# Ch6-SeasonalReorderLevels by xiagong0815

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SCM 463 – Ch6 HW problems – Reorder Levels with Seasonality

1.) Suppose your weekly forecasts have a mean absolute percentage error (MAPE) of 15%.
You want a service level of 98%. Demand for March is forecasted to be 600 units, and
demand in April is expected to be 700. Lead time is 2 weeks. Compute the reorder levels for
March.

For 98% service, we want z= 2.05.
In March, demand per week is 150. MAPE = 15% means stdev/week = 1.25 * 0.15 * average =
1.25 * 0.15 * 150 = 28.1.
In April, demand per week is 175. Stdev/wk = 1.25 * 0.15 * 175 = 32.8.

Weeks 1-3 of March, ROL = 150*2 + 2.05 * 28.1 * sqrt(2) = 300 + 81 = 381
Week 4 of March, ROL = 150 + 175 + 2.05 * sqrt(28.12 + 32.82) = 325 + 2.05 * 43.2 = 414

2.) Suppose your weekly forecasts have a mean absolute percentage error (MAPE) of 10%.
You want a service level of 99%. Demand for June is forecasted to be 900 units, and
demand in July is expected to be 600. Lead time is one week. Compute the reorder levels to
use in June.

For 98% service, we want z= 2.33.
In June, demand per week is 225. MAPE = 10% means stdev/week = 1.25 * 0.1 * average =
1.25 * 0.1 * 225 = 28.1.
In July, demand per week is 150. Stdev/wk = 1.25 * 0.1 * 150 = 18.75.

If LT = 1 week:
Weeks 1-4 of June, ROL = 225 + 2.33 * 28.1 = 225 + 65.5 = 290.5

If the problem had been written with LT = 2 weeks:

Weeks 1-3 of June, ROL = 225*2 + 2.33 * 28.1 * sqrt(2) = 450 + 92.3 = 542.3
Week 4 of June, ROL = 225 + 150 + 2.33 * sqrt(28.12 + 18.752) = 375 + 2.33 * 33.8 = 454

3.) Suppose your weekly forecasts have a mean absolute percentage error (MAPE) of 18%.
You want a service level of 95%. Demand for August is forecasted to be 1200 units, and
demand in September is expected to be 1500. Lead time is 2 weeks. Compute the reorder
levels for August.

For 98% service, we want z= 1.64.
In August, demand per week is 300. MAPE = 18% means stdev/week = 1.25 * 0.18 * average =
1.25 * 0.18 * 300 = 67.5.
In September, demand per week is 375. Stdev/wk = 1.25 * 0.18 * 375 = 84.4.

Weeks 1-3 of August, ROL = 300*2 + 1.64 * 67.5 * sqrt(2) = 600 + 156 = 756.
Week 4 of March, ROL = 300 + 375 + 1.64 * sqrt(67.52 + 84.42) = 675 + 1.64 * 108 = 852.

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