| Course | SOP-7200 Strategic Operations Management |
|---|---|
| Module | Module 3 |
| Paper type | Written assignment 3: supply chain and inventory problems |
| Length | About 1,038 words, 6 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | Master of Business Administration |
| Updated | October 2026 |
Free sample paper for SOP 7200 Module 3
Cartons, Discounts and Safety Stock: Inventory Problems for a Fulfillment Center
Student Name
Master of Business Administration, Thomas Edison State University
SOP-7200: Strategic Operations Management
Mentor Name
Month Day, Year
Cartons, Discounts and Safety Stock: Inventory Problems for a Fulfillment Center
These problems return to Port Newark Fulfillment, the composite third-party center in Elizabeth, New Jersey, used in the earlier assignments, and apply the Module 3 material in Krajewski et al. (2016) on supply chain design and inventory management. Two kinds of inventory matter here. The center owns its packaging supplies, chiefly corrugated cartons, and it holds finished goods that belong to its client brands. The general manager wants a purchasing policy for cartons and advice for two clients whose stock behaves very differently. Each answer gives the formula, the inputs with units and the decision.
Problem 1: Economic Order Quantity for Cartons
The center's most used carton, a medium box, is consumed at 312,000 units a year, about 6,000 a week. Each purchase order costs $85 to place, receive and inspect. Cartons cost $0.48 each, and the center's annual holding rate is 25 percent of unit cost, so holding one carton for a year costs $0.12. The economic order quantity, derived in its classic form by Harris (1990) in a paper first published in 1913, takes the square root of two times annual demand times order cost, over the holding cost.
EOQ = square root of (2 x 312,000 x $85 / $0.12) = square root of 442,000,000, or about 21,024 cartons. The center would order about 14.8 times a year, roughly every three and a half weeks. Annual ordering cost is 14.84 x $85, about $1,261, and annual holding cost is (21,024 / 2) x $0.12, also about $1,261. The two are equal at the optimum, which is a useful check on the arithmetic. Total ordering and holding cost is about $2,523 a year.
Problem 2: Quantity Discount
The carton supplier offers $0.45 per carton on orders of 40,000 or more. At the lower price the holding cost becomes $0.1125, and the EOQ rises only to about 21,713, well below the 40,000 needed for the discount. Following the textbook procedure, the center should compare total annual cost, including purchase cost, at the EOQ under the regular price and at the smallest quantity that qualifies for the discount.
| Option | Order quantity | Purchase cost ($) | Ordering cost ($) | Holding cost ($) | Total ($) |
|---|---|---|---|---|---|
| Regular price, $0.48 | 21,024 | 149,760 | 1,261 | 1,261 | 152,282 |
| Discount price, $0.45 | 40,000 | 140,400 | 663 | 2,250 | 143,313 |
The discount lowers total annual cost by about $8,970. Holding cost nearly doubles, but the purchase saving of $9,360 outweighs it. The decision depends on one practical point the formula ignores: 40,000 flat cartons occupy about four pallet positions more than the current order, so the general manager should confirm that mezzanine space is free before accepting. With space available, the center should take the discount.
Problem 3: Reorder Point and Safety Stock
The center works six days a week, so carton use averages 1,000 a day, with a standard deviation of 180 a day. The supplier's lead time is a steady four days. Under a continuous review system, the reorder point equals average demand during lead time plus safety stock. Variability over the four-day lead time is 180 x square root of 4, or 360 cartons. For a 95 percent cycle-service level, z is 1.645, so safety stock is 1.645 x 360, about 592 cartons, and the reorder point is 4,000 + 592 = 4,592 cartons.
Raising the service level to 99 percent, with z of 2.33, would lift safety stock to about 839 cartons, an extra 247 cartons costing roughly $30 a year to hold. Since a stockout of medium cartons would stop the packing line and miss same-day shipments, the order winner identified in the first assignment, the higher service level is cheap insurance and is recommended.
Problem 4: Inventory Turnover for Two Clients
Turnover equals a year's cost of goods sold over the average value of stock on hand, and weeks of supply is average inventory divided by weekly cost of goods sold. A household goods brand shows cost of goods sold of $18.2 million and average inventory of $2.6 million, a turnover of 7.0 and about 7.4 weeks of supply. A supplement brand shows cost of goods sold of $9.8 million against average inventory of $0.6 million, a turnover of about 16.3 and 3.2 weeks of supply. The household brand ties up far more stock per dollar of sales. Its predictable demand suggests it could hold less, which would also free storage positions the center could rent to other clients.
Problem 5: Supply Chain Design and the Bullwhip Effect
Over the past year, weekly retail sales of the supplement brand's best seller had a standard deviation of 1,200 units, but the brand's orders from its contract manufacturer had a standard deviation of 3,100 units, about 2.6 times as large. Lee et al. (1997) called this amplification of demand variation up the supply chain the bullwhip effect and traced it to four causes: forecasts updated from orders rather than from end demand, batching of orders, price promotions that encourage forward buying, and rationing games during shortages. The brand's records show the first three. It forecasts from the center's shipment data instead of retail sales, orders once a month and runs quarterly promotions.
