Warehouse Storage Optimizer

Effective Item Volume:

\\[ V_i^{\text{eff}} = V_i \cdot S \\]

Priority Weight:

\\[ W_i = P_i \\]

Total Weight:

\\[ W_{\text{total}} = \sum W_i \\]

Allocated Volume per Item:

\\[ A_i = \min\left(V_i^{\text{eff}}, \frac{W_i}{W_{\text{total}}} \cdot V_{\text{warehouse}} \cdot A_{\text{factor}}\right) \\]

Total Allocated Volume:

\\[ A_{\text{total}} = \sum A_i \\]

Space Utilization Score:

\\[ U = \min\left(100 \cdot \frac{A_{\text{total}}}{V_{\text{warehouse}}}, 100\right) \\]

Where:

• \\( V_i^{\text{eff}} \\): Effective volume for item \\( i \\) (cubic meters)
• \\( V_i \\): Base volume of item \\( i \\) (cubic meters)
• \\( S \\): Stacking factor (Loose: 0.8, Standard: 0.9, Optimal: 1.0)
• \\( W_i \\): Priority weight for item \\( i \\) (Low: 1, Medium: 2, High: 3)
• \\( W_{\text{total}} \\): Sum of weights
• \\( A_i \\): Allocated volume for item \\( i \\) (cubic meters)
• \\( V_{\text{warehouse}} \\): Total warehouse volume (cubic meters)
• \\( A_{\text{factor}} \\): Accessibility factor (0.9)
• \\( A_{\text{total}} \\): Total allocated volume (cubic meters)
• \\( U \\): Space utilization score (%)

\\[ V_{\text{Pallets}}^{\text{eff}} = 200 \cdot 0.8 = 160 \ \text{m³}, \quad V_{\text{Boxes}}^{\text{eff}} = 100 \cdot 0.8 = 80 \ \text{m³} \\] \\[ W_{\text{Pallets}} = 3, \quad W_{\text{Boxes}} = 1 \\] \\[ W_{\text{total}} = 3 + 1 = 4 \\] \\[ A_{\text{Pallets}} = \min\left(160, \frac{3}{4} \cdot 500 \cdot 0.9\right) = \min(160, 337.5) = 160 \ \text{m³} \\] \\[ A_{\text{Boxes}} = \min\left(80, \frac{1}{4} \cdot 500 \cdot 0.9\right) = \min(80, 112.5) = 80 \ \text{m³} \\] \\[ A_{\text{total}} = 160 + 80 = 240 \ \text{m³} \\] \\[ U = 100 \cdot \frac{240}{500} = 48 \ \% \\]

\\[ V_{\text{Pallets}}^{\text{eff}} = 300 \cdot 0.9 = 270 \ \text{m³}, \quad V_{\text{Boxes}}^{\text{eff}} = 200 \cdot 0.9 = 180 \ \text{m³}, \quad V_{\text{Crates}}^{\text{eff}} = 100 \cdot 0.9 = 90 \ \text{m³} \\] \\[ W_{\text{Pallets}} = 3, \quad W_{\text{Boxes}} = 2, \quad W_{\text{Crates}} = 1 \\] \\[ W_{\text{total}} = 3 + 2 + 1 = 6 \\] \\[ A_{\text{Pallets}} = \min\left(270, \frac{3}{6} \cdot 1000 \cdot 0.9\right) = \min(270, 450) = 270 \ \text{m³} \\] \\[ A_{\text{Boxes}} = \min\left(180, \frac{2}{6} \cdot 1000 \cdot 0.9\right) = \min(180, 300) = 180 \ \text{m³} \\] \\[ A_{\text{Crates}} = \min\left(90, \frac{1}{6} \cdot 1000 \cdot 0.9\right) = \min(90, 150) = 90 \ \text{m³} \\] \\[ A_{\text{total}} = 270 + 180 + 90 = 540 \ \text{m³} \\] \\[ U = 100 \cdot \frac{540}{1000} = 54 \ \% \\]

\\[ V_{\text{Pallets}}^{\text{eff}} = 1000 \cdot 1.0 = 1000 \ \text{m³}, \quad V_{\text{Boxes}}^{\text{eff}} = 800 \cdot 1.0 = 800 \ \text{m³}, \quad V_{\text{Crates}}^{\text{eff}} = 600 \cdot 1.0 = 600 \ \text{m³} \\] \\[ V_{\text{Drums}}^{\text{eff}} = 400 \cdot 1.0 = 400 \ \text{m³}, \quad V_{\text{Bags}}^{\text{eff}} = 200 \cdot 1.0 = 200 \ \text{m³} \\] \\[ W_{\text{Pallets}} = 3, \quad W_{\text{Boxes}} = 3, \quad W_{\text{Crates}} = 2, \quad W_{\text{Drums}} = 2, \quad W_{\text{Bags}} = 1 \\] \\[ W_{\text{total}} = 3 + 3 + 2 + 2 + 1 = 11 \\] \\[ A_{\text{Pallets}} = \min\left(1000, \frac{3}{11} \cdot 3000 \cdot 0.9\right) = \min(1000, 818.18) = 818.18 \ \text{m³} \\] \\[ A_{\text{Boxes}} = \min\left(800, \frac{3}{11} \cdot 3000 \cdot 0.9\right) = \min(800, 818.18) = 800 \ \text{m³} \\] \\[ A_{\text{Crates}} = \min\left(600, \frac{2}{11} \cdot 3000 \cdot 0.9\right) = \min(600, 545.45) = 545.45 \ \text{m³} \\] \\[ A_{\text{Drums}} = \min\left(400, \frac{2}{11} \cdot 3000 \cdot 0.9\right) = \min(400, 545.45) = 400 \ \text{m³} \\] \\[ A_{\text{Bags}} = \min\left(200, \frac{1}{11} \cdot 3000 \cdot 0.9\right) = \min(200, 272.73) = 200 \ \text{m³} \\] \\[ A_{\text{total}} = 818.18 + 800 + 545.45 + 400 + 200 = 2763.64 \ \text{m³} \\] \\[ U = 100 \cdot \frac{2763.64}{3000} \approx 92.1 \ \% \\]