Question

Littlefield Laboratories, LLC (LL) provides an integrated genetic test called MaterniT 21 PLUS for expected parents in Northern California. LL charges its customers a premium price of $1,900 per test and promises to return the result within 24 hours after receiving the order; otherwise a rebate will be provided. LL runs 24x7 and customer orders for the test come in to the lab with blood samples on a continuous basis. Demand for the test is relatively stable at an average of 3,000 tests per month, with an estimated standard deviation of 100 tests for the weekly demand. Each test requires an advanced testing kit that can be purchased from a sole supplier at a wholesale price of $600 each. LL can purchase the testing kits from the supplier in a batch. The supplier charges a fixed setup cost (including shipping) of $6,000 for each batch LL orders, regardless of the size of the batch. It will take exactly 7 days for the supplier to deliver the batch to LL after LL places the order. If LL runs out of inventory for less than a week, the backlog cost is estimated to be $156 per unit. As soon as the batch is delivered, LL pays the supplier out of is operational cash account, which generates interest for LL on a compound annual growth rate (CAGR) of 8%. Test kits are very small parts that do not require any physical resources (e.g., extra space or climate control) to hold.

1. Which of the following are necessary inventory control decisions LL has to make? (Select all that apply.) Group of answer choices

Determining how many testing machines to purchase.

Determining how many units of testing kits to order in a batch.

Determining how many operators to staff in each shift.

Determining the reorder point that triggers the testing kit replenishment order.

Determining how often to order testing kits.

Determining what price promotions can be offered to customers.

2. Which of the following are appropriate strategies for making the inventory decisions. (Select all that apply.) Group of answer choices

Use the EOQ model to determine how many testing kit units to order each time.

Use the EOQ model to determine how often to place testing kit orders.

Use the EOQ model to determine the reorder point to trigger the replenishment order in order to keep a good amount of testing kits on hand during the 7‐day supplier lead time.

Use the EOQ model to determine how many operators to staff in each shift.

Use the order-up-to model to determine the optimal reorder point.

Use the order-up-to model to determine how many testing machines to purchase.

3. LL plans to use the EOQ model to make some of its inventory decisions. Which of the following hypotheses, if true, will make the EOQ method invalid? (Select all that apply.) Group of answer choices

The incoming demand is relatively stable at a constant rate that can be easily estimated.

The supplier can offer discounts on the fixed setup charge based on ordering quantities, e.g., 50% off if the batch size is larger than 10,000 units.

The supplier can offer discounts on the per unit wholesale price based on ordering quantities, e.g., 10% off if the batch size is larger than 5,000 units.

LL’s operational cash is put into an actively managed account with a systematic withdrawal plan that allows LL to withdraw a flexible amount of fund only on the first of each month to pay employees and bills and make necessary procurements.

The supplier’s setup charge and wholesale price are constants.

4. LL plans to set its reorder point at 700 units, which equals the average weekly demand LL faces. Which of the following are true? (Select all that apply.) Group of answer choices

If LL keeps 700 units on hand during the 7‐day supplier lead time, LL has a 50% chance of running out of inventory before the supplier delivers the ordered batch of testing kits.

If LL keeps 700 units on hand during the 7‐day supplier lead time, LL has a 50% chance of having leftover inventory when supplier delivers the ordered batch of testing kits.

700 is the optimal reorder point for LL to set. LL should set a reorder point higher than 700 in order to have a positive safety stock buffer.

LL should set a reorder point lower than 700 in order to have a negative safety stock buffer.

5. LL has made an inventory decision of ordering 3000 units in a batch each time it orders from the supplier. Which of the following are true? (Select all that apply.) Group of answer choices

This is the EOQ solution.

LL is expected to order 12 times a year.

LL is expected to order once per month.

The solution will impose an annual inventory holding cost that is much higher than the annual total setup cost.

The solution will impose an annual total setup cost that is much higher than the annual inventory holding cost

6.LL plans to place an order of 3000 units to its supplier on a monthly basis. LL is also considering to set the reorder point to 900 units to trigger the order. Once the ordered batch is delivered in exactly 7 days, any leftover testing kit inventory LL has will impose a $4 per unit of carrying cost for another month. Which of following are true? (Select all that apply.) Group of answer choices

Setting the reorder point at 900 units, or 2 standard deviations above the mean weekly demand, will give LL approximately a 97.5% probability of not running of inventory during the 7‐day supplier lead time.

Setting the reorder point at 900 units, or 2 standard deviations above the mean weekly demand, will give LL approximately a 2.5% probability of not running of inventory during the 7‐day supplier lead time.

