Question

1. A) A firm has a daily demand of 450 units. The lead time of receiving supplies is 3 days. If demand has a standard deviation of 100 units per day, what should be their safety stock? The firm plans for a 95% service level.
   2. What should be their reorder point?

Note: ?0.95 = 1.64.

2. A) This firm decides to increase their service level to 98%. What should be their safety stock?
   2. What should be their reorder point?

Note: ?0.98 = 2.05

3. A company presently has 3 warehouses, each carrying 3,500 units of inventory. With this strategy, the company is able to meet its demand at 2.5% stockout rate.

1. The company decides to downsize and keep only 2 warehouses. How many units of inventory will the company need to carry at each of the two warehouses if it wants to continue a 2.5% stockout rate?
2. Instead, the company decides to increase the number of warehouses to 4. How many units of inventory will the company need to carry at each of the four warehouses if it wants to continue a 2.5% stockout rate?

4. The details of the demand of a firm over the past 4 months is given in Table 1.

Table 1. Details of demand over the past 4 months

Month	Demand
1	9070
2	8775
3	9865
4	9250

1. If the firm uses 3-month moving average for its demand forecasts, what would be the forecast for the demand in the next month?
2. What would be the demand forecast for month 5 if we use a 3-month weighted moving average with the following weights from the earliest month to the most recent: 0.5, 0.3, 0.2?
3. The firm has been using exponential smoothing for its demand forecast using 0.3 as the smoothing constant. Demand forecast for month 4 was 9150, what would be the forecast for demand in month 5 using the same method?

5. Actual demand values and demand forecasts over the past 4 months of a firm are given in Table 2.

   Table 2. Details of actual demand and demand forecast over the past 4 months

   Month	Demand	Forecast
   1	9070	9030
   2	8775	8851
   3	9865	9926
   4	9250	9310

6. Calculate the Mean Absolute Deviation (MAD) for this forecasting method. Round your answer to two decimal points.
7. Calculate the Root Mean Square Error (RMSE) for this forecasting method. Round your answer to two decimal points.

Answer 1

1.

A.

Safety stock = Z*Standard deviation*(Lead time)^.5

Z at 95% = 1.64

Safety stock = 1.64*100*3^.5

Safety stock = 284.06 or 284 units

B.

Reorder point = daily demand*lead time + safety stock

Reorder point = 450*3 + 284

Reorder point = 1634 units

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2.

When service level is 98%

A.

Safety stock = Z*Standard deviation*(Lead time)^.5

Z at 98% = 2.05

Safety stock = 2.05*100*3^.5

Safety stock = 355.07 or 355 units

B.

Reorder point = daily demand*lead time + safety stock

Reorder point = 450*3 + 355

Reorder point = 1705 units

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