5.3 Results
5.3.3 Sensitivity Analysis
In order to understand how the output of the inventory control model responds to input value changes, this section investigates the model sensitivity to several parameters. The following parameters are tested:
target fill rate, procurement lead time, return lead time, transportation lead time between warehouses and order quantity.
Target Fill rate
Because XYZ is only a small fraction of the complete portfolio and target fill rates need to be met for the complete portfolio and not per product family, it is interesting to see how the model behaves when the target fill rates change. This way, the company gains more insight into how much more or less inventory is needed to obtain a certain fill rate requirement, i.e. it might be possible that with a small amount of extra inventory a much higher target fill rate could be reached. The results are shown in figure 5.4.
One can see that as the target fill rate increases, the inventory value also increases. Increasing from 90%
to 95% results in a lower increase in inventory value than increasing from 95% to 99%. This relationship makes sense because of two possible reasons:
1. the optimization algorithm allocates the parts that result in the highest relative increase in aggre-gate fill rates, against the lowest cost. Expensive parts, that do not have a high demand rate, are allocated as one of the last parts.
2. the more parts are allocated, the lower the increase in aggregate fill rate. Parts with low demand rates are allocated last in the optimization algorithm. Adding one item with a low demand rate, increases the aggregate fill rate only to a small extent. An increase of 1 percent in the aggregate fill rate requires more parts, after having allocated many parts.
Figure 5.4: Fill rate sensitivity
Fill Rate per Part
The model uses aggregate fill rate per warehouse as objective requirement. This means that it might happen that some parts have a very lower fill rate, whereas other parts have very high fill rates. The probability that some parts have very low fill rates increases as the target aggregate fill rate decreases.
The fill rates per part are analysed for two target fill rates: 90% and 95%.
The results are shown in table 5.12. The number of parts with a low fill rate in the inbetween hubs is for both 90% target fill rate and 95% target fill rate relatively low. However, for the central warehouse a relatively large number of parts has a fill rate of 0 in both scenarios. This can be explained by the large number of parts in the central warehouse compared to the inbetween hubs, as well as the higher demand rate for many parts, i.e. if the central warehouse has 10 parts and 5 out of 10 parts have a daily demand rate of 10 and the other 5 have a daily demand rate of 1, then the parts with a low daily demand rate contribute less to the aggregate fill rate. Therefore the aggregate fill rate can be met with
less low demand parts (see equation 4.15). For this to be true, it must be the case that the parts with a fill rate of 0 both have a low demand rate and a high price, because in this case the program would prefer not to allocate inventory to these parts. This was indeed observed. The average standard price of all parts in the central warehouse is$11686 and the average daily forecast 0.01188. The average daily forecast of the parts with a fill rate of 0 is 0.0016 and the price$41522.
In addition, this explains the steep increase from 95% to 99% in figure 5.4: with a 99% target fill rate, also the expensive parts have to be allocated.
APR Target FR
90%
Target FR 95%
Part FR (%) Parts (units) Parts (units)
0 0 0
Part FR (%) Parts (units) Parts (units)
0 82 42
Part FR (%) Parts (units) Parts (units)
0 0 0
Table 5.12: Difference in units between current stock levels and proposed stock levels
In conclusion, the target fill rate has a significant effect on the reorder points, base stock levels and inven-tory positions. The inveninven-tory on hand seems to increase exponentially as the target fill rate approaches 100%. When choosing target fill rates, it is important to realize that using lower target fill rates can lead to more parts having very low fill rates, especially in the central warehouse.Procurement lead time
Procurement lead times are important in determining the base stock levels and reorder points. Reducing procurement lead times might lead to decreased total costs. Because of a lower demand during lead time and thus pipeline inventory, the need to have high base stock levels and reorder points is decreased. The effect of the procurement lead times on the inventory values is shown in figure 5.5. The inventory value shows a positive correlation to procurement lead time.
Figure 5.5: Procurement lead time sensitivity
As expected, procurement lead times have an effect on the inventory positions. Contrary to the expecta-tion is that this effect is not significant: the difference in expected inventory on hand between a decrease of 40% and an increase of 40% in procurement lead time is $336,516.98, which is equal to 4%. Note that the average of the procurement lead times is 80 days with a minimum of 7 and a maximum of 287, meaning that a 40% decrease/increase is relatively large. The reason that the effect is not significant is because of the low demand rates of the parts, which means that most parts already have a high fill rate with 1 unit in inventory.
In section 4.1 it was explained that the supplier lead times might fluctuate. This section shows that the effect of fluctuating lead times on expected inventory values is small. This means that the assumption of constant lead times can be justified.
If the company wants to reduce procurement lead times to decrease the total costs, they should take into account the small effect that reducing procurement lead times has on the inventory levels. Reducing lead times comes at extra costs, because of the higher service level requirements expected from the suppliers.
These costs should be taken into account when considering the decrease of procurement lead times, especially because of the small effect of the lead times on the inventory values.
Return lead time for repairables
Another possibility to reduce inventory costs is to reduce the return lead time for the repairable parts (because of the same reasons as a decrease in procurement lead time). The results of this sensitivity are shown in graph 5.6.
