OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

The owner of a local computer store rents printers to some of her preferred customers. She is interested in arriving at a forecast of rentals so that she can order the correct quantities of ink cartridges that go with the printers. Data for the last 10 weeks is shown below:

Week Rentals Week Rentals 1 25 6 22 2 28 7 26 3 30 8 24 4 26 9 20 5 27 10 23

Generate a forecast for week 11 using a five-week moving average. Generate a forecast for week 11 using single exponential smoothing with a smoothing constant of 0.8. Which of the two forecasts for week 11 do you prefer and why?

What is the best forecast you can get using single exponential smoothing?

The manager of a public library must schedule employees to reshelve books and periodicals checked out of the library. The number of items checked out will determine the labour requirements. The following data reflects the number of items checked out of the library for the past three years:

Month Year 1 Year 2 Year 3 January 1847 2045 1986 February 2669 2321 2564 March 2467 2419 2635 April 2432 2088 2150 May 2464 2667 2201 June 2378 2122 2663 July 2217 2206 2055 August 2445 1869 1678 September 1894 2441 1845 October 1922 2291 2065 November 2431 2364 2147 December 2274 2189 2451

The manager needs a time series forecasting method for forecasting the number of items to be checked out during the next month (January of year 4). Find the best exponential (single or double/with or without trend) smoothing forecast you can.

By best here we mean the forecast corresponding to the minimum value of MSD.

Compare this forecast with that obtained using Holt-Winters additive model and a seasonal cycle of 12 (months).

The Central Building Supply Company serves the building industry in the Midwest region. Many items are stocked, and close inventory control is necessary to assure customers of efficient service. Recently, business has been increasing and management is concerned about stockouts. A forecasting method that will estimate demand next month is required so that adequate replenishment quantities can be purchased. An example of the sales growth experienced over the last 50 months is the demand for item J785, a common door hinge. This growth in demand is shown below:

Month J785 Month J785 Month J785 sales sales sales 1 80 2 132 3 143 4 180 5 200 6 168 7 212 8 254 9 397 10 385 11 472 12 397 13 476 14 699 15 545 16 837 17 743 18 722 19 735 20 838 21 1057 22 930 23 1085 24 1090 25 1218 26 1296 27 1199 28 1267 29 1300 30 1370 31 1489 32 1499 33 1669 34 1716 35 1603 36 1812 37 1817 38 1798 39 1873 40 1923 41 2028 42 2049 43 2084 44 2083 45 2121 46 2072 47 2262 48 2371 49 2309 50 2422

- Plot the data - does this plot tell you anything useful?
**Hint**the data can be plotted by choosing any forecasting method and then plotting the results after solution. - Investigate different forecasting methods for forecasting demand for J785.
- Which of these methods do you consider to be the "best" method and why.
- Hence forecast demand for month 51.

Again by best here we mean the forecast/method that corresponds to the minimum value of MSD.