# Chapter 11 (4) OPMA

The basic purpose of inventory analysis in manufacturing and stockkeeping services is to specify (1) when items should be ordered and (2) how large the order should be.

Holding (or carrying) costs. This broad category includes the costs for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital. Obviously, high holding costs tend to favor low inventory levels and frequent replenishment.

When the stock of an item is depleted, an order for that item must either wait until the stock is replenished or be canceled. There is a trade-off between carrying stock to satisfy demand and the costs resulting from stockout. This balance is sometimes difficult to obtain, because it may not be possible to estimate lost profits, the effects of lost customers, or lateness penalties.

Independent demand, the need for any one item is a direct result of the need for some other item, usually a higher-level item of which it is part.

Fixed-time period model has a larger average inventory because it must also protect against stockout during the review period, T; the fixed-order quantity model has no review period.

The fixed-order quantity model favors more expensive items because average inventory is lower.

The basic distinction is that fixed-order quantity models are “event triggered” and fixed-time period models are “time triggered.”

The basic distinction is that fixed-order quantity models are “event triggered” and fixed-time period models are “time triggered.”

Companies using the probability approach generally set the probability of not stocking out at 95 percent. This means we would carry about 1.64 standard deviations of safety stock.

The fixed-order quantity system focuses on order quantities and reorder points. Procedurally, each time a unit is taken out of stock, the withdrawal is logged and the amount remaining in inventory is immediately compared to the reorder point. If it has dropped to this point, an order for Q items is placed. If it has not, the system remains in an idle state until the next withdrawal.

Fixed-time period models generate order quantities that vary from period to period, depending on the usage rates. The standard fixed-time period models assume that inventory is counted only at the time specified for review

Fixed-time period models generate order quantities that vary from period to period, depending on the usage rates. These generally require a higher level of safety stock than a fixed-order quantity system.

The optimal stocking level, using marginal analysis, occurs at the point where the expected benefits derived from carrying the next unit are less than the expected costs for that unit.

The “sawtooth effect” relating Q and R in Exhibit 11.5 shows that when the inventory position drops to point R, a reorder is placed.

Price-break models deal with the fact that, generally, the selling price of an item varies with the order size.

Step 1. Sort the prices from lowest to highest and then, beginning with the lowest price, calculate the economic order quantity for each price level until a feasible economic order quantity is found. By feasible, we mean that the price is in the correct corresponding range.

Step 2. If the first feasible economic order quantity is for the lowest price, this quantity is best and you are finished. Otherwise, calculate the total cost for the first feasible economic order quantity (you did these from lowest to highest price) and also calculate the total cost at each price break lower than the price associated with the first feasible economic order quantity. This is the lowest order quantity at which you can take advantage of the price break. The optimal Q is the one with the lowest cost.

What accounts for the emergence of the direct-to-store model? Global sourcing and the upstream migration of value-added logistics services are certainly primary drivers.

The average cost of inventory in the United States is 30 to 35 percent of its value.

Savings from reduced inventory results in increased profit.

A. Raw materials

B. Finished products

C. Component parts

D. Just-in-time

E. Supplies

A. Economic Order Inventory

B. Work-in-process

C. Quality units

D. JIT Inventory

E. Re-order point

A. To maintain dependence of operations

B. To provide a feeling of security for the workforce

C. To meet variation in product demand

D. To hedge against wage increases

E. In case the supplier changes the design

A. To provide a safeguard for variation in raw material delivery time

B. To take advantage of economic purchase-order size

C. To maintain independence of operations

D. To meet variation in product demand

E. To keep the stock out of the hands of competitors

A. Phone calls

B. Taxes

C. Clerical

D. Calculating quantity to order

E. Postage

A. Normal variation in shipping time

B. A shortage of material at the vendor’s plant causing backlogs

C. An unexpected strike at the vendor’s plant

D. A lost order

E. Redundant ordering systems

When material is ordered from a vendor, delays can occur for a variety of reasons: a normal variation in shipping time, a shortage of material at the vendor’s plant causing backlogs, an unexpected strike at the vendor’s plant or at one of the shipping companies, a lost order, or a shipment of incorrect or defective material.