Figure 5.6: Return lead time sensitivity
Decreasing return lead times leads to a decrease in inventory values. Surprisingly however is that higher return lead times do not necessarily lead to higher inventory values. At one point the inventory value decreases as the lead time increases. The reason for this might be because repairable parts are usually the more expensive parts and often have low demand rates. High fill rates for those parts are already obtained with 1 unit in inventory. Because of the low demand rates, increasing the return lead time will only have an effect on the reorder points if the increase is substantial. For example: one part has a demand rate of 0.002. The return lead time is 34 days and the repair lead time is 150 days. The demand during lead time becomes 0.368. If the return lead time now becomes 40 days instead of 34 days, the demand during lead time is 0.38. In both cases a high fill rate is achieved if 1 unit is held in inventory.
Comparing the reorder points of the +10% scenario with the +20% scenario, we observed that the reorder points of the expensive (repairable) parts increased. This is as expected. There was one repairable part, part number 1134278, which showed no increase in reorder point. Due to the increase in return lead time, while having the same reorder point, the expected inventory on hand decreased. Because this was an expensive part,$187.424.16, a relatively large decrease was seen in the expected inventory value.
In general the picture shows that the company would benefit from reduced return lead times. Because reducing return lead times is possible by better management, the company should aim to investigate ways on how to reduce return lead times.
Furthermore, because of the long return lead times of repairable parts, the company was interested in knowing costs incurred by these long return lead times. In the current practice the base stock levels are not constantly recalculated based on (increased) return lead times. This means that in practice, a backorder would occur that forces the company to procure a new part, while in fact this part should have been on hand. An approach to quantify the costs associated with this is made in the following way:
The base stock levels and reorder points for the repairable parts from the scenario with a target fill rate of 90% are used as input for the model. Then the return lead times are increased stepwise. During every step, the expected inventory on hand is tracked. This method was used because the 90% target fill rate scenario shows the expected inventory on hand needed to fulfil demands, such that a 90% fill rate is reached. If that inventory is not on hand, chances are that demands at that moment cannot be fulfilled and the 90% fill rate target is not reached. By not correcting for the longer return lead times, the base stock levels remain the same as with the shorter lead times. This leads to a shortage of inventory on hand. The shortage of inventory on hand indicates the loss of expected inventory and thus the costs of not having that inventory on hand.
Results can be seen in figure 5.7. The relationship is linear, which is sensible because all other variables are kept constant. It costs approximately$30,000 for every day that the repairable parts are not returned in time. Moreover, changes in aggregate fill rate are negligible, due to the small percentage of repairable parts compared to the non-repairable parts. Adding 12 days to the return lead times, leads to an 89%
fill rate for the central warehouse of NA. This is a small decrease compared to the 90% fill rate if all parts are returned in time.
Figure 5.7: Return lead time increase, while keeping other variables constant
An important take-away from this subsection is that the company should aim to actively manage return lead times in two ways. First by reducing the return lead times and second by ensuring that parts are returned in time.
Transportation lead time between warehouses
The transportation lead time from central warehouse to local warehouse is set at 14 days. Sensitivity analysis is performed on this parameter for two reasons:
1. The transportation lead times might fluctuate.
2. It might be interesting for the company to see if cost reductions are possible by reducing the transportation lead times. Lower transportation lead times could mean that less inventory must be stocked in the inbetween hubs. Transportation lead times can be reduced by for example consolidating parts weekly instead of biweekly. This option is interesting if transportation costs between the warehouses are low. Following the same reasoning, if transportation costs are high, it might be more cost efficient to have longer shipment (by consolidating shipments) lead times and to hold more inventory in the inbetween hubs.
Results are shown in figure 5.8. Overall shorter transportation lead times result in lower inventory values.
However, at one point (from +0% to +40%) the inventory value decreases as the shipment lead time increases. This could be due to the same reasons as with the return lead time: if the base stock level remained the same, but the demand during lead time increased, the expected inventory on hand would be lower. This was checked by looking at the reorder points and base stock levels. These remained the same, or increased in the scenario with +40%. Afterwards, the inventory on hand was checked. It was observed that there were indeed 3 high-value parts that had the same base stock levels, but lower
expected inventory on hand. Overall one could say that an increase in transportation lead time between warehouses leads to inventory values. If the increase is not substantial, this could however lead to lower inventory values.
Figure 5.8: Transportation lead time between warehouses sensitivity
To conclude, decreasing the transportation time between the central warehouse and inbetween hubs leads to lower inventory values, because the central warehouse is able to send parts quickly to the other warehouses. Increasing the transportation lead time does not necessarily lead to higher inventory values.
This result can be attributed to a decrease in inventory on hand of a very small amount of high-value parts.
When considering a decrease in transportation lead time, a trade-off needs to be made between extra transportation costs (due to sending parts more often to other warehouses) and the lower inventory values. In section 3.3 it was shown that transportation costs are relatively cheap. Taking into account the low transportation costs and the decrease in inventory values, it might be worthwhile for the company to investigate this issue further and to see if it indeed is profitable to reduce the transportation lead times.
