Modeling (R, Q) Policy in a Two-Level Supply Chain System with Fuzzy Demand

In this paper a two level supply chain system is studied, in which the final demand is assumed to be fuzzy with triangular membership function. The inventory control policy of (r, Q) is followed for this system and unsatisfied demand is assumed to be back ordered. The objective is to minimize the total cost of the system, including ordering, holding and shortage costs. The model happens to be a nonlinear programming. Considering the complexity arising from the model, we also develop a genetic algorithm to obtain a near-optimal solution. The method is illustrated through some numerical examples.

[1]  Johan Marklund,et al.  Decentralized inventory control in a two-level distribution system , 2000, Eur. J. Oper. Res..

[2]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[3]  Mitsuo Gen,et al.  An Application of Fuzzy Set Theory to Inventory Control , 1996 .

[4]  Juite Wang,et al.  Fuzzy decision modeling for supply chain management , 2005, Fuzzy Sets Syst..

[5]  R. Ganeshan.  Managing supply chain inventories: A multiple retailer, one warehouse, multiple supplier model , 1999 .

[6]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[7]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[8]  Zbigniew Michalewicz,et al.  The use of genetic algorithms to solve the economic lot size scheduling problem , 1998, Eur. J. Oper. Res..

[9]  Huey-Ming Lee,et al.  Economic reorder point for fuzzy backorder quantity , 1998, Eur. J. Oper. Res..

[10]  Mohammad Reza Akbari Jokar,et al.  Cost evaluation of a two-echelon inventory system with lost sales and approximately Poisson demand , 2006 .

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

[12]  S. Chopra,et al.  Supply Chain Management: Strategy, Planning & Operation , 2007 .

[13]  R. Hill.  The single-vendor single-buyer integrated production-inventory model with a generalised policy , 1997 .

[14]  Kwong-Sak Leung,et al.  A novel splicing/decomposable binary encoding and its operators for genetic and evolutionary algorithms , 2007, Appl. Math. Comput..

[15]  Radivoj Petrovic,et al.  Modelling and simulation of a supply chain in an uncertain environment , 1998, Eur. J. Oper. Res..

[16]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[17]  Mitsuo Gen,et al.  An application of fuzzy set theory to inventory control models , 1997 .

[18]  Dobrila Petrovic,et al.  Simulation of supply chain behaviour and performance in an uncertain environment , 2001 .

[19]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[20]  Keith J. Burnham,et al.  A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand , 2006 .

[21]  Pierpaolo Pontrandolfo,et al.  A fuzzy echelon approach for inventory management in supply chains , 2003, Eur. J. Oper. Res..

[22]  Liang-Yuh Ouyang,et al.  A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand , 2002, Comput. Oper. Res..

[23]  Rong-Song He,et al.  Improving real-parameter genetic algorithm with simulated annealing for engineering problems , 2006, Adv. Eng. Softw..

[24]  Xiaohua Yang,et al.  A gray-encoded, hybrid-accelerated, genetic algorithm for global optimizations in dynamical systems , 2005 .

[25]  Radivoj Petrovic,et al.  Supply chain modelling using fuzzy sets , 1999 .

[26]  Kwang Y. Lee,et al.  Optimization method for reactive power planning by using a modified simple genetic algorithm , 1995 .

[27]  Fassil Nebebe,et al.  Determination of economic production-shipment policy for a single-vendor-single-buyer system , 2000, Eur. J. Oper. Res..

[28]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  M. A. Abido,et al.  Optimal multiobjective design of robust power system stabilizers using genetic algorithms , 2003 .

[30]  J. Winch,et al.  Supply Chain Management: Strategy, Planning, and Operation , 2003 .

[31]  Suresh Kumar Goyal,et al.  An optimal policy for a single-vendor single-buyer integrated production–inventory system with capacity constraint of the transport equipment , 2000 .

[32]  Andrew Wirth,et al.  Genetic Algorithms and Machine Scheduling With Class Setups , 1997 .

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