Supply Chain View

I have just read a paper published in the Jan 07 edition of the Journal of the Operational Research Society (JORS) entitled “A new approach of forecasting intermittent demand for spare parts inventories in the process industries”. The authors – ZS Hua, B Zhang, J Yang and DS Tang from the University of Science and Technology of China, Hefei, PRC – have produced an interesting case-based study of the petrochemical industry which illustrates some more general points.

The authors looked at the spare parts requirements for the maintenance of capital equipment in a mid-sized Chinese plant (capacity 400m tonnes petroleum). The product range was broad (35,000 parts) with a large proportion of slow-moving, intermittently-demanded parts.

Analysing the demand

The first point to note is that they separated the forecasting of the incidence of non-zero demand from the estimation of the magnitude of that demand. Where demand is intermittent but essentially a single-piece flow (often the case for automotive spares), this isn’t necessary and a Poisson model of demand works well. The Chinese data doesn’t show this – perhaps because of the effects of scheduled maintenance, perhaps because engineers are creating stocks close to point of use and reordering in large batches.

When it comes to forecasting the incidence of non-zero demands, the researchers use a couple of properties of the data set they have to achieve a better result than you might get with, for example, exponential smoothing. For a start they have found enough autocorrelation in the data to merit a first-order Markov model for demand. (In less mathematical language, they are seeing effects such as runs on demand followed by intervals of zero demand, much more so that you would expect from random effects.)

Hua and colleagues have used a fairly simple autoregressive model here, but the comments of D.S.G. Pollock I quoted in an earlier post are still pertinent: autoregression, particularly with small numbers of observations, should be treated with a lot of care. The authors themselves note that their method requires a “that the number of non-zero demands in the historical data set should not be too small”.

The maintenance schedule effect

The second feature of their case study they have made use of in their forecasting method is the coincidence of spares usage with scheduled maintenance and periodic plant overhaul. So they have used the equipment maintenance plans as explanatory variables in their forecast and used regression analysis to decide what weight to give them. (The classic example for forecasting using explanatory variables must be ice cream sales – so it is said, the weather forecast can be used as an input to the forecast.)

It’s very easy to get carried away with clever OR solutions to problems that might better be solved by sorting out the underlying process, so my first reaction to this was to wonder why spares were not simply scheduled to the engineers to meet the maintenance plans.

But on reflection I think the approach in the paper is valid. The reason is that during the course of a maintenance job you usually find some other problems within a piece of equipment that require spares other than those planned for the service.

It’s something we saw few years ago we looked at spares requirements for automobile dealers and found that exactly this effect made forward planning of parts based on service jobs fairly hard – there is a high likelihood of an unplanned part needing replacement, leading to low first-time fix if those parts aren’t immediately available from stock.

For forecasting the magnitude of each of the non-zero demands, the authors used a variation on the bootstrapping technique. All of these different approaches are wrapped up together sensibly in an integrated technique – something they call the “Integrated Forecasting Method”.

Conclusions

On balance this is a clever bespoke method for a particular forecasting problem, but with little direct application to other operations. Parts of the approach are adaptable, and it is a useful case study. I would also like to have seen some analysis of the impact on service availability and inventory – that is after all why we try to improve forecast accuracy in the first place.

Links

The complete JORS article is available online at http://www.palgrave-journals.com/jors/journal/v58/n1/pdf/2602119a.pdf

The Operational Research Society: http://theorsociety.com
The Journall of the Operational Research Society: http://www.palgrave-journals.com/jors/index.html
University of Science and Technology of China, Hefei, PRC: http://www.ustc.edu.cn/en/

Wikipedia entries on Autocorrelation and Explanatory Variables:
http://en.wikipedia.org/wiki/Autocorrelation
http://en.wikipedia.org/wiki/Explanatory_variable