Krajewski et al. (2016) distinguish efficient supply chains, built for low cost when demand is predictable, from responsive ones, built for speed and flexibility when demand is uncertain. The household brand, with steady demand, fits an efficient design: larger, less frequent replenishment and lower stock. The supplement brand's demand is less predictable, so it needs a responsive design, yet its monthly batches and promotions add variation of its own making. The recommendation is to share point-of-sale data with the brand's planners, move to weekly replenishment and smooth promotional pricing, which together should reduce the amplification without adding inventory.
Conclusion
The center should order medium cartons in lots of 40,000 to capture the discount if space allows, reorder at about 4,839 cartons to protect a 99 percent service level, and advise its clients according to their demand: leaner stock for the predictable household brand and shared sales data with smaller, more frequent orders for the supplement brand. Each recommendation follows from a calculation, and each supports the fast, accurate shipping the center competes on.
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
Krajewski, L. J., Malhotra, M. K., & Ritzman, L. P. (2016). Operations management: Processes and supply chains (11th ed.). Pearson.
Lee, H. L., Padmanabhan, V., & Whang, S. (1997). Information distortion in a supply chain: The bullwhip effect. Management Science, 43(4), 546-558. https://doi.org/10.1287/mnsc.43.4.546
Reading the SOP 7200 Module 3 assignment instructions
The third SOP-7200 written assignment again consists of end-of-chapter problems, this time from the supply chain and inventory chapters, and counts toward the 22 percent that the four written assignments carry together. Expect problems on inventory measures, order quantities, discounts, reorder points and supply chain design. Keep every inventory formula on the same time basis: annual demand with annual holding cost in the order quantity, and daily demand with a daily standard deviation over a lead time in days for safety stock. When a discount is offered, compare total cost including purchase cost, not just ordering and holding cost. For design questions, tie the recommendation to how predictable each product's demand is. Show the z value you used and say which service level it represents.
How the SOP 7200 Module 3 example is put together
The paper treats the center's own supplies and its clients' stock as two separate inventory problems. The carton problems build on each other, from the order quantity to the discount comparison and then the reorder point, and a table sets the two pricing options side by side. The client problems move from a measure, turnover, to a pattern, the bullwhip effect, and then to a design choice between efficient and responsive chains. Notice that the paper checks the order quantity by confirming that ordering and holding costs are equal, and that it raises a practical constraint, storage space, that the formula leaves out. The conclusion gathers the decisions in one paragraph.
Reading the SOP 7200 Module 3 grading rubric
Mentors grade the third problem set out of 100, the same as the others. They reward correct formulas with consistent units, total-cost comparisons that include purchase cost when discounts apply, and safety stock sized to variability across the whole lead time, not a single day. Interpretation weighs heavily: a reorder point means more when the paper explains what a stockout would cost. Answers that connect inventory decisions to the firm's competitive priorities, and supply chain design to demand predictability, show command of the module. Clear tables, labeled problems and APA references for Krajewski and the studies used round out a high score.
SOP 7200 Module 3 help from the desk
Mismatched units cause most errors here: weekly demand paired with a yearly holding cost, or a daily standard deviation that was never multiplied by the square root of lead time. Students also accept a discount without comparing total cost or reject it without noticing that purchase savings dominate. Our writers can work SOP 7200 inventory and supply chain problems from the chapters your module assigns. Start each problem by listing the inputs with their units, convert them to one time basis, and then calculate. Finish with one sentence on what the manager should do, and note any practical limit, such as space or shelf life, that the formula ignores. A brief check, such as equal ordering and holding costs at the EOQ, catches errors early.
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SOP 7200 Module 3 questions, answered
Where can I find a free SOP 7200 Module 3 sample paper?
The third Strategic Operations Management problem set is shown in full above, with order quantity, quantity discount, reorder point, turnover and bullwhip problems for a fulfillment center.
How do you decide whether to take a quantity discount?
Compare total annual cost, including purchase, ordering and holding cost, at the regular-price EOQ and at the smallest quantity that earns the discount, then choose the lower total.
How is safety stock calculated?
Take the z value for the target service level and multiply it by demand variability across the lead time, found by scaling the daily standard deviation by the square root of the number of lead-time days.
What causes the bullwhip effect?
Lee, Padmanabhan and Whang traced the bullwhip effect to four habits: forecasting from orders instead of real consumer demand, ordering in batches, discount-driven buying and shortage gaming.
When should a supply chain be efficient rather than responsive?
Efficient chains suit products with predictable demand where low cost matters most; responsive chains suit products with uncertain demand where speed and flexibility matter.