BUS606: Operations and Supply Chain Management

As shown in Figure 4, the original inventory status data indicates that the cumulative on-order and on-hand inventory in Scenario 1 often exceeded the maximum inventory position line, particularly on the work days of 46~53, which signifies a substantial decline in stock without purchase order refills. Moreover, the on-hand inventory was not consistent with the on-order stock which fluctuated significantly. As shown in the diagram, substantial declines occurred on work days 41~61. It also indicates that the safety inventory was set as "used only during work days 51–61".

Figure 4. Inventory status of part 1 in Scenarios 1 and 2.

Furthermore, Figure 4 shows the inventory level mapping after substituting the parts data in the Scenario 2 mathematical model, which shows a more stable inventory status than in the other scenario. Compared to the maximum inventory position of the cumulative on-order and on-hand inventory, Scenario 1 shows that the inventory level in this study was much lower compared to Scenario 2. Hence, in Scenario 2, the mathematical model, the quantity of the required parts in stock in the supply chain was also lower compared to Scenario 1. The on-hand inventory in Scenario 2 was also more consistent with the on-hand inventory position line of Scenario 1, indicating that the model in this study was more consistent with the indicator line set in the actual situation. In addition, with regard to the safety inventory, the model was able to help workers quickly respond when the on-hand inventory dropped lower than the indication line by pulling back the on-hand inventory to the on-hand inventory position. Therefore, it can be concluded that the model under study and the purpose of setting the safety inventory indicatory line based on the actual situation were more consistent with each other.

In addition to the reduced inventory costs presented by the data, since the on-hand inventory in the Scenario 2 model was stable, the distribution center employees (warehouse) can determine exactly how much space to set aside for the parts. Compared to the instability of Scenario 1, the inventory space demand of the Scenario 2 model will continually require less space, which corresponds to lower inventory costs.

As shown in Figure 5, the original inventory status data indicate that the cumulative on-order and on-hand inventory of Scenario 1 was not at all consistent with the maximum inventory position line, which was often higher or lower than the other indicators. This shows a problem with the parts inventory. Moreover, the on-hand inventory was not consistent with the inventory position. It fluctuated between high and low, specifically during several sections of work days that were much higher than the on-hand inventory position. Conversely, the safety inventory of the parts was not utilized very often. The diagram shows that the safety inventory was only used for six days, causing a backlog of inventory.

Figure 5. Inventory status of part 2 in Scenarios 1 and 2.

After substituting the parts data in the mathematical model in Scenario 2, Figure 5 shows that the inventory status was more stable. When we compare the on-order inventory to that on-hand and the maximum inventory position line of Scenario 1, the inventory in Scenario 2 is seen to be much lower than that of Scenario 1. Therefore, under the mathematical model in scenario 2, the quantity of parts needed to be stocked in the supply chain was lower compared to that of Scenario 1. However, inventory in Scenario 2 was more consistent with the on-hand inventory position line in Scenario 1, indicating that the model in this study better meets the indication line set in Scenario 1. Although the peak value of the on-hand inventory failed to meet the on-hand inventory position set in Scenario 1, the safety inventory in the Scenario 2 model compared to the Scenario 1 shows that the parts were used. Therefore, it can be concluded that the on-hand inventory peak value in the Scenario 2 model was not at all consistent with the on-hand position set in the actual situation because the on-hand inventory and safety inventory position set in Scenario 1 was too high. Hence, according to our findings, the new on-hand inventory position and the inventory position modeled in Scenario 2 was much more effective.

In addition to reducing inventory costs, since the on-hand inventory in the Scenario 2 model was stable, the distribution center employees (warehouse) will know exactly how much space to set aside for the inventory parts. Compared to the instability of Scenario 1 and Scenario 2 requires much less space, thus lowering inventory costs.

The original inventory status data of parts number 3-1, seen in Figure 6, shows that the cumulative on-order and on-hand inventory of Scenario 1 were not at all consistent with the maximum inventory position line, which was often higher or lower than the indicators with a large gap. This signifies a problem with the parts inventory. In addition, the on-hand inventory parts were completely inconsistent with the on-hand inventory position. The diagram shows that at 1~48 work days, it was higher than the on-hand inventory, and the safety inventory was infrequently used. The diagram also shows this with the safety inventory set at 120 work days. The on-hand inventory was lower than the safety inventory's position only at three stages, indicating that the safety inventory was only used three times. Thus, we can conclude that this scenario suffers from an excessive number of inventory parts.

Figure 6. Inventory status of part 3 in Scenarios 1 and 2.

