Question

1. Consider the basic EOQ model (no uncertainty). Optimal order quantity (Q ∗) is 1,800 units. What is the average inventory level (I ∗)?

a. 900 units

b. 1,800 units

c. 600 units

d. 1,000 units

e. 3,600 units

2. Consider the basic EOQ model (no uncertainty). Annual holding cost (AHC) is $2,400. Find annual ordering cost (AOC).

a. Cannot be answered because there is missing information

b. AOC=$0, since there is no uncertainty

c. $1,200, since AOC=AHC/2 at economic order quantity.

d. $4,800, since AOC=2 x AHC at economic order quantity

e. AOC=$2,400, since AHC=AOC at the economic order quantity

3. Consider the basic EOQ model (no uncertainty). Optimal number of orders per year (N ∗) is 4. Find optimal cycle time (time between orders),  T ∗, in weeks.

a. 13 weeks

b. Cannot be answered because there is missing information

c. 4 weeks

d. 8 weeks

e. 0.25 weeks

4. An online retail store sells robotic vacuum cleaners. Average demand per day (d ¯) is 120 units, with a std. dev. of (σ d) 40 units. Lead time (L T) is 9 days (constant). Find demand during lead time (D D L), safety stock (S S) and reorder point (R O P) for z = 3.

a. DDL=900 units, SS=1,440 units, ROP=360 units

b. Cannot be answered because there is missing information

c. DDL=500 units, SS=350 units, ROP=850 units

d. DDL=1,440 units, SS=360 units, ROP=1,080 units

e. DDL=1,080 units, SS=360 units, ROP=1,440 units

Answer 1

Question 1: Consider the basic EOQ model (no uncertainty). Optimal order quantity (Q ∗) is 1,800 units. What is the average inventory level (I ∗)?

Answer: 900 units

Explanation:

Average Inventory Level (I), is given by:

Average inventory = Q* / 2

Average Inventory Level (I) = 1800 / 2 = 900

Question 2: Consider the basic EOQ model (no uncertainty). Annual holding cost (AHC) is $2,400. Find annual ordering cost (AOC).

Answer: Cannot be answered because there is missing information

Explanation:

Annual Ordering Cost is given by:

Annual Ordering Cost = (D x S) / EOQ

Here:

Annual Demand (D), EOQ, and Order Cost (S) are not provided, hence the Annual Ordering Cost (AOC) cannot be computed.

Question 3: Consider the basic EOQ model (no uncertainty). Optimal number of orders per year (N ∗) is 4. Find optimal cycle time (time between orders), T ∗, in weeks.

Answer: Cannot be answered because there is missing information

Explanation:

Time Between Orders (TBO) is given by:

TBO = EOQ / Annual Demand (D)

(or)

TBO = Number of working days / Number of orders per year

Here:

EOQ, Number of working days, and Annual Demand are not provided, hence Time Between Orders (TBO) cannot be computed.

Question 4: An online retail store sells robotic vacuum cleaners. Average demand per day (d ¯) is 120 units, with a std. dev. of (σ d) 40 units. Lead time (L T) is 9 days (constant). Find demand during lead time (D D L), safety stock (S S) and reorder point (R O P) for z = 3.

Answer: DDL=1,080 units, SS=360 units, ROP=1,440 units

Explanation:

Given that:

• Average Demand(d) = 120
• Std. Dev(σd) = 40
• Lead Time (Lt) = 9
• Service Level (Z) = 3

Now:

Demand during Leadtime is given by:

Demand during Lead Time (DDL) = d x Lt

Demand during Lead Time (DDL) = 120 x 9 = 1080 units

Now:

Safety Stock is given by:

Safety Stock (SS) = Z x σd x Sqrt(Lt)

Safety Stock (SS) = 3 x 40 x Sqrt(9) = 360 units

Now:

Reorder Point is given by

Reorder Point (ROP) = d x Lt + SS

Reorder Point (ROP) = 120 x 9 + 360 = 1440 units