Opperations Management Exam 2

Reorder Point = what?

(Order Lead time x Usage Rate) + Safety Stock

How to find average number of stockout per year?

(average number of orders per year) x (1-target service level %...exp .01)

How do you find the average inventory level?

(cycle stock+safety stock)

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. In the question above, what is the average time between stockouts, measured in years?

.25

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. Suppose in the scenario above (D = 20,000 units per year and Q = 250 units per order) our order point R is set to have a 99 % service level. Now what is the average number of stock-outs per year?

.8

Average time (years) between stockouts

1/average number of stockouts per year

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. If I was going to find the reorder point R needed to achieve 95% service level for this item, I would use _____ as the average demand during lead time

175 25 per day x 7 days

z-value for 99% service level

2.33

Demand during lead time is normally distributed with mean 𝜇μ = 100 and standard deviation 𝜎σ = 30. If I set my order point to R = 175, then my order point is how many standard deviations above the mean?

2.5 175 = 100 + z(30). Solve for z: z = (175 - 100) / 30 = 75 / 30 = 2.5 CHECK YOUR WORK: 100 + 2.5(30) = 175

Average demand during lead time is 50 units. I have set my reorder point to R = 70 units. How many units of safety stock am I carrying?

20 Safety stock is R - average demand during lead time = 70 - 50 = 20. On average you have used 50 of those 70 units so on average you have 20 units remaining when the order is received.

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. In the question above, what is the average number of stock-outs per year if my order point R is chosen to have a 95% service level?

4

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. If I was going to find the reorder point R needed to achieve 95% service level for this item, I would use _____ as the standard deviation of demand during lead time. (Round your answer to two decimal places.)

4 x 7‾√7= 10.58

Average demand during lead time is 50 units and I want to carry 15 units of safety stock. I need to set my order point to R =

65 50 + 15 = 65. On average you will use 50. You are planning to have more than that, so you are covered when demand is greater than average. You are "covered" up to 65 units demand during lead time. If demand during lead time is more than 65 units, you will have shortages.

Average demand during lead time is 50 units. I have set my reorder point to R = 70 units. This means I should order when my inventory position gets down to

70 R = 70. This means you order when your inventory position gets down to 70. Those 70 units will have to last you until the order is received.

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. Annual demand for an inventory item is 20,000 units per year. I order this item using an order quantity Q = 250 units per order. What is my average number of orders per year?

80

At the current demand rate, daily demand for an inventory item is normally distributed with mean = 25 units and standard deviation 4. We use this item 365 days per year, and the order lead time is 7 days (1 week) whenever we reorder to replenish our inventory. If I was going to determine the order quantity Q to use in a (Q, R) system for this item, my EOQ analysis would use D = ____________ units. {Assume you are going to use a yearly carrying cost H = $ per unit per year in your EOQ formula.}

9125 The EOQ model would need to convert the daily demand rate to an equivalent annualdemand rate (if the current daily rate lasted forever). 25 per day x 365 days = 9125 units per year. 25 per day x 250 days = 6250 units per year. Problem stated we use the item 365 days per year.

Equation for total cost

= S(D/Q) + H (Q/2).... (PxD)

The projected demand rate for an inventory item is 300 units per week, and we use the item 52 weeks per year We buy the item at a cost of $30 per unit. Our fixed ordering cost ("S") is $100 per order, and our annual carrying cost rate is 20% What is the Economic Order Quantity (EOQ) for this item?

EOQ = SQRT ( 2 ××15600 ××100 / 6) = SQRT(520,000) = 721.11 units per order Assuming we need to order some integer # of units, we can round to ordering 721 units per order. (In practice we may even round to a nice even 700, 725, or even 750. For the purpose of evaluating our solution we will use 721.)

What formula do you use to find Q?

EOQ Formula= given on exam

How do you find cycle stock?

Q/2

How do you find safety stock?

R-mue (mean)

If I set up my order point R to have a 95% service level, which of the following are true? (Select all that apply.)

There is a 95% chance (.95 probability) that demand during lead time will be less than or equal to R There is a 5% chance (.05 probability) that I will have inventory shortages before my order is received. P(Demand during lead time ≤≤ R) = .95 Each time I order, there is a 95% chance that having R units on hand when I place the order will be enough to last through the order lead time without having inventory shortages

Total Cost Equation & what its used for

To minimize total cost

If order lead time is 10 days and usage rate is 5 units per day, and you would like to have a safety stock of 25, the reorder point is

(10 x 5) + 25 = 75

The projected demand rate for an inventory item is 300 units per week, and we use the item 52 weeks per year We buy the item at a cost of $30 per unit. Our fixed ordering cost ("S") is $100 per order, and our annual carrying cost rate is 20% Using your answer to the question above, compute the total annual ordering cost (AOC) and total annual carrying cost (ACC) if we use the EOQ order quantity.

Using Q = 721: D/Q = 15,600 / 721 = 21.64 orders per year At a fixed ordering cost of $100 per order, total annual ordering cost (AOC) = 100 ××21.64 = $2164 per year Q/2 = 721/2 = 360.5 average cycle stock inventory level (# units) At a carrying cost of $6 per unit per year, total annual carrying cost (ACC) = 6 ××360.5 = $2163 per year When we use the exact EOQ, AOC is equal to ACC. Because we rounded our solution, AOC is approximately equal to ACC. It should also make sense that because we rounded the order quantity down (from 721.11 to 721), AOC is slightly larger than ACC.

H

carrying cost

What do you use to find R

mean (u) + z* stdev

D

mean units x days

How do you find mue?

mean x order lead time

S

ordering cost

How to find average numbers of orders per year?

ordering cost (S) x (D/Q)

How do you find the standard deviation?

stdev* (sqrt of order lead time)