A deteriorating multi-item inventory model with price discount and variable demands via fuzzy logic under resource constraints

An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a wholesaler having showrooms at different places under a single management system is considered under random business periods with fuzzy resource constraints. The wholesaler replenishes the products instantaneously and earns commissions on MRP which vary with the ordered quantities following All Unit Discount (AUD), Incremental Quantity Discount (IQD) or IQD in AUD policy. Demand at showrooms are imprecise and related to selling prices by 'verbal words' following fuzzy logic. The wholesaler shares a part of commission with customers. The business periods follows normal distribution and converted to deterministic ones through chance constraint technique. The fuzzy space and budget constraints and fuzzy relations are defuzzified using possibility measures, surprise function and Mumdani fuzzy inference technique. The model is formulated as profit maximization for the wholesaler and solved using a real coded Genetic Algorithm (GA) and illustrated through some numerical examples and some sensitivity analysis. A real-life problem of a developing country is presented, solved using the above mentioned procedures and an appropriate inventory policy is suggested.

[1]  Bhaba R. Sarker,et al.  Optimal manufacturing batch size with rework process at a single-stage production system , 2004, Comput. Ind. Eng..

[2]  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..

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

[4]  Gary B. Lamont,et al.  A Statistical Comparison of Multiobjective Evolutionary Algorithms Including the MOMGA-II , 2001, EMO.

[5]  Hang Yin,et al.  Stability analysis of the simplest Takagi-Sugeno fuzzy control system using Popov criterion , 2007 .

[6]  Chandan Gurnani.  Economic analysis of inventory systems: a reply , 1985 .

[7]  Leopoldo Eduardo Cárdenas-Barrón.  Optimal manufacturing batch size with rework in a single-stage production system - A simple derivation , 2008, Comput. Ind. Eng..

[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]  Chi-Bin Cheng,et al.  Group opinion aggregationbased on a grading process: A method for constructing triangular fuzzy numbers , 2004 .

[10]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Economic production quantity with rework process at a single-stage manufacturing system with planned backorders , 2009, Comput. Ind. Eng..

[11]  Ilkyeong Moon,et al.  The effects of inflation and time-value of money on an economic order quantity model with a random product life cycle , 2000, Eur. J. Oper. Res..

[12]  Leopoldo Eduardo Cárdenas-Barrón.  On optimal manufacturing batch size with rework process at single-stage production system , 2007, Comput. Ind. Eng..

[13]  A. Goswami,et al.  An inventory model for deteriorating items with stock-dependent demand rate , 1996 .

[14]  Leopoldo Eduardo Cárdenas-Barrón.  On optimal batch sizing in a multi-stage production system with rework consideration , 2009, Eur. J. Oper. Res..

[15]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

[16]  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..

[17]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[18]  Manoranjan Maiti,et al.  A Deterministic Inventory Replenishment Problem for Deteriorating Items with Time-Dependent Demand and Shortages for the Finite Time Horizon , 1997 .

[19]  Hui-Ming Wee,et al.  Economic order quantity model for deteriorating items with planned backorder level , 2011, Math. Comput. Model..

[20]  Manoranjan Maiti,et al.  Two storage inventory model with random planning horizon , 2006, Appl. Math. Comput..

[21]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

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

[23]  Bhaba R. Sarker,et al.  Optimal batch sizing in a multi-stage production system with rework consideration , 2008, Eur. J. Oper. Res..

[24]  Manoranjan Maiti,et al.  Production-inventory Model for a deteriorating Item with Imprecise Preparation Time for Production in a Finite Time Horizon , 2006, Asia Pac. J. Oper. Res..

[25]  S. Kar,et al.  An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon , 2009 .

[26]  B. Mandal,et al.  An Inventory Model for Deteriorating Items and Stock-dependent Consumption Rate , 1989 .

[27]  Nils Brunsson.  My own book review : The Irrational Organization , 2014 .