A. Annualized cost of materials

B. Handling

C. Insurance

D. Pilferage

E. Storage facilities

Holding costs include the costs for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital.

A. Order placing

B. Breakage

C. Typing up an order

D. Quantity discounts

E. Annualized cost of materials

Holding costs include the costs for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capital.

A. Holding costs

B. Setup costs

C. Ordering costs

D. Fixed costs

E. Shortage costs

In making any decision that affects inventory size, the following costs must be considered.

1. Holding (or carrying) costs.

2. Setup (or production change) costs.

3. Ordering costs.

4. Shortage costs.

A. Economic order quantity model

B. The ABC model

C. Periodic replenishment model

D. Cycle counting model

E. P model

A. The EOQ model

B. The least cost method

C. The Q model

D. Periodic system model

E. Just-in-time model

A. Fixed-time period

B. Fixed-order quantity

C. P model

D. First-in-first-out

E. The wheel of inventory

The fixed-order quantity model is a perpetual system, which requires that every time a withdrawal from inventory or an addition to inventory is made, records must be updated to reflect whether the reorder point has been reached.

A. Lead times are averaged

B. Ordering costs are variable

C. Price per unit of product is constant

D. Back orders are allowed

E. Stock-out costs are high

These assumptions are unrealistic, but they represent a starting point and allow us to use a simple example:

1. Demand for the product is constant and uniform throughout the period.

2. Lead time (time from ordering to receipt) is constant.

3. Price per unit of product is constant.

4. Inventory holding cost is based on average inventory.

5. Ordering or setup costs are constant.

6. All demands for the product will be satisfied. (No backorders are allowed.)

A. Ordering or setup costs are constant

B. Inventory holding cost is based on average inventory

C. Diminishing returns to scale of holding inventory

D. Lead time is constant

E. Demand for the product is uniform throughout the period

These assumptions are unrealistic, but they represent a starting point and allow us to use a simple example:

1. Demand for the product is constant and uniform throughout the period.

2. Lead time (time from ordering to receipt) is constant.

3. Price per unit of product is constant.

4. Inventory holding cost is based on average inventory.

5. Ordering or setup costs are constant.

6. All demands for the product will be satisfied. (No backorders are allowed.)

A. C

B. TC

C. H

D. Q

E. S

S = Setup cost or cost of placing an order

A. Annual purchasing cost, annual ordering cost, fixed cost

B. Annual holding cost, annual ordering cost, unit cost

C. Annual holding cost, annual ordering cost, annual purchasing cost

D. Annual lead time cost, annual holding cost, annual purchasing cost

E. Annual unit cost, annual set up cost, annual purchasing cost

Total Annual Cost = Annual Purchase Cost + Annual Ordering Cost + Annual Holding Cost.

A. 550

B. 500

C. 715

D. 450

E. 475

Fifty (50) times ten (10) equals 500.

A. 421

B. 234

C. 78

D. 26

E. 312

78 times 3 = 234

A. 576

B. 240

C. 120.4

D. 60.56

E. 56.03

240 = Square root of (2 x 12,000 x 6/2.5)

A. 909

B. 707

C. 634

D. 500

E. 141

Q = 707.1 = Square root of (2 x 50,000 x 25/5)

A. 5,060

B. 2,320

C. 2,133

D. 2,004

E. 1,866

Q = 2,320.5 = Square root of (2 x 35,000 x 50/0.65)

A. $849

B. $1,200

C. $1,889

D. $2,267

E. $2,400

1,200 = Square root of (2 x 36,000 x 80/4). Number of orders per year = 36,000/1,200 = 30 x $80 = $2,400

A. $1,501,600

B. $1,498,200

C. $500,687

D. $499,313

E. None of the above

Q = 400. Average Inventory = Q/2 = 200. Holding cost/year = $4. Thus, annual holding cost = $800. Annual set-up cost = 10,000/400 = 25 x $32 = 800. Demand x cost per unit = 10,000 x $150 = 1,500,000. Hence, TC = $1,500,000 + 800 + 800 = $1,501,600.

