An evaluation of routing and volume-based storage policies in an order picking operation

Decision Sciences, Spring 1999 by Petersen, Charles G II, Schmenner, Roger W

From the full factorial ANOVA the only thing that is not significant at a .01 level is the three-way interaction between storage policies, pick list size, and demand skewness. There are several reasons why almost everything is significant. Although the cell size is only 30 observations, there are eight storage policies, six routing policies, five pick list sizes, and three levels of demand skewness. This makes for a total of 21,600 observations, and with so many observations, statistical significance is much easier to show. In addition, differences between the routing and storage policies are substantial, as can be observed from Table 3. The routing heuristics range from 7.1% to 30.9% over optimal, and the storage policies range from 1.3% to 18.4% over within-middle. Such diversity enhances statistical significance.

There are several reasons why the three-way interaction of Store*Pick*Skew is the only one not significant. For one, storage policies have more variance than routing policies. This is evident from the Mean Square for Within Store (6,112.1), which is over three times larger than the Mean Square for Within Route (1,694.5). In addition, storage policies are not as affected by pick list size and demand skewness as routing policies. This is shown in the two-way interactions. The two-way interactions involving pick list size show that the Mean Square Between for Route*Pick (239,685) is six times larger than the Mean Square Between for Store*Pick (39,533). Also, the two-way interactions involving demand skewness show that the Mean Square Between for Route*Skew (245,929) is almost twice as large as the Mean Square Between for Store*Skew (130,789). When you combine the larger Mean Square Within with a smaller Mean Square Between you end up with a smaller F statistic, and therefore less statistical significance.

General Results

The mean route (ft) for the factor levels of route and store is presented in Table 3. First, the three advanced heuristics (largest gap, composite, and midpoint) were, on average, 7.1%, 10.2%, and 12.0% over optimal. The simpler return and transversal strategies performed more poorly, 27.9% and 30.9% over optimal. Naturally, different routing heuristics perform better in different situations. If one chooses the best routing heuristic in each situation, the optimal outperforms the best routing heuristic by only 3.3%.

Second, within-aisle storage with a middle P/D had the shortest mean route length, although within-aisle storage with a corner P/D resulted in a mean route length of only 1.3% over the middle P/D. The other storage policies were between 8.4% and 18.4% longer than within-aisle storage with middle P/D. This suggests a tentative conclusion:

1. Largest gap is the best general routing heuristic, and within-aisle storage is the best general storage policy.

Although the largest gap is the best general routing heuristic and within-aisle is the best general storage policy, it does not follow that the two combined yield the best pairing of routing and storage policies. In order to ascertain the best combination, one needs to look at the two- and three-way interactions. This analysis begins with an examination of the storage policies with optimal routing. Next, the interaction between routing and storage policies is investigated, followed by the interaction among routing policies, demand skewness, and pick list size.