Order quantity
The order quantity sensitivity is displayed in table 5.13. The difference in inventory value between a decrease of 50% in order quantity and an increase of 50% is $201,522.22 . A decrease of 50% leads to a smaller difference between the current inventory value than an increase of 50%. This result can be explained by the fact that 91% of the parts have economic order quantities of 1 and that they account for 66% of the total demand. Decreasing the order quantities of the parts only changes the order quantities of the parts with an order quantity higher than 1 and since these parts only constitute for a small percentage of the total, the impacts on the inventory are insignificant.
Inventory Value( $) EOQ*0.5 8,357,754.76
EOQ 8,365,030.10
EOQ*1.5 8,559,276.98 Table 5.13: Order quantity sensitivity
Summary
In this section the results of implementing the proposed control model are discussed. It was shown that a 90% target fill rate can be reached with an inventory value of$10,540,890.58 less. The analysis also revealed that many parts are currently overstocked and some also understocked.
In addition parameter values were changed in order to see how the model behaves. The following parameters were tested:
Target fill rate: target fill rate has a significant effect on the outcomes of the inventory values.
The higher the target fill rate, the higher the increase in inventory value.
Procurement lead time: lower procurement lead times lead to lower inventory values, but only by a small percentage.
Return lead time: decreasing the return lead times leads to lower inventory values, but higher return lead times do not necessarily lead to higher inventory values.
Transportation lead time between warehouses: shorter transportation lead times lead to less in-ventory being stocked in the inbetween hubs, but higher return lead times do not necessarily lead to higher inventory values.
Order quantity: higher order quantities lead to higher inventory values, but to a small extent.
6 Conclusion and Recommendations
6.1 Conclusion
1. Why do parts come back unused or used after testing?
An effort was made to find out why parts come back unused or used after testing. Data-analysis revealed that Japan shows a significantly higher number of returns compared to the other countries.
Moreover, Europe has a relatively high percentage of used for testing returns. Finally, many parts come back year after year which indicates that the returns are structural. Additionally, the interview confirmed that the field service engineer orders parts together because correct diagnosis is difficult and the engineer wants to prevent long downtime.
The analysis did have a major drawback, which is the small sample size. Hence, every conclusion drawn from this analysis serves solely as a guideline.
2. What are the costs associated with the unused or used after testing?
The total costs associated with the unused and used for testing returns in the period 01/01/2018-31/10/2018 for the company as calculated in this research are$3,542,667.45.
3. What is an appropriate mathematical model for the inventory control of XYZ tools?
The main criteria for selecting an appropriate model were the following:
The model should be able to deal with high value, low demand parts.
The model should have a multi-echelon approach
The model should have a multi-item approach
The model should have aggregate fill rate as service measure
The model described by Topan et al.(2017) was selected as most appropriate model for company X.
4. How does the modified inventory control model perform compared to the current inventory control model?
The proposed inventory control model outperforms the current inventory control model. Using the proposed control model would lead to a significant decrease of inventory, whilst meeting the 90%
target fill rate for the three regions, EU, NA and APR. The improvement potential is especially significant for the inventory of the central warehouse, NA. A reduction of$10,540,6890.58 can be realized in comparison with the current stock policy. Furthermore, comparison between the stock levels of the current model compared to the reorder points and base stock levels of the proposed control model shows that many items are either overstocked or understocked at the moment.
5. What is the effect of long and variable return lead times on the inventory values (and fill rate?) Company X was interested in knowing the effects of the long and variable return lead times of repairable parts for the complete portfolio.
In this research a model was developed specifically for the XYZ product family. Analysis showed that return lead times do have effect on the inventory values. The first important result is that if base stock levels and reorder points are kept as is and the actual return lead times differ from the return lead time as used in the model, the expected inventories will be lower than what the expected inventories should be to obtain a 90% fill rate. This indicates a loss of investment in inventory of approximately $30,000.00 per day, because an investment was made to obtain a certain inventory, while this inventory is not on hand when this it should be. Moreover, changes in
aggregate fill rates due to longer lead times are small, because of the low percentage of repairable parts compared to the non-repairable parts.
In addition, reducing return lead times leads to lower inventory values. Therefore reducing return lead times is in the best interest of the company.
Although the model in this research was only applied to the XYZ product family, their current software tool used to determine reorder points for the legacy tools, Servigistics, shows resemblance to the developed model for XYZ parts. With this research therefore, insight is gained in how return lead times affect stock levels and that it is also important for the legacy tools to have correct return lead times in the ERP system or to at least ensure that parts are returned within the required 14 days.
In general, this research emphasizes the importance of an optimized inventory control model. In the current control model the decisions are based on simple calculations and experience & intuition of the global planners. Inventory values can be further reduced by shortening the transportation lead times between the warehouses. A trade-off however needs to be made between possible extra transportation costs and the decrease in inventory costs. Considering that the transportation costs are relatively low, it is worthwhile for the company to investigate this issue further.