GB527 Unit 5 Inventory Model Example

Reorder 2,200 Coils at 4,327: A Unit 5 Inventory Model for Imported Solenoid Coils

[Student Name]

Purdue University Global

GB527: Global Operations

Unit 5 Inventory Model

[Instructor Name]

[Date]

The manufacturer, its supplier and every figure are composite and illustrative; the methods and sources cited are real.

The Item and the Inputs

Platte Valve Works fits a solenoid coil to every electric valve actuator it builds. The coils come from a supplier near Changwon, South Korea, by sea to Los Angeles and rail to Nebraska. A shortage stops actuator installation, which stops the line.

Annual demand: 24,000 coils, or about 96 a working day over 250 days; daily usage varies by about 18 coils (one standard deviation).

Unit cost: $9.80.

Order cost: $210 per order, covering purchasing time, customs brokerage and receiving inspection.

Holding cost: 22 percent of unit value a year, or about $2.16 per coil.

Lead time: 35 working days on average from order to receipt, with a standard deviation of about 6 days.

Target cycle service level: 95 percent, meaning the plant should not run out in more than about one replenishment cycle in twenty.

Step 1: Order Quantity

The economic order quantity balances ordering cost against holding cost. Doubling the product of yearly demand and order cost, dividing by the yearly holding cost of one coil, and taking the square root gives 2 times 24,000 times $210, over $2.16, rooted: about 2,162 coils.

The supplier packs coils in cartons of 100 and offers a pallet of 2,200. Ordering 2,200 rather than 2,162 changes total annual ordering and holding cost by less than a dollar, since cost barely moves for quantities near the optimum. Silver et al. (2017) note this flatness as a practical strength of the model: small rounding to fit pack sizes costs almost nothing.

Order quantity: 2,200 coils, about eleven orders a year.

Step 2: Safety Stock

Safety stock is the cushion that keeps actuators moving if a shipment is slow or usage runs high before it lands. The calculation is shown twice to make a point.

If only demand varied: spread over 35 days, daily variation of 18 coils grows to 18 times the square root of 35, or about 106 coils. At a 95 percent service level, the z-value is 1.65, so safety stock would be about 176 coils.

If both demand and lead time vary: the lead-time spread combines both sources: the square root of 35 times 18 squared plus 96 squared times 6 squared, or about 586 coils. Safety stock is 1.65 times 586, or about 967 coils.

Lead-time variation, not demand variation, drives the safety stock: a six-day spread in an ocean lead time requires more than five times the buffer that day-to-day demand alone would.

Chopra and Meindl (2019) give this combined formula for cases where both demand and lead time are uncertain, and an import supplier with port and rail legs is exactly such a case.

Step 3: Reorder Point

The reorder point is expected demand during the lead time plus safety stock: 96 times 35, or 3,360, plus 967, or about 4,327 coils.

The trigger must use inventory position, coils on hand plus coils on order but not yet received, not coils on hand alone. With a 35-day lead time and an order quantity of 2,200, there will usually be one or two orders on the water. A rule based on stock on the shelf alone would reorder too late.

The rule: order 2,200 coils whenever inventory position falls to 4,327.

Step 4: The Seasonal Adjustment

Average demand hides the season. From January to April, actuator production uses about 160 coils a day, and daily usage swings by roughly 30. Using the same formula, the peak-season reorder point is 160 times 35, or 5,600, plus safety stock of about 1,611, for about 7,211 coils.

The plant should switch to the peak reorder point in late November, so that orders placed then arrive as the January peak begins, and switch back in late March. Using one annual reorder point year-round would leave the plant short in the season when a shortage costs most.

Why Not Simply Order More

A common response to an import lead time is to order large quantities a few times a year. Heizer et al. (2020) note that holding more stock than needed ties up cash and floor space and hides problems that smaller, more frequent orders expose. Ordering 6,000 coils four times a year would cut ordering cost by about $1,500 but add about $4,100 a year in holding cost, and would leave the plant with stock of an older coil design if the supplier revised it. The economic order quantity, adjusted for the season, keeps those costs in balance.

What the Policy Costs

Average inventory is about half the order quantity plus safety stock, or about 2,067 coils outside the peak, worth about $20,300. Safety stock alone costs about $2,100 a year to hold. Raising the service level to 98 percent would raise safety stock to about 1,200 coils, adding about $500 a year in holding cost, which is small against the cost of a line stoppage.

Limits

The model assumes demand and lead time follow roughly normal distributions and are independent. A port closure or a strike would break that assumption, as the next unit's disruption shows, and safety stock sized for normal variation will not cover it. The service level also counts cycles, not units; a stockout late in a cycle may be short, but in peak season even a short one stops the line.

References

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

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.