## 5 Result and Discussion  
### Results of Linear Programming  
For Case \(1\) (Section 4.1), warehouse utilization is based on the demand box percentage and maximum limits provided by the company. The limitations are the percentage of boxes: \(x_{1}\) = 55 to 60%, or 7200 boxes; \(x_{2}\) = 20 to 30%, or 3600 boxes; and \(x_{3}\) = 10 to 25%, or 1200 boxes. Using the LP Excel Solver, the analysis found that a storage rack volume of 475.188 m\({}^{3}\) is used compared to the total volume of the warehouse of 2793.648 m\({}^{3}\). The given variable constraint and the maximum box limits are reached. Opportunities for improvement are available since only 17.01% of the warehouse storage is utilized, leading to the consideration of Case 2. Case 2 (Section 4.1) looks at maximizing the full warehouse space and determining the maximum quantity of each box based on the demand percentage. The main motive is to maximize the utilization of the warehouse rack space, and the values of the variables are increased six-fold: \(x_{1}\)\(\leq\) 43,200; \(x_{2}\)\(\leq\) 21,600; and \(x_{3}\)\(\leq\) 7200. The results for Case 2 showed that 100% of the warehouse storage space is utilized, and the quantities of Box 1, Box 2, and Box 3 that can be stored are 42,002, 21,600, and 7200 units, respectively. These variables increased significantly by 483 to 500% compared to Case 1, and the warehouse utilization is 100%. Furthermore, the optimum quantity of products that can be stored on shelves can be 70,802 boxes. The logistics team can decide on the quantity of product which can be stored on the respective shelves. For Case 3 (Section 4.1), the limitations are based on the products' monthly demand (i.e., July-October) and the total number of units stored in their respective boxes. In this case, the percentages of boxes are considered, following the supplier warehouse standards provided by the respective department. Therefore, the percentages of boxes with respect to the number of products are as follows: \(x_{1}\) = 55 to 60%, or 4,032,000 products in Box 1; \(x_{2}\) = 20 to 30%, or 1,152,000 products in Box 2; and \(x_{3}\) = 10 to 25%, or 288,000 products in  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rack** & \(D_{j}^{+}\) & \(D_{j}^{-}\) & \(DA_{i}\)=\(\frac{D_{j}^{-}}{D_{j}^{-}+D_{j}^{-}}\) & **Rank** \\ \hline A1 & 1.004 & 0.872 & 0.4650 & 14 \\ \hline A2 & 0.890 & 0.980 & 0.52  
Box 3. The results for Case 3 show that the optimum quantities of boxes the supplier needs to store in the warehouse are 91,660 of Box 1, 57,600 of Box 2, and 19,200 of Box 3 to meet the customer demand over the four-month period that is considered peak season for the supplier warehouse. Considering the weekly supply, the optimum storage quantities are 5729 of Box 1, 3600 of Box 2, and 1200 of Box 3, totaling 10,529 boxes per week to meet customer demand. Finally, in Case 4 (Section 4.1), the limitations are based on the weekly product demand and the total number of units that can be stored in their respective boxes. Similar to Case 3, the optimum quantity of products that can be stored in the warehouse based on the weekly product demand is determined. The percentages of boxes with respect to the number of products are as follows: \(x_{1}=55\) to 60%, or 288,000 products; \(x_{2}=20\) to 30%, or 90,000 products, and \(x_{3}=10\) to 25%, or 24,000 products. The results for Case 4 show that the optimum quantities of boxes the supplier needs to store in the warehouse are 5343 of Box 1, 4500 of Box 2, and 1600 of Box 3 to meet customer demand over a week, totaling a minimum of 11,443 boxes. When comparing the cases for the LP, Case 1 and Case 2 focus on warehouse utilization with respect to the number of boxes required to fill its capacity; Case 3 and Case 4 focus on the customer demand for the product, such that the supplier stores the minimum quantities of boxes in the warehouse according to the required units ordered.