Chapter 20, Problem 23P

1.

To determine

Compute the optimal batch size for HA2 under EOQ model and indicate whether Company B’s response over the customer rights is correct or not.

Explanation of Solution

Economic order quantity (EOQ): Economic order quantity is ideal order quantity that the company should purchase the inventory with the ideal level. The economic order quantity (EOQ) approach assumes that some inventory must be held for future production. The main objective of the EOQ is to balance the ordering costs against the holding costs of inventory.

Compute the optimal batch size for HA2 under EOQ model and indicate whether Company B’s response over the customer rights is correct or not as follows:

$\begin{array}{c}\text{Economic order quantity = }\sqrt{\frac{2\times \text{Annual demand (D)}\times \text{Cost per order (P)}}{\text{Annual carrying cost per unit (C)}}}\\ \text{=}\sqrt{\frac{2\times 36,000\times \$6,000}{\$3}}\\ \text{=}\sqrt{144,000,000}\\ =12,000\end{array}$

Hence, the optimal batch size for HA2 under EOQ model is 12,000 units.

Description:

Company B’s response over the customer rights is correct for the current production environment, because the setup time is two days for the production and company has produced 750 units per day. Thus, the time required to produce the additional 9,000 units is 14 days (1).

Working note (1):

Calculate the time required to produce the additional 9,000 units.

$\begin{array}{c}\begin{array}{l}\text{Time required to }\\ \text{produce 9,000 units }\end{array}\}\text{= }\left(\text{Setup time+}\left[\frac{\text{Number of additional units}}{\text{Units produced per day}}\right]\right)\\ =2\text{ days + }\frac{9,000\text{ units}}{750\text{ units}}\\ =14\text{ days}\end{array}$

2.

To determine

Compute the additional inventory that is needed to meet the customer requirements and indicate whether company B should carry more inventories.

Explanation of Solution

Compute the additional inventory that is needed to meet the customer requirements and indicate whether company B should carry more inventories as follows:

In this case, company B would have produced 3,750 units (2) within the seven working days whereas company has 5,250 units $\left(9,000\text{ units}-3,750\text{ units}\right)$ which are more than the units available to meet the demand. In order to solve current delivery problem, company B requires more inventory than the currently carried. The demand for HA2 can be more than the expected demand, and if extra demand occurs from large order then the level of inventory would be increased based on the demand in the sales. Hence, company B should explore alternative inventory management approaches such as JIT or TOC in order to increase the inventory.

Working note (2):

Calculate the number of additional units.

$\begin{array}{c}\begin{array}{l}\text{Number of }\\ \text{additional units}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Days in week}-\\ \text{Setup time}\end{array}\right)\times \text{Production units per day}\\ \text{=}\left(7\text{ days}-2\text{ days}\right)\times 750\text{ units}\\ \text{=3,750 units}\end{array}$

3.

To determine

Calculate the new optimal batch size under economic order quantity (EOQ) model and new lead time, and indicate whether company B would have been able to meet the customer’s time requirements.

Explanation of Solution

Calculate the new optimal batch size under economic order quantity (EOQ) model and new lead time, and indicate whether company B would have been able to meet the customer’s time requirements as follows:

Economic order quantity:

$\begin{array}{c}\text{Economic order quantity = }\sqrt{\frac{2\times \text{Annual demand (D)}\times \text{Cost per order (P)}}{\text{Annual carrying cost per unit (C)}}}\\ \text{=}\sqrt{\frac{2\times 36,000\times \$94}{\$3}}\\ \text{=}\sqrt{2,256,000}\\ =1,502\end{array}$

New lead time:

$\begin{array}{c}\text{New lead time = }\left(\begin{array}{l}\text{Reduced set up time +}\\ \left[\begin{array}{l}\left(\frac{\text{Economic order quantity}}{\text{Increased units per day}}\right)\times \\ \text{Hours worked per day}\end{array}\right]\end{array}\right)\\ =1.5\text{ hours+}\left(\frac{1,502\text{ units}}{2,000\text{ units}}\times 8\text{ hours}\right)\\ =7.5\text{ hours}\end{array}$

Description:

In this case, company B could satisfy the customer’s time requirement in less than 7.5 hours at a production rate of 2,000 units per day. Above calculation indicates that the company should take attention on setup, moving and waiting activities to reduce the lead time of production. Just in time method would provide easy way to reduce the lead time of production with the help of shorter production cycle. EOQ reveals that the batch size has reduced to 13% $\left(\frac{1,502\text{ units}}{2,000\text{ units}}\right)$  before the improvements.

4.

To determine

Calculate the batch size if set up time and cost are reduced to 0.5 hour and $10 respectively, calculate the batch size if set up time and cost are reduced to 5 minutes and $0.864 respectively and comment its implication.

Explanation of Solution

Calculate the batch size if set up time and cost are reduced to 0.5 hour and $10 respectively as follows:

$\begin{array}{c}\text{Economic order quantity = }\sqrt{\frac{2\times \text{Annual demand (D)}\times \text{Cost per order (P)}}{\text{Annual carrying cost per unit (C)}}}\\ \text{=}\sqrt{\frac{2\times 36,000\times \$10}{\$3}}\\ \text{=}\sqrt{240,000}\\ =490\end{array}$

Reduced setup time and cost would reduce the batch size to 490 units.

Calculate the batch size if set up time and cost are reduced to 5 minutes and $0.864 respectively as follows:

$\begin{array}{c}\text{Economic order quantity = }\sqrt{\frac{2\times \text{Annual demand (D)}\times \text{Cost per order (P)}}{\text{Annual carrying cost per unit (C)}}}\\ \text{=}\sqrt{\frac{2\times 36,000\times \$0.864}{\$3}}\\ \text{=}\sqrt{20,736}\\ =144\end{array}$

If cost is reduced to 0.864, then batch size is reduced to 144 units.

The demand units per day can be produced in less than one hour with the ability to produce 2,000 units per day.