| Course | BU 421 Operations Management |
|---|---|
| Unit | Unit 5 |
| Paper type | Inventory policy write-up |
| Length | About 880 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Management |
| Updated | September 2026 |
Free sample paper for BU 421 Unit 5
Order 10,000 Hinges When Stock Falls to 3,661: An Inventory Policy Write-Up for a Composite Cabinet Plant's Soft-Close Hinges, Including the Discount Decision
Student Name
Business, Herzing University
BU 421: Operations Management
Instructor Name
March 11, 2026
Order 10,000 Hinges When Stock Falls to 3,661: An Inventory Policy Write-Up for a Composite Cabinet Plant's Soft-Close Hinges, Including the Discount Decision
The Item and Its Parameters
Tallgrass Cabinet Works, the invented Omaha cabinet plant used in this course, buys concealed soft-close hinges from a regional hardware distributor. Almost every door the plant ships hangs on two of them, and a stockout stops the packing line within hours, because a cabinet cannot ship without its doors hung. This write-up sets an order quantity and a reorder point for the hinge and tests a quantity discount the distributor has offered. Every parameter is stated with its unit and time base, since mixing an annual demand with a monthly cost is the error that would spoil every result below. The figures belong to the composite case.
| Parameter | Value | Unit and basis |
|---|---|---|
| Annual demand (D) | 104,000 | Hinges per year, from the 2027 plan of 52,000 boxes |
| Working days | 250 | Days per year |
| Average daily demand | 416 | Hinges per working day |
| Standard deviation of daily demand | 60 | Hinges per working day, from 2025 usage records |
| Lead time (L) | 8 | Working days from order to receipt |
| Unit cost (C) | $3.20 | Per hinge, standard price |
| Ordering cost (S) | $65 | Per order: purchasing $15, receiving and inspection $21, freight $25, payables $4 |
| Holding rate (i) | 24% | Per year: capital 10%, storage 6%, handling and insurance 3%, obsolescence 5% |
| Holding cost (H = iC) | $0.768 | Per hinge per year |
| Pack size | 200 | Hinges per carton |
The Order Quantity
The economic order quantity balances the cost of placing orders against the cost of holding stock. Harris (1990) first derived it in 1913 as the quantity at which the two costs are equal and their sum is smallest. The formula is EOQ equals the square root of 2DS divided by H.
Substituting the values: 2 times 104,000 times $65 is 13,520,000. Divided by $0.768, that gives 17,604,167. The square root is about 4,196 hinges. Rounded to whole cartons of 200, the order quantity becomes 4,200 hinges, or 21 cartons.
At 4,200 hinges, the plant places 104,000 divided by 4,200, or about 24.8 orders a year, one every 10.1 working days. Annual ordering cost is 24.8 times $65, or $1,609.52. Average cycle stock is half the order, 2,100 hinges, and annual holding cost is 2,100 times $0.768, or $1,612.80. The total is $3,222.32, with the two halves nearly equal, as the model predicts at its optimum.
How Flat the Cost Curve Is
A manager deciding whether rounding matters needs to know how quickly cost rises away from the optimum. Ordering 3,000 hinges, about 30 percent less, raises ordering cost to $2,253.33 and lowers holding cost to $1,152.00, a total of $3,405.33, only 5.7 percent above the optimum. Ordering 6,000, about 43 percent more, gives $1,126.67 of ordering cost and $2,304.00 of holding cost, a total of $3,430.67, 6.5 percent above. Silver et al. (2017) note that this flatness is one of the model's most useful properties: errors in the inputs or rounding to a convenient pack size cost little. For the hinge, rounding to cartons costs nothing measurable, and even rounding to a full pallet would cost only a few hundred dollars a year.
The Reorder Point and Safety Stock
Expected demand during the eight-day lead time is 416 times 8, or 3,328 hinges. Demand varies from day to day, so the plant needs safety stock to cover lead times in which usage runs high. The standard deviation of demand over the lead time is 60 times the square root of 8, or about 170 hinges. The plant has set a 97.5 percent cycle service level for hinges, meaning a stockout in no more than one replenishment cycle in 40, because a stockout stops shipping. The corresponding z value is 1.96, so safety stock is 1.96 times 170, or about 333 hinges. The reorder point is 3,328 plus 333, or 3,661 hinges.
This calculation assumes the lead time itself is steady. The distributor's delivery records show eight days in 46 of the last 50 orders and nine days in the other four, so the assumption is reasonable, but the buyer should recheck it quarterly. A longer or more variable lead time would call for a larger safety stock.
The Quantity Discount
The distributor has offered $3.05 a hinge on orders of 10,000 or more. With a discount, the right comparison is total annual cost including the purchase price, since a lower price can outweigh higher holding cost. At $3.05 the holding cost falls to $0.732 a hinge, and the EOQ at that price is about 4,298, below the 10,000 needed for the discount, so the discount is evaluated at exactly 10,000.
| Policy | Orders per year | Ordering cost | Holding cost | Purchase cost | Total annual cost |
|---|---|---|---|---|---|
| 4,200 at $3.20 | 24.8 | $1,609.52 | $1,612.80 | $332,800 | $336,022 |
| 10,000 at $3.05 | 10.4 | $676.00 | $3,660.00 | $317,200 | $321,536 |
The Policy
Taking the discount saves about $14,486 a year. Holding cost more than doubles, but the price reduction of 15 cents on 104,000 hinges is worth $15,600, far more than the added holding cost. The larger order also means ordering only about ten times a year instead of 25. The extra stock, about 29 more cartons at the top of each cycle, fits on two pallet positions the stockroom already has.
