,et al.  Towards the theory of fuzzy differential equations , 2002, Fuzzy Sets Syst..

[29]  Manoranjan Maiti,et al.  An EPQ model with price discounted promotional demand in an imprecise planning horizon via Genetic Algorithm , 2009, Comput. Ind. Eng..

[30]  Manoranjan Maiti,et al.  Inventory model with fuzzy lead-time and dynamic demand over finite time horizon using a multi-objective genetic algorithm , 2012, Comput. Math. Appl..