Solutions--Chapter 3

OPERATIONS  MANAGEMENT

CHAPTER 3

Problem #1

 A naïve forecast uses a single previous value of a time series as the basis for a forecast.  It can be used for a stable series (variations around an average), with a seasonal variation or with a trend.

 ·        With a stable series, you use the last data point as the forecast for the next period.

·        If there is a seasonal variation, the value is that of the series’ last season.

·        For data with a trend, the forecast is equal to the last value of the series plus or minus the difference between the last two values of the series.

 Plotting the data sets reveals sales fo blueberry muffins are stable (they vary around an average)

therefore, a naive forecast can be made by using the last value or 33.

Cinnamon buns show a trend:

The last change was from 31 to 33 or a change of  2

Using the last value and adding 2 produces a forecast of 35.

Cupcakes appear to have a seasonal variation with the peaks every 5 days. 

This would make the next peak occur on Day 16.t

Estimate would be 47.

The use of sales data implies that sales adequately reflect the demand, i.e.:  there were no

stockouts.

PROBLEM  #3

Exponential smoothing is a type of weighed average.  Each new forecast is equal to the previous forecast plus a percentage of the previous error.  Using this method, the forecast for the period _t is equal to the forecast for the previous period  plus ((the actual demand for the previous period - the forecast for the pervious period) * the smoothing constant).  NOTE that the actual demand for the previous perios – the forecast for the previous period is the error for that period,

·        August usage forecast was for 88% or plant capacity

·        August’s actual usage was 89.6% of capacity

·        Smoothing constant is .1

Therefore the forecast for September is:

            88 + .1(89.6 – 88) or 88.16

Assuming that the actual usage in September was 92% of capacity, the forecast for October was:

            88.16 + 1(92 – 88.16) or 88.54

PROBLEM 6

The equation of a trend line is as follows:

The forecast for period  t = the value of the forecast when t = 0.  +  (the slope of the line * the number of periods) , or:

The forecast = 500 – (200/10)t  or  500 – 20t

PROBLEM 9

 Depends on Trend adjusted exponential smoothing, Which has the ability to adjust to changes in the trend.  Trend projections are much simpler to do with a trend line but trend adjusted smoothing, one can adjust the trend when a time series exhibits a trend. 

the trend-adjusted forecast is composed of two elements:  a smoothing error and the trend estimate. Step 1 is to determine the trend.  In this example, the original estimate of trend was calculated based on the changes for three periods.