OMS 605-Alexander Thurston 31/1/2012 1

The Alexander and Thurston case is a classic example of the application of the Q, r model, where there is

a necessity to balance both the number of items held in inventory(and hence manage inventory cost)

- In this case, the inventory manager is in charge of the DC and needs to focus on the performance of

the DC in order to save his job. In our analysis of the inventory in the system, we will be focusing mainly

on the performance parameters of the DC.

Facts of the Case

-The flow of goods in the supply chain system is

DC==> (regional facilities==>customer sites)

- The fill rate for the DC is around 85%(partly due to lack of inventory and partly due to other reasons)

- Inventory costs are at around $6~7, spread between DC and the field.

Proposed solution:

Retain the earlier calculation for max inventory level (m) but change the reorder point r to

r= [1.4*(µ)*(l+10)]/365

Question 1:- The possibility of having lesser inventory and higher fill rate.

In inventory management, inventory and fill rates are typically trade offs, i.e if you increase one,

the other one increases proportionally. It is not possible to have lesser inventory and higher fill rate.

However, the rate of increase of fill rate increases rapidly initially but decreases at higher inventory

Therefore, it would be a wise policy to target fill rates of upto 90 % (say ) and have some stockout

rather than achieve 100 % fill rate with double the inventory cost when compared to 90% fill rate.

`

However, in the present case, it would be advisable to improve the other bottlenecks in the system

like downtime waiting for a repair technician to arrive in order to achieve the maximum fill rate

possible.

- The present system uses a method wheremaximum inventory level (m) and reorder point (r) are calculated

on the basis of usage (u).

well as improve customer service by achieving higher fill rate (i.e ensure stockout occurs less frequently)

Inventory level ==>

Fill

Rat

e==

>

Field

Aniruddha Srinath Rehan Syed Sam Beck Yue Ma

OMS 605-Alexander Thurston 31/1/2012 2

We used the equation I=(Q+1)/2+r-θ to evaluate which one is better. In the old policy, I=(10u/39+1)+u/13-θ

which gives us (16u+39)/78-θ inventory. On the other hand, the president's policy gives I=(u/6+1)/2+u/6-

θ=(u+2)/6-θ which equals (13u+26)/78. This is obviously smaller than the old policy. Thus we conclude that the

new policy devised better than the old one in terms of the facilities and sites.

Questions 3: After inserting the suggested new reorder point into the inventory investment calculations using

the Q,r model (please refer to sheet 2), we adjusted the coefficent given in the new reorder point to determine

a coefficient that would meet the desired fill rate of 90% and lower the inventory investment. After running

several iterations, we discovered that the formula of r= [.7*(µ)*(l+10)]/365 decreased the inventory

investment by a factor of 2 and met the fill rate of 90%.

Question 2:- Comparing the old and the new policiies, we confirmed that the president's policy is better than

the old one. As can be seen in the excel calculations using the Q,r model (please refer to sheet 1), the inventory

investment at the dc is lower using the new policy compared to the old policy. As for the field inventory, we

used the equation I = (Q+1)/2 + r -θ and compared the results using the respective reorder points. In this case

as well, the average inventory at the field sites was lower with the new policy compared to the old one.

Aniruddha Srinath Rehan Syed Sam Beck Yue Ma

OMS 605-Alexander Thurston 31/1/2012 3

Question 4:- Allocation of inventory between the DC and the field.

In order to calculate based on this model, we also need the demand at the field center. Since this is not

given, we are not able to declare exactly how much the inventory costs will reduce. However, it is reduced

for sure as the costs are being considered for inventory planning.

Note:- The Q, r solver and the single base models were used for our calculations, they are attached with

this sheet.

Based on the pooling concept, the inventory manager should keep the lower cost-high demand parts at the

field and keep the higher cost-low demand parts at the delivery center.

Therefore, we would multiply the maximum inventory level by 1/(c+1), with c being equal to the unit cost of

the product. This way, with higher cost parts, we will keep a lower inventory and with lower cost parts, the

impact of having a higher inventory will not be as large.

The current model distributes the inventory solely based on the usage class, therby taking into account the

demand of each product. However, it does not take into account the product's cost.

Aniruddha Srinath Rehan Syed Sam Beck Yue Ma