A Partial Backlogging Inventory Model for Deteriorating Item under Fuzzy Inflation and Discounting over Random Planning Horizon: A Fuzzy Genetic Algorithm Approach

Algorithm 2

An algorithm to determine 𝑍, for Model 2.

(1) Set 𝑍=𝑍₀−𝜀,𝐹=𝑍₀−𝜀,𝐹₀=𝑍₀−𝜀,𝑡𝑜𝑙=0.0001.

(2) Generate 𝑝₀ uniformly from the 1−𝛼₂ cut set of fuzzy

  number 𝑝.

(3) Set 𝑍₀ = value of 𝐸{𝑓(𝑥,𝑦,𝑝) for 𝑝=𝑝₀.

(4) If 𝑍₀<𝑍.

(5)    then go to step 11.

(6) End If

(7) Repeat step-2 to step-6 𝑁 times.

(8) Set 𝐹=𝑍.

(9) Set 𝑍=𝑍+𝜀.

(10) Go to step-2.

(11) If (𝑍=𝐹) // In this case optimum value of 𝑍<𝑍₀−𝜀

(12)  Set 𝑍=𝐹₀−𝜀,𝐹=𝐹−𝜀,𝐹₀=𝐹₀−𝜀.

(13)  Go to step-2

(14) End If

(15) If (𝜀<𝑡𝑜𝑙)

(16)  go to step-21

(17) End If

(18) 𝜀=𝜀/𝑁

(19) 𝑍=𝐹+𝜀

(20) Go to step-2.

(21) Output 𝐹.