An interpolating by pass to Pareto optimality in intuitionistic fuzzy technique for a EOQ model with time sensitive backlogging

Abstract This article fuzzyfies EOQ crisp model with backlogged while demand of the customers varies with selling price and promotional effort. The demand rate in stock out situation decreases with duration of the shortage period and it comes back to its initial rate since promotional effort continues. The cost function consists of set up cost, inventory cost, shortage cost and cost for promotional effort. The coefficient vectors of the concerned minimization cost function are considered as fuzzy numbers which are transformed into interval numbers. Then, the interval objective function has been transformed into a classical multi-objective EOQ model using intuitionistic fuzzy technique. A comparative study on Pareto optimality and optimality under Lagrange’s interpolating polynomial function has been made illustrating numerical example.

[1]  Shib Sankar Sana,et al.  The EOQ model - A dynamical system , 2012, Appl. Math. Comput..

[2]  Hui-Ming Wee,et al.  An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain , 2012 .

[3]  Manoranjan Maiti,et al.  Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level , 1998, Comput. Oper. Res..

[4]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[5]  Ata Allah Taleizadeh,et al.  An improved solution to replenishment lot size problem with discontinuous issuing policy and rework, and the multi-delivery policy into economic production lot size problem with partial rework , 2012, Expert Syst. Appl..

[6]  Jing-Shing Yao,et al.  Production , Manufacturing and Logistics Fuzzy inventory with backorder for fuzzy order quantity and fuzzy shortage quantity , 2003 .

[7]  Masatoshi Sakawa,et al.  Interactive Computer Programs for Fuzzy Linear Programming with Multiple Objectives , 1983, Int. J. Man Mach. Stud..

[8]  Liang-Yuh Ouyang,et al.  Production , Manufacturing and Logistics Optimal pricing , shipment and payment policy for an integrated supplier – buyer inventory model with two-part trade credit , 2007 .

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

[10]  Satoko Titani,et al.  Intuitionistic fuzzy logic and intuitionistic fuzzy set theory , 1984, Journal of Symbolic Logic.

[11]  Michael Zhang,et al.  Optimal fences and joint price and inventory decisions in distinct markets with demand leakage , 2010, Eur. J. Oper. Res..

[12]  L. Barbosa,et al.  Deterministic Inventory Lot Size Models--A General Root Law , 1978 .

[13]  Shib Sankar Sana.  An EOQ model of homogeneous products while demand is salesmen's initiatives and stock sensitive , 2011, Comput. Math. Appl..

[14]  Madhumangal Pal,et al.  Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages , 2013, Eur. J. Oper. Res..

[15]  Shib Sankar Sana,et al.  An EOQ model for salesmen's initiatives, stock and price sensitive demand of similar products - A dynamical system , 2011, Appl. Math. Comput..

[16]  Timothy L. Urban,et al.  Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns , 1997 .

[17]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note , 2007 .

[18]  Yi-Chih Hsieh,et al.  An EOQ model with stock and price sensitive demand , 2007, Math. Comput. Model..

[19]  Huey-Ming Lee,et al.  Economic order quantity in fuzzy sense for inventory without backorder model , 1999, Fuzzy Sets Syst..

[20]  Shib Sankar Sana,et al.  Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach , 2015, Ann. Oper. Res..

[21]  B. Sarkar,et al.  A stock-dependent inventory model in an imperfect production process , 2010 .

[22]  B. Sarkar,et al.  An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand , 2013 .

[23]  Biswajit Sarkar,et al.  A finite replenishment model with increasing demand under inflation , 2010, Int. J. Math. Oper. Res..

[24]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[25]  Chih-Hsun Hsieh,et al.  Optimization of fuzzy production inventory models , 2002, Inf. Sci..

[26]  Liang-Yuh Ouyang,et al.  Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number , 2004 .

[27]  Adrijit Goswami,et al.  Fuzzy EOQ models with ramp type demand rate, partial backlogging and time dependent deterioration rate , 2012, Int. J. Math. Oper. Res..

[28]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Solving the vendor-buyer integrated inventory system with arithmetic-geometric inequality , 2011, Math. Comput. Model..

[29]  Timothy L. Urban,et al.  Single-period inventory dependent demand models , 1988 .

[30]  Hon-Shiang Lau,et al.  Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model , 2003, Eur. J. Oper. Res..

[31]  Kin Keung Lai,et al.  Analysis of the impact of price-sensitivity factors on the returns policy in coordinating supply chain , 2008, Eur. J. Oper. Res..

[32]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[33]  C. Kao,et al.  Lot size-reorder point inventory model with fuzzy demands , 2002 .

[34]  Didier Dubois,et al.  Terminological difficulties in fuzzy set theory - The case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

[35]  Ata Allah Taleizadeh,et al.  A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand , 2013, Inf. Sci..

[36]  K. S. Chaudhuri,et al.  Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale , 2011, Appl. Math. Comput..

[37]  Shib Sankar Sana,et al.  Demand influenced by enterprises' initiatives - A multi-item EOQ model of deteriorating and ameliorating items , 2010, Math. Comput. Model..

[38]  R. S. Sachan.  On (T, Si) Policy Inventory Model for Deteriorating Items with Time Proportional Demand , 1984 .

[39]  Shib Sankar Sana,et al.  Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index , 2013 .

[40]  Shib Sankar Sana.  An EOQ model for stochastic demand for limited capacity of own warehouse , 2015, Ann. Oper. Res..

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

[42]  Shan-Huo Chen,et al.  Backorder Fuzzy Inventory Model under Function Principle , 1996, Inf. Sci..

[43]  Radivoj Petrovic,et al.  EOQ formula when inventory cost is fuzzy , 1996 .

[44]  Leopoldo Eduardo Cárdenas-Barrón,et al.  A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model , 2012, Expert Syst. Appl..

[45]  Plamen P. Angelov,et al.  Optimization in an intuitionistic fuzzy environment , 1997, Fuzzy Sets Syst..