# Inventory Management Analysis This document addresses several inventory management questions for Products A through E, based on data. The analysis covers EOQ calculation, total costs, safety stock, and Kanban bin size. --- ## Product Data Summary | Product | Orders | Demand (units) | Lead Time (days) | V ($/unit) | C ($/unit) | Carrying Cost % | Standard Deviation Demand | Standard Deviation Lead Time | Fill Rate (%) | |---------|---------|----------------|------------------|------------|------------|----------------|---------------------------|------------------------------|--------------| | A | 7 | 20 | 2 | $2.00 | $2.25 | 22.5% | 5 | 1 | 99 | | B | 5 | 50 | | $5.00 | $2.00 | 20% | | | 98 | | C | | 80 | 2 | $8.00 | $1.50 | 15% | | | 95 | | D | | 40 | 4 | $4.00 | $2.00 | 22.5% | 5 | 2 | 95 | | E | | 60 | 1 | $6.00 | $2.00 | 25% | 2 | | 90 | --- ## 1. EOQ for Product A ### Formula: \[ EOQ = \sqrt{\frac{2DS}{H}} \] - \( D = 20 \) units/year - \( S = \text{Ordering cost} \) (assumed to be $30 based on data) - \( H = \text{Holding cost per unit} = V \times \text{Carrying Cost \%} \) ### Calculation: \[ H = 2 \times .225 = \$.45 \] \[ EOQ = \sqrt{\frac{2 \times 20 \times 30}{.45}} = \sqrt{\frac{120}{.45}} \approx \sqrt{2666.67} \approx 51.64 \text{ units} \] **Answer:** **EOQ for Product A ≈ 52 units** --- ## 2. Total Cost for Product B ### Components: - **Ordering Cost:** \( \frac{D}{Q} \times S \) - **Holding Cost:** \( \frac{Q}{2} \times H \) ### Assumptions: - \( D = 50 \) units/year - \( Q = \text{EOQ} \) (calculated as above or use data; approximate with demand and costs) - \( S = \$30 \) - \( H = 5.00 \times .2 = \$1.00 \) ### Calculation: Using EOQ: \[ EOQ = \sqrt{\frac{2 \times 50 \times 30}{.00}} = \sqrt{300} \approx 54.77 \text{ units} \] - **Ordering Cost:** \[ (50 / 54.77) \times 30 \approx .91 \times 30 \approx \$27.30 \] - **Holding Cost:** \[ (54.77 / 2) \times 1.00 \approx 27.39 \text{ dollars} \] **Total Cost ≈ \$27.30 + \$27.39 ≈ \$54.69** **Answer:** **Total Cost ≈ \$55** --- ## 3. Inventory Holding Cost for Product C ### Calculation: \[ H = V \times \text{Carrying Cost \%} = 8 \times .15 = \$1.20 \] ### Holding Cost: \[ \frac{Q}{2} \times H \] Assuming \( Q \) similar to demand: \[ Q \approx 80 \text{ units} \] \[ \text{Holding Cost} = \frac{80}{2} \times 1.20 = 40 \times 1.20 = \$48 \] **Answer:** **Inventory Holding Cost ≈ \$48** --- ## 4. EOQ for Product D ### Calculation: \[ D = 40, \quad S = \$30, \quad H = 4 \times .225 = \$.90 \] \[ EOQ = \sqrt{\frac{2 \times 40 \times 30}{.90}} = \sqrt{\frac{240}{.90}} \approx \sqrt{2666.67} \approx 51.64 \text{ units} \] **Answer:** **EOQ for Product D ≈ 52 units** --- ## 5. Inventory Holding Cost for Product E ### Calculation: \[ H = 6 \times .25 = \$1.50 \] \[ Q \approx 60 \text{ units} \] \[ \text{Holding Cost} = \frac{60}{2} \times 1.50 = 30 \times 1.50 = \$45 \] **Answer:** **Inventory Holding Cost ≈ \$45** --- ## 6. Safety Stock for Product A (99% fill rate) ### Formula: \[ SS = Z \times \sigma_{LT} \times \sqrt{D} \] - \( Z \) for 99% ≈ 2.33 - \( \sigma_{LT} = \) standard deviation of lead time demand (assumed to be \( \sigma_D \times \sqrt{LT} \)) - \( \sigma_D = 5 \) - \( LT = 2 \) days \[ \sigma_{LT} = 5 \times \sqrt{2} \approx 5 \times 1.414 \approx 7.07 \] \[ SS = 2.33 \times 7.07 \times \sqrt{20} \approx 2.33 \times 7.07 \times 4.47 \approx 2.33 \times 31.65 \approx 73.8 \text{ units} \] **Answer:** **Safety stock ≈ 74 units** --- ## 7. Combined Standard Deviation of Lead Time and Demand for Product B - Since \( \sigma_D = \), the combined variability is: \[ \sigma_{total} = \sqrt{(\sigma_D^2 \times LT) + (\sigma_{LT}^2 \times D^2)} \] But since lead time is zero, the variability is zero: **Answer:** **Standard deviation = units** --- ## 8. Safety Stock for Product C (98% fill rate) - \( Z \) for 98% ≈ 2.05 - \( \sigma_D = \), \( \sigma_{LT} = \) Thus, **safety stock = units** due to no variability. --- ## 9. Safety Stock for Product D (95% fill rate) - \( Z \) ≈ 1.645 - \( \sigma_D = 5 \), \( LT = 4 \) days, \( \sigma_{LT} = 2 \) Calculations: \[ SS = Z \times \sqrt{(\sigma_D^2 \times LT) + (\sigma_{LT}^2 \times D^2)} \approx 1.645 \times \sqrt{(25 \times 4) + (4 \times 40^2)} \] \[ = 1.645 \times \sqrt{100 + 4 \times 160} = 1.645 \times \sqrt{100 + 640} = 1.645 \times \sqrt{650} \approx 1.645 \times 80.62 \approx 132.7 \text{ units} \] **Answer:** **Safety stock ≈ 133 units** --- ## 10. Safety Stock for Product E (90% fill rate) - \( Z \) ≈ 1.28 - \( \sigma_D = 2 \), \( LT = 1 \) day, \( \sigma_{LT} = \) \[ SS = 1.28 \times 2 \times \sqrt{1} = 1.28 \times 2 = 2.56 \text{ units} \] **Answer:** **Safety stock ≈ 3 units** --- ## 11. Kanban Bin Sizes ### Formula: \[ Bin \, Size = \text{Demand during lead time} + \text{Safety stock} \] - Demand during lead time: \[ D_{LT} = \frac{D}{365} \times LT \] ### Calculations: | Product | Lead Time | Demand per day | Demand during LT | Safety Stock | Bin Size | |---------|--------------|------------------|------------------|--------------|----------| | A | 2 days | 20 / 365 ≈ .055 | .11 | 74 | 74 + .11 ≈ 75 units | | B | days | 50 / 365 ≈ .137 | | | units | | C | 2 days | 80 / 365 ≈ .219 | .44 | | .44 units (round to 1) | | D | 4 days | 40 / 365 ≈ .11 | .44 | 133 | 133 + .44 ≈ 134 units | | E | 1 day | 60 / 365 ≈ .164 | .164 | 3 | 3 + .164 ≈ 3 units | --- # Final Summary - **EOQ for Product A:** ~52 units - **Total Cost for Product B:** ~$55 - **Inventory Holding Cost for Product C:** ~$48 - **EOQ for Product D:** ~52 units - **Inventory Holding Cost for Product E:** ~$45 - **Safety Stock:** - Product A (99%): ≈ 74 units - Product B (98%): units - Product C (98%): units - Product D (95%): ≈ 134 units - Product E (90%): ≈ 3 units - **Kanban Bin Sizes:** - Product A: 75 units - Product B: units - Product C: 1 unit - Product D: 134 units - Product E: 3 units This detailed analysis guides optimal inventory levels, reorder points, safety stocks, and Kanban bin sizing for each product based on demand variability and service level targets.