Optimization and Engineering

, Volume 15, Issue 3, pp 751–772 | Cite as

A two storage production-repairing model with fuzzy defective rate and displayed inventory dependent demand

  • Madhab Mondal
  • Manas Kumar Maiti
  • Manoranjan Maiti


A two storage production-repairing system for a single item with stock-dependent demand is considered. Item is produced with fuzzy defective rate at a production center with a warehouse. Units are bulkly transformed from production center (PC) to a showroom (SR) at the market for sale and excess units are stored at the production center warehouse. After the production period, repairing process is commissioned and then defective units are repaired to new condition before being sold again. Model is formulated as a profit maximization problem using fuzzy differential equation and three different approaches—α-cut of fuzzy average profit, expected value and necessity measure of fuzzy event for defuzzification. A genetic algorithm (GA) with binary mode representation, Roulette wheel selection and random mutation process is used to solve the model. In the first approach, using fuzzy preference ordering of intervals (FPOI), α-cut of fuzzy average profit is optimized using the above GA to derive optimum decisions for the decision maker (DM). In second approach, expected value of average profit is obtained and is optimized using the above GA for optimal decision. In another approach fuzzy objective is directly optimized using necessity measure of fuzzy events for finding marketing decisions. The proposed model is illustrated with numerical examples and results obtained using different approaches are compared.


Two warehouse Fuzzy defective rate Production-repairing Bulk transportation Fuzzy differential equation Genetic algorithm 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Madhab Mondal
    • 1
  • Manas Kumar Maiti
    • 2
  • Manoranjan Maiti
    • 3
  1. 1.Department of MathematicsMahishadal Girls’ CollegePurba-MedinipurIndia
  2. 2.Department of MathematicsMahishadal Raj CollegePurba-MedinipurIndia
  3. 3.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityPaschim-MedinipurIndia

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