UMass Lowell
College of Management
63.371
T. Sloan
Forecasting Example Problems with Solutions
1. The Instant Paper Clip Office Supply Company sells and delivers office supplies to companies, schools, and
agencies within a 50-mile radius of its warehouse. The office supply business is competitive, and the ability
to deliver orders promptly is a big factor in getting new customers and maintaining old ones. (Offices
typically order not when they run low on supplies, but when they completely run out. As a result, they
need their orders immediately.) The manager of the company wants to be certain that enough drivers and
vehicles are available to deliver orders promptly and that they have adequate inventory in stock. Therefore,
the manager wants to be able to forecast the demand for deliveries during the next month. From the records
of previous orders, management has accumulated the following data for the past 10 months:
Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct.
Orders 120 90 100 75 110 50 75 130 110 90
a. Compute the monthly demand forecast for February through November using the naive method.
b. Compute the monthly demand forecast for April through November using a 3-month moving average.
c. Compute the monthly demand forecast for June through November using a 5-month moving average.
d. Compute the monthly demand forecast for April through November using a 3-month weighted moving
average. Use weights of 0.5, 0.33, and 0.17, with the heavier weights on the more recent months.
e. Compute the mean absolute deviation for June through October for each of the methods used. Which
method would you use to forecast demand for November?
Solution:
a. The naive method simply uses the demand for the current month as the forecast for the next month:
Ft+1 =Dt. So for February we would have FFeb. =DJan. = 120. Similarly, FNov. =DOct. = 90. See the
table below for the other months.
b. For a simple 3-month moving average, we take the average of the previous three months’ demand
as our forecast for next month: Ft+1 =Dt+Dt−1+Dt−2
3. Since we need at least three months to
compute the average, and we only have data beginning in January, April is the earliest month for
which we can compute the forecast: FApr. =DMar. +DFeb. +DJan.
3=100 + 90 + 120
3= 103.3. The
forecasts for the other months are reported in the table below.
c. The 5-month moving average is similar to the 3-month moving average, except now we take the
average of the previous five months’ demand. We start with the forecast for June (since we need
at least five months’ worth of previous demand): FJun. =DMay +DApr. +DMar. +DFeb. +DJan.
5=
110 + 75 + 100 + 90 + 120
5= 99.0. The forecasts for the remaining months are computed similarly,
and the values are reported in the table below.
d. Simple moving averages (like parts band cabove) place an equal weight on all of previous months.
A weighted moving average allows us to put more weight on the more recent data. For a weighted
3-month moving average we have Ft+1 =w1Dt+w2Dt−1+w3Dt−2. (Note that the weights should
add up to 1.) Using the weights specified in the question, the forecast for April is computed as
FApr. = 0.5(DMar.) + 0.33(DFeb.) + 0.17(DJan. ) = 0.5(100) + 0.33(90) + 0.17(120) = 100.1. Forecasts for
May through November are reported in the table below.
1Spring 2007
