MT237 Unit 5 Inventory Calculation Example

Late Ships, Not Busy Weeks: A Unit 5 Inventory Calculation for Lift Columns From Penang

[Student Name]

Purdue University Global

MT237: Supply Chain Systems

Unit 5 Inventory Calculation

[Instructor Name]

[Date]

Prairie Rise Desk Co., its demand, lead times, costs and every result are composite and illustrative; the sources cited are real.

Inputs

Prairie Rise Desk Co. uses about [936] lift-column sets a week, one set per desk, with a weekly standard deviation of about [210] sets. Columns come from Penang in a container ordered every four weeks. The lead time from order to arrival averages nine weeks, but actual arrivals have spread around that average by about 1.6 weeks (one standard deviation), because sailings slip, ports congest and the supplier sometimes ships late. Each set costs about [$118], and the company's carrying cost is 22 percent a year, about [$25.96] a set. A set short costs about [$142] in lost margin and expediting, since a desk without columns cannot ship.

The Protection Period

Because Prairie Rise orders every four weeks and waits nine for delivery, each order must protect against thirteen weeks of uncertainty. Silver et al. (2017) show that when both demand and lead time vary, the standard deviation of demand over the protection period combines the two: the variation in weekly demand scaled by the length of the period, and the variation in lead time scaled by average demand.

Demand alone contributes about 757 sets: 210 a week, widened by the square root of thirteen weeks. The lead time part is average weekly demand times the lead time's standard deviation, 936 times 1.6, about 1,498 sets. Because the two sources are independent, they combine like the sides of a right triangle, giving a total of about 1,678 sets.

The lead time part is nearly twice the demand part. Most of the uncertainty Prairie Rise must cover comes from not knowing when the ship will arrive, not from not knowing how many desks will sell.

Five Service Levels

Safety stock equals a z value for the chosen cycle service level times 1,678. At 95 percent, the z value of about 1.645 gives about 2,760 sets, costing about [$71,700] a year to carry. Expected shortages, calculated with the standard normal loss function over thirteen order cycles a year, cost about [$64,700]. The total is about [$136,400].

At 97.5 percent, safety stock rises to about 3,290 sets, carrying cost to about [$85,400] and expected shortage cost falls to about [$29,300], for a total of about [$114,600]. At 98.6 percent, safety stock is about 3,690 sets, carrying about [$95,700] against shortages of about [$15,300], a total of about [$111,000]. At 99 percent, safety stock is about 3,900 sets and the total about [$111,800]. At 99.5 percent, it is about 4,320 sets and the total about [$117,100].

The total is lowest near 98.6 percent. Below it, shortages cost more than the stock saved; above it, the extra stock costs more than the shortages avoided.

Nearly two thirds of the columns held as insurance are there because nobody knows when the ship will dock.

What Would Move the Answer

The best service level depends on the ratio between the cost of a shortage and the cost of carrying a set. If the cost of being short were higher, for example if the office retailer began charging a larger fee for canceled orders, the best level would rise above 99 percent and safety stock would grow. If columns became cheaper to hold, through a lower interest rate or a lower purchase price, the best level would also rise a little. If shortages could be covered by an air shipment at modest cost, the shortage cost would fall and so would the best level. The calculation should be rerun whenever any of these inputs changes by more than about a fifth, and at least once a year before the January peak, when the cost of a shortage is highest because every lost desk is a lost promotional sale.

If Shipments Could Be Seen

The second table asks what would happen if Prairie Rise could track containers closely enough to know arrival dates within about half a week. If the lead time's standard deviation fell from 1.6 weeks to 0.5, the total standard deviation would fall from about 1,678 to about 890 sets. At the same 98.6 percent service level, safety stock would fall from about 3,690 to about 1,960 sets, saving about [$45,000] a year in carrying cost alone.

Lee and Whang (2000) argued that sharing shipment and inventory data reduces uncertainty for every partner in a chain, and this calculation puts a figure on that claim for one item. The visibility would not shorten the voyage; it would only tell Prairie Rise sooner when the voyage was running late, so the company could react before it ran short.

What the Calculation Suggests

Prairie Rise should set its lift-column safety stock at about 3,690 sets for now and treat shipment visibility as the main way to reduce it. Chopra and Meindl (2019) note that reducing supply uncertainty can lower safety stock as effectively as reducing demand uncertainty, and here it is the larger lever. A later unit will price the visibility itself.

References

Chopra, S., & Meindl, P. (2019). Supply chain management: Strategy, planning, and operation (7th ed.). Pearson.

Lee, H. L., & Whang, S. (2000). Information sharing in a supply chain. International Journal of Manufacturing Technology and Management, 1(1), 79-93. https://doi.org/10.1504/IJMTM.2000.001329

Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017). Inventory and production management in supply chains (4th ed.). CRC Press.