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An Optimum Inventory Policy for Exponentially Deteriorating Items, Considering Multi Variate Consumption Rate with Partial Backlogging


Customer purchasing deeds may be affected by factors such as selling price and inventory level instead of demand which is considered either constant or function of a single variable which is not feasible. Consequently, in the present study, we have considered the demand rate as a function of stock-level and selling price both. In the present study, in order to develop this model, it has been assumed that items are exponentially decaying and shortages are partially backlogged and the most realistic backlogging rate is considered. In this research, we proposed a partial backlogging inventory model for exponentially decaying items considering stock and selling price dependent demand rate in fuzzy environment. In developing the model demand rate, ordering cost, purchasing cost, holding cost, back ordering cost and opportunity cost are considered as triangular fuzzy numbers. Graded mean integration representation method is used for defuzzification. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of system parameters is also discussed.


  • Himanshu Pandey, Department of mathematics and statistics, DDU Gorakhpur University, Gorakhpur
  • Ashutosh Pandey, Department of mathematics and statistics, DDU Gorakhpur University, Gorakhpur



Inventory model, triangular fuzzy numbers, signed distance, stock and price dependent Demand, exponential distribution


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