The critical ratio is $156/($156+$4) = 0.975.

Setting the reorder point at 900 units, or 2 standard deviations above the mean weekly demand, can be considered optimal.

With a reorder point of 900 units, LL will not have a sufficient safety stock buffer during the 7‐day supplier lead time to take on incoming customer orders.

Answer 1

1. Important data and key decisions pertaining to efficient inventory control shall be as follows.

Cost of Test = $ 1900

Average Monthly Demand = 3000 tests.

(Decision 1)Therefore, Average Weekly Demand = 3000/4 = 750 test.

Standard Deviation = 100

Therefore, Highest Weekly Demand = 750 + 100 = 850 tests

Similarly, Lowest Weekly Demand = 750 - 100 = 650 tests

(Decision 2)Test Demand Range = 650  - 850 (demand per batch)

Wholesale Cost Per Test Unit = $600

Fixed Cost Per Batch = $6000

Delivery Period = 7 days.

(Decision 3) Orders Frequency has to be determined = 7 days.

(Decision 4) Average weekly order = Average weekly Test Demand = 750 units

Fixed Cost Per Testing Kit (Assuming 750 kits per batch) = 6000/750 = $80.

Landed Cost Per Kit = 600 + 80 = $680

If order batch size > 850; Fixed Cost per piece is further reduced. But for each additinal testing kit $600 gets paid from company account blocking capital for additional week.

For efficient inventory management, key decisions from above can be:

(a) Determining how many testing machines to purchase. (Decision 4)

(b) Determining how many testing kits to be ordered per batch.  (Decision 1, 2)

(c) Determining Reorder Point that triggers testing kit replenishment order. (Decision 3)

(d) Determining how often to order kits. (Decision 3)

3.

3. LL plans to use the EOQ model to make some of its inventory decisions. Which of the following hypotheses, if true, will make the EOQ method invalid? (Select all that apply.)

The incoming demand is relatively stable at a constant rate that can be easily estimated.

The supplier can offer discounts on the fixed setup charge based on ordering quantities, e.g., 50% off if the batch size is larger than 10,000 units

The supplier can offer discounts on the per unit wholesale price based on ordering quantities, e.g., 10% off if the batch size is larger than 5,000 units.

4.

Ans: 1) If LL keeps 700 units on hand during the 7‐day supplier lead time, LL has a 50% chance of running out of inventory before the supplier delivers the ordered batch of testing kits.

2) LL should set a reorder point higher than 700 in order to have a positive safety stock buffer.

Monthly demand = 3000 tests

Annual demand = D = Monthly Demand * 12 months = 3000 * 12 = 36000 tests

Cost per kit = $600

Interest rate = 8%

Holding cost = H = 8% * 600 = $48

Ordering costs = S = $6000

Backlog cost = B = $156

We find the EOQ using POM-QM as shown below:

On solving, we get

Hence, EOQ = 3430.63 units

Accordingly, we get the correct option as:

Option 1 is incorrect as EOQ = 3430.63 units and we are ordering 3000 units

Order Quantity = Q = 3000. No. of Annual orders = D / Q = 36000 / 3000 = 12 orders

Option 2 is correct. Option 3 is also correct as the order quantity = Monthly demand

Since we are ordering lower quantity as compared to EOQ, there are more no. of orders hence more annual ordering cost. Therefore, option 4 is incorrect and option 5 is correct.

6.

Answer:

LL is expected to order 12 times a year

LL is expected to order once per month

The solution will impose an annual total setup cost that is much higher than the annual inventory holding cost

Monthly demand = d = 3000 tests

Std. Deviation = = 100 tests

Daily demand = Monthly demand / 30 = 100 tests

Weekly Demand = d = Daily demand * 7 = 700 tests

Reorder point = ROP = 900 units

Lead time = L = 7 days = 1 week

Reorder point = d1 * L + Z * *

900 = 700 * 1 + Z * 100 *

Z = 2

For Z = 2, Service level = 97.72%

Service level is the probability of not running out.

Hence, option 1 is correct and Option 2 is incorrect.

Critical ratio = = = 97.5%

Hence, option 3 is correct.

Since the critical ratio matches the service level for 900 units reorder point, Option 4 is correct.

Option 5 incorrect as 900 units satisfies 97.5% service level.

Answer:

Setting the reorder point at 900 units, or 2 standard deviations above the mean weekly demand, will give LL approximately a 97.5% probability of not running of inventory during the 7‐day supplier lead time.

The critical ratio is $156/($156+$4) = 0.975

Setting the reorder point at 900 units, or 2 standard deviations above the mean weekly demand, can be considered optimal.