Figure 6 shows the inventory map after substituting the parts data in the mathematical model in Scenario 2. This indicates that the inventory status examined in this study was more stable. The cumulative on-order and on-hand inventory, which was compared to the maximum inventory position line of Scenario 1, show that the inventory in this study was much lower than in Scenario 1. Therefore, under the mathematical model in Scenario 2, the number of parts needed to be stocked in the supply chain was lower than in Scenario 1. Conversely, the on-hand inventory in Scenario 2 was more consistent with the on-hand inventory position line in Scenario 1, indicating that the model in this study better meets the indication line set in the actual situation. In addition, with regard to the safety inventory, the model was able to help employees quickly respond when the on-hand inventory dropped lower than the indication line by pulling back the on-hand inventory to the on-hand inventory position. Therefore, it can be concluded that the model in this study and the purpose of setting the safety inventory indicatory line based on the actual situation are more consistent with each other.

In addition to the reduced inventory costs presented by the data, since the on-hand inventory in the Scenario 2 model was stable, the distribution center (warehouse) employees can determine exactly how much space to set aside for the parts. Compared to the instability of Scenario 1, the space required for inventory in the Scenario 2 model was significantly reduced, thus lowering the inventory costs.

The original inventory status data of parts number 4-1, as shown in Figure 7, indicate that the on-hand inventory was not consistent with the on-hand position. This was due to the fact that the on-hand inventory had not been replenished to the on-hand position for a long time; however, the on-hand inventory peak values only exceeded the on-hand position three times. Moreover, the safety inventory of the parts was low. The diagram shows that there were roughly 40 safety inventory indicator lines and the minimum on-hand inventory of the parts within 120 work days was 29, indicating that the safety inventory indicators had been set too high.

Figure 7. Inventory status of part 4 in Scenarios 1 and 2.

After substituting the parts data in the mathematical model in Scenario 2, the inventory mapping, seen in Figure 7, indicates that the inventory status was more stable than in Scenario 1. When we compared the cumulative on-order and on-hand inventory to the maximum inventory position in Scenario 1, we found the inventory in Scenario 2 to be much lower. In contrast, the on-hand inventory in Scenario 2 was more consistent with the on-hand inventory position in Scenario 1, indicating that the model in this study was more in line with the indicator lines set in the actual situation. Additionally, whenever the on-hand safety inventory in Scenario 2 dropped below the indicator line, the employees were able to quickly move the on-hand inventory back to the correct inventory position. Hence, the model in Scenario 2 was more effective for setting up the safety inventory indicator lines.

Table 4 and Figure 8 show the statistical inventory and the corresponding manufacturers in Scenario 2 as well as the inventory of Scenario 1 in the DC warehouse. It is clear that the inventory of parts provided by manufacturer 1 is reduced by 35% in the Scenario 2 model; the inventory of parts provided by manufacturer 2 is reduced by 60% in this model; the inventory of parts provided by manufacturer 3 is reduced by 38% in this model; the inventory of parts provided by manufacturer 4 is reduced by 9% in the Scenario 2 model. Overall, this model shows a 36% reduction, which indicates that the inventory in Scenario 2 is indeed lower than it was in Scenario 1. Therefore, this model will help warehouse managers to significantly reduce their inventory compared to Scenario 1. The manufacturers of 1 and 3 reduced inventory by 35% and 38%, respectively. Manufacturer 2 had the highest rate of reduction at 60%.

Figure 8. Inventory levels of Scenario 1 and corresponding manufacturing supplier numbers under Scenario 2.

Table 4. The inventory in Scenario 1 and of the corresponding manufacturers in Scenario 2.

We resolved and found 20 Pareto points after filtering out the inappropriate solutions which are shown in Table 5. As shown in Figure 9, using total carbon emissions as the X-axis and total cost as the Y-axis, the total carbon emissions of the Pareto points 16~20 increased significantly; however, the total cost reduction was higher. The 20 Pareto points in Scenario 1 had a much higher usage ratio of over 50% than those in Scenario 2, which were only 15:5. Therefore, the Pareto points are less obvious when they are closest to their highest point and if the usage ratio in Scenario 2 is higher than 50%. As shown in Figure 9, the distribution condition of the Pareto points chosen for this study corresponds to the Pareto boundary solution proposed by Messac et al. (The formula is: $y=2 \mathrm{E}-07 x^{2}- 1.2011 x+2 E+06$)

Figure 9. The distribution diagram of total carbon emissions and total cost.

Table 5. Pareto points for total carbon emissions and total cost.