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Give step-by-step explanationA distribution warehouse supplies industrial components to a network of retailers across the region. The company currently operates without a formal inventory policy, often placing orders based on manager judgment. This has led to occasional stockouts and high holding costs. Management now wants to implement a structured continuous review inventory system that minimizes total inventory-related costs while maintaining product availability. The warehouse is focusing on a fast-moving component with the following operational data: + Annual demand: 12,000 units + Ordering cost per order: $100 + Unit purchase cost: $10 + Annual holding cost rate: 20% of unit cost + Supplier lead time: 5 working days = Working days per year: 300 + Standard deviation of daily demand: 5 units + Desired service level: 95% (Z = 1.645) The management wants to determine the optimal order quantity and reorder point, including safety stock for demand fluctuations during lead time. The objective is to ensure product availability while minimizing the combined cost of ordering and holding inventory. (3) Safety Stock and ROP with Safety Stock Calculate the safety stock required to achieve a 95% service level using the given Z-score. Then determine the adjusted ROP. Formulas: + Safety Stock=Z x 0 x JL = ROP with safety stock = Average demand during lead time + Safety stock Where: + Z=1.645 (for 95% service level) + 0 = Standard deviation of daily demand + L=Lead time in days Show both safety stock and ROP with safety stock, rounded to the nearest whole unit. (4) Total Annual Inventory Cost Compute the total inventory cost using the EOQ and safety stock from above. Include: + Annual ordering cost = (Annual demand + EOQ) x Ordering cost + Annual holding cost = (Average inventory x Holding cost per unit) Note: Average inventory = EOQ + 2 + Safety stock Present the total cost in dollars, rounded to two decimal places. (5) Inventory Replenishment Flowchart Design a simple conceptual flowchart that illustrates the warehouse's continuous inventory review process. Include these basic steps in your diagram: + Monitoring inventory levels + Comparing inventory to the reorder point « Placing an order if needed « Receiving and inspecting the shipment + Updating inventory records Use standard flowchart shapes (e.g., rectangle for process, diamond for decision, arrows for flow). No numerical values are required in the diagram.

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Give step-by-step explanationUploaded ImageUploaded ImageUploaded ImageA distribution warehouse supplies industrial components to a network of retailers across the region. The company currently operates without a formal inventory policy, often placing orders based on manager judgment. This has led to occasional stockouts and high holding costs. Management now wants to implement a structured continuous review inventory system that minimizes total inventory-related costs while maintaining product availability. The warehouse is focusing on a fast-moving component with the following operational data: + Annual demand: 12,000 units + Ordering cost per order: $100 + Unit purchase cost: $10 + Annual holding cost rate: 20% of unit cost + Supplier lead time: 5 working days = Working days per year: 300 + Standard deviation of daily demand: 5 units + Desired service level: 95% (Z = 1.645) The management wants to determine the optimal order quantity and reorder point, including safety stock for demand fluctuations during lead time. The objective is to ensure product availability while minimizing the combined cost of ordering and holding inventory. (3) Safety Stock and ROP with Safety Stock Calculate the safety stock required to achieve a 95% service level using the given Z-score. Then determine the adjusted ROP. Formulas: + Safety Stock=Z x 0 x JL = ROP with safety stock = Average demand during lead time + Safety stock Where: + Z=1.645 (for 95% service level) + 0 = Standard deviation of daily demand + L=Lead time in days Show both safety stock and ROP with safety stock, rounded to the nearest whole unit. (4) Total Annual Inventory Cost Compute the total inventory cost using the EOQ and safety stock from above. Include: + Annual ordering cost = (Annual demand + EOQ) x Ordering cost + Annual holding cost = (Average inventory x Holding cost per unit) Note: Average inventory = EOQ + 2 + Safety stock Present the total cost in dollars, rounded to two decimal places. (5) Inventory Replenishment Flowchart Design a simple conceptual flowchart that illustrates the warehouse's continuous inventory review process. Include these basic steps in your diagram: + Monitoring inventory levels + Comparing inventory to the reorder point « Placing an order if needed « Receiving and inspecting the shipment + Updating inventory records Use standard flowchart shapes (e.g., rectangle for process, diamond for decision, arrows for flow). No numerical values are required in the diagram.

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Asked by: Test User 100135
Created at: 2025-05-14 23:04:50

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Let's walk through the step-by-step solution for the requirements in your inventory management scenario: --- ## **Step 1: Calculate EOQ (Economic Order Quantity)** The EOQ formula is: \[ EOQ = \sqrt{\frac{2DS}{H}} \] Where: - \( D \) = Annual demand = **12,000 units** - \( S \) = Ordering cost per order = **$100** - \( H \) = Annual holding cost per unit = **20% x $10 = $2** \[ EOQ = \sqrt{\frac{2 \times 12000 \times 100}{2}} = \sqrt{\frac{2,400,000}{2}} = \sqrt{1,200,000} = 1,095 \text{ units (rounded to the nearest unit)} \] --- ## **Step 2: Calculate Safety Stock and Reorder Point (ROP) with Safety Stock** ### **Safety Stock Formula:** \[ \text{Safety Stock} = Z \times \sigma \times \sqrt{L} \] - \( Z \) = 1.645 (for 95% service level) - \( \sigma \) = Standard deviation of daily demand = **5 units** - \( L \) = Lead time in days = **5 days** \[ \text{Safety Stock} = 1.645 \times 5 \times \sqrt{5} = 1.645 \times 5 \times 2.236 = 1.645 \times 11.18 = 18.38 \text{ units} \] **Rounded:** **18 units** --- ### **ROP with Safety Stock:** \[ \text{ROP} = \text{Average demand during lead time} + \text{Safety Stock} \] - Daily demand = 12,000 units / 300 days = **40 units/day** - Average demand during lead time = 40 x 5 = **200 units** - Safety Stock = **18 units** \[ ROP = 200 + 18 = 218 \text{ units} \] --- ## **Step 3: Compute Total Annual Inventory Cost** ### **1. Annual Ordering Cost:** \[ \text{Annual Ordering Cost} = \left(\frac{12,000}{1,095}\right) \times 100 = 10.96 \times 100 = \$1,096 \] ### **2. Annual Holding Cost:** - Average inventory = EOQ/2 + Safety Stock = 1,095/2 + 18 = 547.5 + 18 = **565.5 units** - Holding cost per unit = **$2** \[ \text{Annual Holding Cost} = 565.5 \times 2 = \$1,131 \] ### **3. Total Annual Inventory Cost:** \[ \text{Total Annual Inventory Cost} = 1,096 + 1,131 = \$2,227 \] --- ## **Step 4: Inventory Replenishment Flowchart** Here’s a simple text-based flowchart outline: 1. **Start** 2. **Process:** Monitor Inventory Levels 3. **Decision (Diamond):** Is Inventory ≤ ROP? - **No:** Return to Monitor Inventory Levels - **Yes:** Place Order 4. **Process:** Receive and Inspect Shipment 5. **Process:** Update Inventory Records 6. **Return to:** Monitor Inventory Levels --- ## **Summary Table of Calculated Values:** | Metric | Value | |------------------------------|--------------| | EOQ | 1,095 units | | Safety Stock | 18 units | | ROP (with Safety Stock) | 218 units | | Annual Ordering Cost | $1,096 | | Annual Holding Cost | $1,131 | | **Total Annual Inventory Cost** | **$2,227** | --- Let me know if you want a graphical flowchart, or need any calculations clarified!

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