A. 120

B. 126

C. 630

D. 950

E. 1,200

Average demand is 120 + 125 + 124 + 128 + 133/5 = 126. Lead time = 5 days so the reorder point is 126 x 5 = 630.

A. 540

B. 270

C. 115

D. 90

E. 60

Average demand is 37 + 115 + 93 + 112 + 73 + 110/6 = 90. Lead time = 3 days so the reorder point is 90 x 3 = 270.

A. 1.28

B. 1.64

C. 1.96

D. 2.00

E. 2.18

Companies using this approach generally set the probability of not stocking out at 95 percent. This means we would carry about 1.64 standard deviations of safety stock,

A. The product of average daily demand times a standard deviation of lead time

B. A “z” value times the lead time in days

C. The standard deviation of vendor lead time times the standard deviation of demand

D. The product of lead time in days times the standard deviation of lead time

E. The product of the standard deviation of demand variability and a “z” score relating to a specific service probability.

A. Standard deviation of daily demand

B. Number of standard deviations for a specific service probability

C. Stockout cost

D. Economic order quantity

E. Safety stock level

A. 10

B. 20

C. 40

D. 100

E. 400

The standard deviation of usage during lead time is equal to the square root of the sums of the variances of the number of days of lead time. Since variance equals standard deviation squared, the standard deviation of usage during lead time is the square root of 4(10×10) = square root of 400 = 20.

A. 50

B. 100

C. 400

D. 1,000

E. 1,600

the standard deviation of usage during lead time will be the square root of (25 x (20 x 20)) = square root of 10,000 = 100

A. About 2.16

B. About 3.06

C. About 4.66

D. About 5.34

E. About 9.30

The standard deviation (Equation 11.6) of daily demand = Square root of (14/3) = 2.1602. This number squared is 4.6667. The square root of (2 (days) times 4.6667) = the square root of 9.3333 or 3.055.

A. About 6

B. About 16

C. About 61

D. About 66

E. About 79

(average daily demand times number of days of lead time) plus (standard deviation during lead time) times (desired Z score) =

(12 x 5) + (3 x 1.96) = 60 + 5.88 = 65.88 = 66 units

A. About 17.9

B. About 19.7

C. About 24.0

D. About 27.3

E. About 31.2

Desired z score for service probability coverage of 95% = 1.64. Equation 11.5 is (average daily demand times number of days of lead time) plus (standard deviation during lead time) times (desired z score) = (8 x 3) + (2 x 1.64) = 24 + 3.28 = 27.28 = about 27.3 units

A. Forecast average daily demand

B. Safety stock

C. Inventory currently on hand

D. Ordering cost

E. Lead time in days

It requires:

1. The number of days between reviews

2. Lead time in days (time between placing an order and receiving it)

3. Forecast average daily demand

4. Number of standard deviations for a specified service probability

5. Standard deviation of demand over the review and lead time

6. Current inventory level (includes items on order)

A. About 1,086

B. About 1,686

C. About 1,806

D. About 2,206

E. About 2,686

q = (200 x (5 + 4) + 1.96 x 3) – 120 =

1,800 + 5.88 – 120 = 1,685.88 = about 1,686

A. 863

B. 948

C. 1,044

D. 1,178

E. 4,510

q = 75 x (10 + 2) + (1.64 x 8) – 50 = 900 + 13.12 – 50 = 863.12 = 863

A. About 30.4

B. About 36.3

C. About 42.3

D. About 56.8

E. About 59.8

q = 15 x (3 + 1) + (2.05 x 6) – 30 = 60 + 12.3 – 30 = 42.3

A. About 27.7

B. About 32.8

C. About 35.8

D. About 39.9

E. About 45.0

The standard deviation of demand over the 12 days of time between reviews and lead time is the square root of (12 x 64) = 27.71

