# A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate
## 6 A Real Case Study  
We visited the West Bengal fisheries corporation Ltd. situated in Sector V, Salt Lake City, Kolkata, West Bengal 700091, India ((latitude, longitude) = (22.5691\({}^{\circ}\) N, 88.4337\({}^{\circ}\) E)) on 10 December 2020. After a long discussion with the manager Mr. [PERSON], we knew that they cleaned the lake properly at the beginning of each cycle. After that, the fingerlings were stocked and fed in the lake until the fingerlings acquired the ideal size for selling. We collected some valuable data related to our proposed model: \(d=4,000,000\) g/year, \(g=912.5\) g/year, \(v_{0}=100\) g,  
\(v_{1}=600\) g,  
\(t_{1}=0.019\) year, \(s=\$0.01\) g, \(f=\$0.8/\)g/year, \(c_{2}=\$100/\)year, \(n_{c}=\$40/\)year, \(B=\$80/\)year, \(\rho=0.4,\text{ and }\sigma=0.2\). The upper bound and lower bound of the demand rate were set to \(d_{0}^{L}=3,600,000\) and \(d_{0}^{U}=4,000,000\). Utilising the above rule, the key values of the demand rate were obtained as follows:\[\left[ \begin{array}{c}l_{1}\\ l_{2}\end{array} \right]\geq\left[ \begin{array}{c}\frac{d\rho}{2\left(d-2d^{l }\right)}\\ \frac{d\sigma}{2\left(2d^{l}-d\right)}\end{array} \right]=\left[ \begin{array}[ ]{c}\frac{4,000,000\times 0.4}{2\left(4,000,000\times 0.2\times 3,000,00\right)} \\ \frac{d\sigma}{2\left(4,000,000\times 0.2\right)}\\ \frac{d\sigma}{2\left(2\times 4,0000\times 0.4,0000\right)}\end{array}  \right]=\left[ \begin{array}{c}-0.25\\ 0.083\end{array} \right]. \tag{41}\]  
Satisfying the above condition, let \(l_{1}=0.38\) and \(l_{2}=0.25\); accordingly, the optimal solutions of the crisp model and several fuzzy models are given in Table 2.  
Table 2 shows that the total inventory cost of the proposed model is $319,476.8 in the crisp case. For a general fuzzy environment, the inventory cost is $308,834.3. In a parabolic dense fuzzy environment, the minimum total inventory cost is $314,155.5 for learning experience \(N=1\), whereas, for TDFLS, the minimum total inventory cost is $300,276.8 with a growing period of 0.5479 years \(\approx\) 200 days, a selling period of 0.4327 years \(\approx\) 158 days, and 2838 ordered items for learning experience \(N=3\). From Table 2, it is also clear that, in the general fuzzy model, the total inventory cost decreases by 3.33%. In the parabolic dense fuzzy model, the total inventory cost decreases by 1.66%, whereas, in the PDFLS model, the total inventory cost decreases by 6.00%. Thus, TDFLS gave the minimum inventory cost of the proposed model. Sensitivity AnalysisFrom Table 2, we can see that parabolic dense fuzzy lock set gave the optimum value of the proposed model. Hence, we conducted a sensitivity analysis over the parabolic dense fuzzy model. We changed each parameter \((v_{0},v_{1},s,f,c_{2},n_{c},\rho,\) and \(\sigma)\) from \(-30\%\) to \(+30\%\), and the results are given in Table 3. Furthermore, a graphical illustration of Table 3 is presented in Section 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Approach** & \(N^{\star}\) & **Time (\(t_{2}^{\star}\))** & **Time (\(t_{3}^{\star}\))** & **Ordered Items (\(y^{\star}\))** & **Total Cost (\(Z^{\star}\))** & \(\frac{Z^{\star}-Z_{\text{Guzz}}}{Z_{\text{Guzz}}}\times\)**100** \\ \hline \hline Crisp & - & 0.5479 & 0.4330 & 2887 & 319,476.8 & - \\ \hline General Fuzzy & - & 0.5479 & 0.4330 & 2790 & 308,834.3 & \(-3.33\) \\ \hline \multirow{3}{*}{Parabolic dense fuzzy} & 1 & 0.5479 & 0.4327 & 2838 & 314,155.5 & \(-1.66\) \\ \cline{2-6}  & 2 & 0.5479 & 0.4321 & 2846 & 315,042.4 & \(-1.39\) \\ \cline{2-6}  & 3 & 0.5479 & 0.4318 & 2852 & 315,633.7 & \(-1.20\) \\ \hline \multirow{3}{*}{PDFLS} & 1 & 05479 & 0.4330 & 2740 & 303,233.0 & \(-5.08\) \\ \cline{2-6}  & 2 & 0.5479 & 0.4331 & 2724 & 301,459.3 & \(-5.64\) \\ \cline{1-1} \cline{2-6}  & 3 & 0.5479 & 0.4330 & 2713 & 300,276.8 & \(-6.00\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical result of the proposed model.