The recommended policy is therefore: order 10,000 hinges whenever stock on hand plus on order falls to 3,661. Each cycle lasts about 24 working days. The buyer should review the policy if annual demand changes by more than 10 percent, if the distributor withdraws the discount or if lead times lengthen. Heizer et al. (2020) caution that the model's inputs, especially holding cost, are often estimated loosely, but here the choice survives even a large error: the discount would stay worthwhile even if the true holding rate were several times the 24 percent used. The one input that could overturn it is demand, since a sharp fall in hinge usage would leave 10,000-piece orders sitting in the stockroom for months. The hinge buyer, the distributor and all prices and rates in this write-up are invented for the course.
References
Harris, F. W. (1990). How many parts to make at once. Operations Research, 38(6), 947-950. https://doi.org/10.1287/opre.38.6.947 (Original work published 1913)
Heizer, J., Render, B., & Munson, C. (2020). Operations management: Sustainability and supply chain management (13th ed.). Pearson.
Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017). Inventory and production management in supply chains (4th ed.). CRC Press.
BU 421 Unit 5 instructions, in plain terms
The inventory unit of BU 421 asks students to design an inventory policy for one item. Standard requirements include annual demand, ordering cost, holding cost and lead time; an economic order quantity with its total annual cost; a reorder point with safety stock for a chosen service level; and a discussion of assumptions. Many prompts add a quantity discount, which changes the comparison because purchase cost is no longer constant. Some ask for a sensitivity check or for what would make the policy change. Expect three to four pages with a parameter table and a cost comparison, in APA 7. The final policy should be stated in terms a buyer could follow, such as order a set quantity when stock falls to a set level.
Inside the BU 421 Unit 5 example
The sample opens with a parameter table, and each figure carries its unit and time base, with ordering and holding costs built from components such as purchasing, receiving, freight, capital, storage and obsolescence. The order quantity section applies the formula step by step and checks that ordering and holding costs come out nearly equal at the optimum. A sensitivity section tests orders 30 percent smaller and 43 percent larger, showing a cost increase of only about 6 percent. Safety stock is built from lead-time demand variation and a z value tied to the service level. The discount section compares total annual cost including purchase price at both quantities. The policy states the order quantity, the reorder point and the conditions under which the buyer should revisit both.
BU 421 Unit 5 rubric: what full points look like
Herzing's inventory rubric typically splits points across correct parameters, the order quantity calculation, the reorder point and safety stock, the discount or sensitivity analysis, and the final recommendation, with a share for clarity and APA. Parameter errors cascade, so instructors look first at whether annual and per-unit figures are consistent. The EOQ earns full credit with its working shown and costs verified. Safety stock is judged on whether the service level is justified and the variation measured over the lead time, not per day. For the discount, top marks go to papers that include purchase cost and evaluate the discount at its threshold when the EOQ falls below it. A clearly worded policy with review triggers completes the grade and shows the student understands the model's limits.
BU 421 Unit 5 help: mistakes that cost points
Mixing time bases is the classic error on the inventory unit, for instance pairing annual demand with a monthly holding cost, which throws the order quantity off by a large factor. Students often forget that safety stock depends on the variation of demand during the lead time, not on a single day. Another common mistake in discount problems is leaving purchase cost out of the total, which makes the discount look worthless. Some papers compute the EOQ at the discounted price and stop, even though it falls below the threshold required. Others give a reorder point without a service level, so no one can say how often it will run out. Finally, a policy with no conditions for review ignores the inputs most likely to change, particularly demand.
Get a BU 421 Unit 5 example written to your instructions
Send the Unit 5 instructions and the BU 421 rubric with whatever demand, cost and lead time figures your assignment specifies. We write a custom example that fixes units first, shows the substitution, tests the cost curve at a practical quantity and ties safety stock to the stated service level. First custom sample free, back in 24 to 48 hours.
More BU 421 papers and business management samples
- BU 421 Unit 1: Competitive priorities brief
- BU 421 Unit 2: Process flow documentation
- BU 421 Unit 3: Capacity planning worksheet
- BU 421 Unit 4: Demand planning record
- BU 421 Unit 6: Waste reduction proposal
- BU 421 Unit 7: Quality control chart record
- BU 421 Unit 8: Supply chain scheduling file
- BU 242 Unit 5: Value proposition
- BU 245 Unit 5: Short report with summary
- BU 302 Unit 5: Communication breakdown analysis
- BU 321 Unit 5: Hypothesis test write-up
BU 421 Unit 5 questions, answered
What happens when the supplier offers a quantity discount?
The comparison widens rather than changes. Compute the total annual cost at the basic order quantity and again at each discount threshold, including purchase cost this time, since price is no longer constant. Then take the lowest total. Show all the candidate quantities you tested, because a discount answer with only the winning line visible cannot be checked by a marker.
Where does the holding cost figure come from?
Usually from the case as a percentage of unit value, sometimes as a direct amount per unit per year. Convert it once, early, and carry the money figure through. It should cover capital tied up, storage, insurance and the risk of obsolescence. If your assignment leaves it open, state your components and say plainly that the composite firm supplied none of them.
How do I choose a service level?
From the cost of a stockout against the cost of holding more, and where the instructions name a level, from that. A part halting a production line justifies a high level; a slow moving item whose buyer can wait does not. Say what drove the choice, since a level chosen without reasoning makes the safety stock behind it unverifiable.
Where can I find a free BU 421 Unit 5 sample paper?
The complete BU 421 Unit 5 inventory policy write-up is published above for free, including the parameter table, the discount comparison and annotations. If your item, costs or service level are different, a free custom write-up can be prepared from your prompt and figures, usually within two days.
Does BU 421 Unit 5 need safety stock if lead time is steady?
Usually yes, because demand still varies from day to day. The sample treats lead time as steady, checks that assumption against 50 past orders, and sizes safety stock from the variation in demand over the eight-day lead time.