A. 25

B. 40

C. 50

D. 73

E. 100

the standard deviation of demand over the 25 days of time between reviews and lead time is the square root of (25 x 100) = 50

A. Greater than 0.357

B. Greater than 0.400

C. Greater than 0.556

D. Greater than 0.678

E. None of the above

P < = Cu/(Cu + Co) = 0.90/1.40 = 0.643. Since P is the probability that the unit will not be sold and 1 - P is the probability of it being sold, the answer to this question is 1 - 0.643 or 0.357.

A. Greater than 0.90

B. Greater than 0.85

C. Greater than 0.75

D. Greater than 0.25

E. None of the above

P < = Cu/(Cu + Co) = 120/480 = 0.25. Since P is the probability that the unit will not be sold and 1 - P is the probability of it being sold, the answer to this question is 1 - 0.25 or 0.75

A. EOQ

B. Fixed-time period

C. ABC classification

D. Fixed-order quantity

E. Single-period ordering system

A. A items get 15%, B items get 35%, and C items get 50%

B. A items get 15%, B items get 45%, and C items get 40%

C. A items get 25%, B items get 35%, and C items get 40%

D. A items get 25%, B items get 15%, and C items get 60%

E. A items get 20%, B items get 30%, and C items get 50%

The ABC approach divides this list into three groupings by value: A items constitute roughly the top 15 percent of the items, B items the next 35 percent, and C items the last 50 percent.

A. The “C” items are of moderate dollar volume

B. You should allocate about 50 % of the dollar volume to “B” items

C. The “A” items are of low dollar volume

D. The “A” items are of high dollar volume

E. Inexpensive and low usage items are classified as “C” no matter how critical

The ABC classification scheme divides inventory items into three groupings: high dollar volume (A), moderate dollar volume (B), and low dollar volume (C).

A. 1.64

B. 1.96

C. 2.05

D. 2.30

E. None of the above

Using the Excel function NORMSINV, the z score for a 98% service probability is 2.05.

A. When the record shows a near maximum balance on hand

B. When the record shows positive balance but a backorder was written

C. When quality problems have been discovered with the item

D. When the item has become obsolete

E. When the item has been misplaced in the stockroom

The computer can be programmed to produce a cycle count notice in the following cases:

1. When the record shows a low or zero balance on hand.

2. When the record shows a positive balance but a backorder was written

3. After some specified level of activity.

4. To signal a review based on the importance of the item (as in the ABC system)

In independent demand, the demands for various items are unrelated to each other.

Reorder point = Average daily demand x Lead time in days = 100 x 5 = 500

Q = square root of ((2 x demand x order cost)/holding cost) = Square root ((2 x 8,000 x 20)/12.50) = Square root (25,600) = 160

q = (300 x (5 + 4) + 1.96 x 12) – 1200 =

2,700 + 23.52 – 1200 = 1,524.52 = about 1,525

Q = square root of ((2 x demand x order cost)/holding cost) = Square root ((2 x 36,000 x 40)/45) = Square root (64,000) = 252.98. Dividing annual demand by Q, 36,000/252.98 = 142.3 orders per year x $40 per order = $5,692 ordering cost per year.

the answer is the square root of the sum of the variances which is the square root of 10 x (14 squared) or the square root of 1960 or 44.27.

1. To maintain independence of operations

2. To meet variation in product demand.

3. To allow flexibility in production scheduling.

4. To provide a safeguard for variation in raw material delivery time.

5. To take advantage of economic purchase order size.

1. Holding (or carrying) costs.

2. Setup (or production change) costs.

3. Ordering costs.

4. Shortage costs.

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