5. Experimental Design and Analysis
5.4 Results and analysis of MCBH and ASBH
Based on the experimental settings described in Section 5.2, a set of experiments is conducted to demonstrate the viability of the proposed overall re-allocating heuristics. The traditional class based allocation approach (CBAA) is chosen as the benchmark to compare with the performance of MCBH and ASBH. Because these three approaches partially involve random assignment, each experimental setting is run for four trials to ensure robustness. After obtaining the storage assignment, the order data of December are used to represent the incoming orders for calculating the travel distance of order picking under different storage assignments.
In implementing CBAA and MCBH, products and locations are divided into two product classes and two zones for simplicity. To explore the effect of the relationship between products, four different levels of reserved proportion, 10%, 20%, 30%, and 40%, are studied in this study. Products are allocated according to association in reserved locations. Table 6 shows the travel distance and computation time of order picking for one month under the allocation generated by MCBH with 10%, 20%, 30%, and 40% reserved proportions. Table 7 summarizes the average travel distance generated from allocation by CBAA and MCBH. In comparison to CBAA, the travel distance generated by MCBH decreased from 1% to 4% and was dependent on the level of reserved proportion. MCBH, which combines the class-based allocation and family grouping approaches, outperforms the traditional class-based approach in terms of travel distance. The results indicate that allocating products that are frequently ordered together in the same aisle can enhance the efficiency of order picking.
Table 6 The travel distance and computation time of allocation by MCBH with December orders
Reserved
proportion Trial Travel distance
Table 7 Comparisons of travel distance between CBAA and MCBH
Approach Dataset Avg. travel distance
for 4 trails Improvement
CBAA December 6,207,567 Benchmark
MCBH/10% December 6,132,639 1.21%
MCBH/20% December 6,095,215 1.81%
MCBH/30% December 6,009,535 3.19%
MCBH/40% December 5,954,207 4.08%
From Table 7, it seems that travel distance decreases as the reserved proportion increases. Furthermore, from the One-Factor ANOVA shown in Table 8, the main effect of the reserved proportion is a significant effect on the improvement of travel distances at the significance level α = 0.01.
Table 8 The ANOVA table of the experiment with MCBH
Source Sum of squares DF Mean square F value P value
Model 7.868E+010 3 2.623E+010 14.42 <0.0003
R.P. 7.868E+010 3 2.623E+010 14.42 <0.0003
Pure
error 2.183E+011 12 1.819E+009 Total 1.005E+011 15
Therefore, increasing the reserved proportion of locations in MCBH can significantly
locations allow for more pairs of products with a higher association to be allocated in the same aisle. Operators can pick more products in the entrance of an aisle such that the travel distance is shortened. From the experimental results, raising the reserved proportion can achieve better picking performance. The proposed heuristics are run on a laptop with 2.20 GHz CPU and 3.49 GB DRAM. Table 6 shows that the computational requirement also increases enormously as the reserved proportion increases because more reserved locations result in more computational effort spent on calculating
AWS . By using MCBH, increasing reserved locations leads to a
jk better result but needs more computational requirements. ASBH is designed to approximate the situation of allocating all products based on their association between one another. The CPU time of ASBH is about 5 minutes, and it is much shorter than that of MCBH. Table 9 summarizes the average travel distance of CBAA and ASBH.Table 9 Comparisons of travel distance between CBAA and ASBH
Approach Dataset Avg. travel distance
for 4 trails Improvement
CBAA December 6207567 Benchmark ASBH December 5399599 13.02%
Compared to CBAA, the travel distance generated by ASBH is decreased by approximately 13%, which is better than the distance generated by MCBH.
ASBHattempts to store products frequently ordered together in the same aisle as much as possible so that the operator can pick more items in an entrance of an aisle. The results demonstrate sizable distance savings achieved solely by considering product relationships when allocating products. Intuitively, the decrease in travel time would be less than 10% according to the results from Table 7. However, the reduction appears to be larger than expected. The additional reduction may have been caused by eliminating the unreserved area. Without the unreserved area, all locations in each aisle are available, which means that ASBH has more flexibility to assign products.
On the other hand, the basic idea of CBAA has been embedded in ASBH. When a pair of products has a high WSC between each other, both of those products each have a high order frequency individually. ASBH first selects and allocates the products with a higher association between each other to the locations near the outbound exit. From above-mentioned point of view, ASBH that keeps both the advantages of family grouping policy and CCBA is superior to MCBH in both effectiveness and efficiency. However, ASBH might not function well if the association between products is sparse. In such a situation, the maximum association mechanism of each aisle would be replaced by random selection. The effect of picking several products frequently ordered together in an aisle might be insignificant.
The experimental results demonstrate how the efficiency of order picking can be improved by using MCBH and ASBH to re-assign storage locations without requiring additional pickers or picking facilities.