Question

In: Operations Management

The actual demand data for an item at a local retailer during the past six weeks...

The actual demand data for an item at a local retailer

during the past six weeks are shown below:

WEEK

ACTUAL DEMAND

(number of units)

Six weeks ago

202

Five weeks ago

201

Four weeks ago

199

Three weeks ago

200

Two weeks ago

203

One week ago

198

THIS WEEK

ACTUAL DEMAND NOT KNOWN

Determine the demand forecast for THIS WEEK using each of the following methods:

a. A 3-week moving average.

[3]

b. A 4-week weighted moving average using weights of 15, 5, 3, and 2 for one week ago, two

weeks ago, three weeks ago, and four weeks ago, respectively. (

Hint

: the higher weights

are applied to the more recent time periods.)

c. Exponential smoothing using the following: smoothing constant,

α

= 0.4 and the demand

forecast for three weeks ago = 199 units.

Expert Solution

a) A 3-periods moving average method averages the actual value for the previous three periods to generate the forecast for the next period. This can be calculated as the sum of the actual value for the previous three periods / 3

So using the above formula the forecast for this week = (200+203+198)/3

= 601/3

= 200.33

b) using a four period weighted moving average method the formula to calculate the forecast is : Sum of the product of the actual value and their respective weights for the previous four periods/(Sum of weights).

So using this formula the forecast for this week= [(2 x 199) + (3 x 200) + (5 x 203) + (15 × 198)]/(2+3+5+15)

= (398+600+1015+2970)/25

= 4983/25

= 199.33

c) Using the exponential smoothing method the formula to calculate the forecast is as follows :

Ft = F(t-1) + [A(t-1) - F(t-1)]

Where Ft = forecast for period t

A(t-1)= actual value for period previous to t

F(t - 1)= forecast for period previous to t

= smoothing constant

So using the above formula with =0.4 and forecast for three weeks ago = 199 , the forecast for the following weeks are :

For two weeks ago = 199 + 0.4(200-199) = 199+0.4= 199.4
For one week ago = 199.4+ 0.4(203-199.4) = 199.4+1.44 = 200.84
For this week = 200.84 + 0.4(198-200.84)= 200.84+(-1.136) = 200.84-1.136 = 199.704

keosha answered 4 months ago

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