MT296 Unit 4 Safety Stock Calculation Example

Ninety-Seven Percent as One Number on the Schedule: A Unit 4 Safety Stock Calculation for a Pierogi Flavor

[Student Name]

Purdue University Global

MT296: Supply Chain Management Applications

Unit 4 Safety Stock Calculation

[Instructor Name]

[Date]

The pierogi maker, its demand data, schedule and costs are composite and illustrative; the sources cited are real.

Inputs

Item: potato-cheddar twelve-count, the plant's best-selling flavor

Weekly demand: average 1,860 cases, standard deviation 290 cases, from the last 52 weeks of shipments

Production cycle: the flavor runs every second week

Schedule freeze: the production schedule is fixed one week ahead

Service target: 97 percent cycle service level, meaning stock covers demand in 97 of every 100 replenishment cycles

Holding cost: $4.93 per case per year, covering freezer space at the plant and the capital tied up in finished goods

The Protection Period

Safety stock must cover the uncertainty in demand over the period during which the plant cannot react. That period is the time between production runs plus the time the schedule is frozen. A case produced this week must last until the next run two weeks later, and the decision about that next run is fixed a week before it. So the protection period is three weeks.

Jacobs and Chase (2020) describe this as a periodic review system, in which inventory is checked at fixed intervals and raised to a target level, and the protection period is the review interval plus the lead time.

The Calculation

The standard deviation of demand over three weeks, assuming weekly demands are independent, grows with the square root of the three weeks: 290 × 1.732, about 502 cases.

For a 97 percent cycle service level, the z-value from the standard normal table is 1.881. Safety stock is z times the protection-period standard deviation: 1.881 × 502, about 945 cases.

Expected demand over the three-week protection period is 3 × 1,860, or 5,580 cases. The order-up-to level is expected demand plus safety stock: 5,580 + 945 = 6,525 cases.

The Scheduling Rule

Every other Monday, when the potato-cheddar run is scheduled, the planner checks inventory position, meaning cases on hand plus cases already scheduled minus cases already promised, and schedules enough production to bring it up to 6,525 cases. If inventory position is 2,100, the run is 4,425 cases.

The scheduler does not need the statistics; the scheduler needs 6,525.

Comparing Service Levels

The table compares four targets.

90 percent: z 1.282; safety stock 644 cases; annual holding cost $3,175

95 percent: z 1.645; safety stock 826 cases; annual holding cost $4,072

97 percent: z 1.881; safety stock 945 cases; annual holding cost $4,659

99 percent: z 2.326; safety stock 1,169 cases; annual holding cost $5,763

Moving from 97 to 99 percent adds 224 cases of safety stock and about $1,105 a year in holding cost. Each step up costs more than the one before, because the normal distribution's tail thins: going from 90 to 95 adds 182 cases, from 97 to 99 adds 224. Chopra (2019) notes that this rising marginal cost is why service targets should be set by what a stockout costs the business, not by a preference for round numbers.

Cycle Service Level and Fill Rate

A 97 percent cycle service level means that 3 in every 100 cycles will see some stockout. It does not mean 3 percent of demand goes unfilled. When a stockout happens, it is usually small, because safety stock covers most of the shortfall. The expected shortage per cycle can be estimated from the standard normal loss function: at z of 1.881, about 0.012 standard deviations, or about 6 cases per cycle. Against two weeks of demand, 3,720 cases, that is a fill rate of about 99.8 percent. Silver et al. (2017) stress the difference, because customers usually experience fill rate, the share of cases delivered from stock, rather than cycle service level.

Checking the Independence Assumption

The square-root rule assumes that one week's demand does not predict the next. For this flavor, the plant's records show only weak correlation between consecutive weeks once the seasonal pattern is removed, so the assumption is reasonable. If a large customer began ordering in two-week blocks, demand would become lumpier and correlated, and the three-week standard deviation would be larger than 502. The planner should recheck the figure whenever a major account changes its ordering pattern.

What If Demand Is Seasonal?

The calculation uses one standard deviation for the whole year. Potato-cheddar demand is seasonal, so the standard deviation is larger in December and smaller in July. A better approach, once the seasonal forecast is in place, is to compute the order-up-to level each month from that month's forecast and its own forecast error. For now, the flat figure is a reasonable start, but the planner should raise the order-up-to level in November and December in proportion to the seasonal index.

Recommendation

The plant should adopt the 97 percent target, with an order-up-to level of 6,525 cases every other week, and revisit it once seasonal forecast errors are available. Moving to 99 percent would cost about $1,105 a year more for a fill rate that is already near 99.8 percent.

References

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

Jacobs, F. R., & Chase, R. B. (2020). Operations and supply chain management (16th ed.). McGraw-Hill.

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