Pitakaso et al. [1] presented a RCWW-STVS algorithm to solve multilevel lot-sizing problems
without resource constraints. To prove their algorithm is superior to Dellaert et al. [2]’s RCWW algorithm,
they presented a result reached by RCWW-STVS algorithm for reference [2]’s instance with product
order of {2, 5, 1, 3, 4, 6, 8, 7, 9}, setup cost accumulative parameters ri ={0.43, 0.43, 0.43, 0.43, 0.43,
0.43, 0.43, 0.43, 0.43} and the inventory costs for material 1 to 9 is {13, 8, 4, 4, 3, 3, 2, 1, 1}.
The product structure is shown in Fig.1. The underlined number is lead time for each material and the
right side number is setup cost for each material. The inner demand relation between materials is 1 to 1.
The result from [1] is presented in Table 1. There are no errors for parameters but the result for reference [2]’s instance. Here we note in Table 1, the demand for material 1 is {0, 0, 0, 0, 10, 15, 10, 12,
20}. Material 1’s production lot, according to [1], is {0, 0, 0, 0, 10, 15, 10, 12, 20}. Then for material 3,
taking into consideration of material 1’s lead time, the demand is {0, 0, 0, 10, 15, 10, 12, 20, 0}. As we
seen from Table 1, the revised setup cost of material 3 is {0, 0, 0, 41.5, 30, 30, 30, 30, 30}. The production lot of material 3 reached by [1] is {0, 0, 0, 10, 25, 0, 12, 20, 0}. However, we can find
that the setup cost in period 6 of material 3 is 30 and the inventory cost in period 5 of material 3 is 4. If
producing 10 products in period 6, the cost is 30. However, according to Pitakaso et al.[1]’s result, 10 units
of material 3 are kept in inventory for 1 period. Then the cost is 10*4=40. So we can easily tell a
production decision {0, 0, 0, 10, 15, 10, 12, 20, 0} is better than another one {0, 0, 0, 10, 25, 0, 12, 20, 0}.
After a practical verification with C program language, we got a result, which is a revision to reference
[1]’s result, for Dellaert et al.[2]’s instance and presented it in Table 2. The material presentation of
MLLS problem is shown in Fig.2. Fig.3 shows the output interface of VC++ program.
