Results and analysis of DMSA

The analysis is divided into two parts. First, an example of 30 newly delivered products with the highest turnover rate is used to evaluate the performance of the proposed DMSA approach. Second, a set of experiments is designed to explore the situation when both the products with high and low turnover rates are considered to be reallocated.

Because the products with a high turnover rate are replenished more frequently, the products in the first experiment are chosen according to turnover rate. The first 30 products with the highest turnover rates contribute more than one-third of the total

order frequencies over the past 11 months. Thus, they are chosen to be the candidates for newly delivered products. In past studies, the random storage assignment policy was usually used as the benchmark for comparison purposes (Hausman et al., 1976;

Larson et al., 1996; Manzini 2006). The results are also benchmarked by the random storage assignment policy by comparing the total travel distance of incoming orders.

By using the random assignment, the total travel distance of orders for December is 7,229,087 meters. Comparatively, the total travel distance by using DMSA is 6,924,575 meters. From these results, the picking distance is shortened by 304,512 meters, a 4.21% reduction. At first glance, the improvement does not seem to be significant. However, DMSA is an adaptive approach that only reallocates a portion of products, which are 30 out of 787 products in the first experiment. The performance of DMSA cannot be directly compared with other approaches that allocate all products.

After evaluating the preliminary performance of DMSA, an experimental design is employed to investigate the performance of DMSA in a more general setting. In reality, both the products with high and low turnover rates have the chance to be restocked and reallocated. Two factors, the sample size and the combination of samples, would vary over time and may have an influence on the performance of DMSA. As a result, a two-factor ANOVA was conducted to explore how the two factors impact the performance of DMSA. The number of newly delivered products needing to be put away is the first factor, Factor A. In general, the average number of products needing to be put away is around 40 items, and the maximum and minimum numbers are 60 and 20, respectively. The second factor is the proportion of products with a higher turnover rate for all put away products, Factor B. Based on the company’s practice, the products with the first 273 highest turnover rates (approximately the top 30% of the 787 products) are defined as high-turnover products, and the rest are treated as low-turnover products. Three levels of proportions are chosen, 30%, 60%, or 90%. Therefore, nine experimental setups are used to obtain the travel distances. The factor settings are illustrated in Table 3. The products in each experimental setting are randomly selected from the high- and low-turnover items, according to the proportion of products with a higher turnover rate. Each setting is run four times. For example, the settings of Factor A as 20 and Factor B as 30% means that the sample of 20 products consists of 6 high-turnover rate products and 14 low-turnover rate products.

Table 4 summarizes the results of the 36 experiments in nine settings. The range of improvement varies from 0.4% to 2.8%. To justify how the two factors affect the reduction of travel distance, a two-factor ANOVA is used to further analyze these results.

Table 3 The experiment settings

Factor Level 1 Level 2 Level 3

Factor A 20 40 60

Factor B 30% 60% 90%

Table 4 The result of the 36 experiments

Setting^* The average moving distance in

four repeat trails (meters) Average improvement comparing with random assignment (7229087 meters)

* The number in front of each dash presents the level of Factor A and the number after the dash presents the level of Factor B.

In the two-factor ANOVA, the assumptions of normality, consistency and randomization are tested, and they are acceptable. Table 5 presents the results of ANOVA. Apparently, the main effect of Factor A, the main effect of Factor B, and the interaction effect between Factors A and B all have significant effects on the improvement of travel distances (α = 0.01). The result means that the travel distance decreases as the number of products needing reallocation (Factor A) and the proportion of high-turnover products in the restocking list (Factor B) increase. In terms of the main effect, the increased number of products needing reallocation leads to more available locations such that a better storage assignment can be conducted with a more flexible arrangement. On the other hand, the high-turnover products are ordered and picked more often than the low-turnover ones. Consequently, as more high-turnover products are involved in re-assignment processes, the total travel distance is reduced. In terms of the interaction effect, the improvement of distance reduction is better while both Factors A and B are set to the higher levels. In such a setting, more products of a high-turnover rate reallocated to more available locations can achieve greater distance reduction.

The experimental results also demonstrate how the efficiency of order picking can be improved by using DMSA to re-assign newly delivered products to the storage locations without incurring any additional pickers or picking facilities. The proposed DMSA approach can greatly reduce the likelihood of entering an aisle for picking one product as well as the number of stops for picking, which results in shorter travel distances. In addition, the CPU time to solve the assignment model is very short (commonly less than 2 seconds).

Table 5 The ANOVA table of the experiments

Source Sum of Squares DF Mean Square F Value P Value Model 1.107E+011 8 1.384E+010 23.72 <0.0001

A 6.269E+010 2 3.135E+010 53.71 <0.0001

B 3.493E+010 2 1.747E+010 29.92 <0.0001

AB 1.312E+010 4 3.279E+009 5.62 0.0020

Pure Error 1.576E+011 27 5.837E+008 Total 1.265E+011 35