P2 (20 points). One product in CSUEB bookstore is computer paper. The manager of the bookstore estimates that the demand is 1,000 boxes and will be sold this year at a constant rate throughout the year. The cost of placing an order is $20 per order. Average carrying cost is $0.50 per box. 2.a) Calculate optimal order quantity. (6pt) 2.b) Calculate the average inventory. (2pt) 2.c) Calculate the total cost based on ordering and holding cost (12 pt)
The Correct Answer and Explanation is:
Let’s solve this step-by-step using the EOQ (Economic Order Quantity) model:
Given:
- Annual demand (D) = 1,000 boxes
- Ordering cost (S) = $20 per order
- Holding cost per unit per year (H) = $0.50 per box
2.a) Optimal Order Quantity (EOQ):
The EOQ formula is: EOQ=2DSHEOQ = \sqrt{\frac{2DS}{H}} EOQ=2×1000×200.5=400000.5=80000≈282.84EOQ = \sqrt{\frac{2 \times 1000 \times 20}{0.5}} = \sqrt{\frac{40000}{0.5}} = \sqrt{80000} \approx 282.84
Optimal order quantity ≈ 283 boxes (rounded to nearest whole number)
2.b) Average Inventory:
Average inventory = EOQ / 2 Average Inventory=2832=141.5 boxes\text{Average Inventory} = \frac{283}{2} = 141.5 \text{ boxes}
2.c) Total Cost (Ordering + Holding):
- Ordering cost = (D / EOQ) × S = (1000 / 283) × 20 ≈ 3.53 × 20 ≈ $70.60
- Holding cost = (EOQ / 2) × H = (283 / 2) × 0.50 = 141.5 × 0.50 = $70.75
Total cost=Ordering cost+Holding cost=70.60+70.75=$141.35\text{Total cost} = \text{Ordering cost} + \text{Holding cost} = 70.60 + 70.75 = \text{\$141.35}
The Economic Order Quantity (EOQ) model is a fundamental tool in inventory management that minimizes the total costs associated with ordering and holding inventory. In this scenario, the CSUEB bookstore manager seeks to manage the inventory of computer paper effectively. The annual demand is 1,000 boxes, the cost to place a single order is $20, and it costs $0.50 to hold a box for a year.
To determine the most cost-effective order size, we apply the EOQ formula: EOQ=2DSHEOQ = \sqrt{\frac{2DS}{H}}
Substituting the given values, we find the EOQ to be approximately 283 boxes. This is the optimal number of boxes to order each time, minimizing the sum of ordering and holding costs.
Once the EOQ is determined, the average inventory held is simply half of that, or about 141.5 boxes. This is because inventory is assumed to be used at a constant rate from the full order down to zero.
To find the total cost, we calculate the ordering and holding costs. The ordering cost is determined by how many orders are placed in a year, and the holding cost depends on the average inventory. Adding these two gives a total cost of approximately $141.35 per year.
By using EOQ, the bookstore can efficiently balance between the high cost of frequent orders and the cost of holding large inventories. This minimizes waste, improves cash flow, and ensures products are available when needed
