Journal of Mathematical Modelling and Algorithms

, Volume 10, Issue 4, pp 341–356

A Multi-Objective Production Inventory Model with Backorder for Fuzzy Random Demand Under Flexibility and Reliability


DOI: 10.1007/s10852-011-9160-6

Cite this article as:
Shah, N.H. & Soni, H. J Math Model Algor (2011) 10: 341. doi:10.1007/s10852-011-9160-6


In this paper, an Economic Production Quantity (EPQ) model is developed with flexibility and reliability consideration of production process in an imprecise and uncertain mixed environment. The model has incorporated fuzzy random demand, an imprecise production preparation time and shortage. Here, the setup cost and the reliability of the production process along with the backorder replenishment time and production run period are the decision variables. Due to fuzzy-randomness of the demand, expected average demand is a fuzzy quantity and also imprecise preparation time is represented by fuzzy number. Therefore, both are first transformed to a corresponding interval number and then using the interval arithmetic, the single objective function for expected profit over the time cycle is changed to respective multi-objective functions. Due to highly nonlinearity of the expected profit functions it is optimized using a multi-objective genetic algorithm (MOGA). The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.


Fuzzy random variable Imprecise preparation time Reliability Flexibility Interval arithmetic 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsGujarat UniversityAhmedabadIndia
  2. 2.Chimanbhai Patel Post Graduate Institute of Computer ApplicationsAhmedabadIndia

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