Operations and Supply Chain Management

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Week 4

Chapter 12

Inventory Management

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Learning Objectives

1 Conduct an A B C analysis

2 Explain and use cycle counting

3 Explain and use the E O Q model for independent inventory demand

4 Compute a reorder point and explain safety stock

5 Apply the production order quantity model

Inventory Management

The objective of inventory management is to strike a balance between inventory investment and customer service

Importance of Inventory

One of the most expensive assets of many companies representing as much as 50% of total invested capital

Less inventory lowers costs but increases chances of shortages, which might stop processes or result in dissatisfied customers

More inventory raises costs but improves the likelihood of meeting process and customer demands

Types of Inventory

Raw material

Purchased but not processed

Work-in-process (W I P)

Undergone some change but not completed

A function of flow time for a product

Maintenance/repair/operating (M R O)

Necessary to keep machinery and processes productive

Finished goods

Completed product awaiting shipment

The Material Flow Cycle

Managing Inventory

How inventory items can be classified (A B C analysis)

How accurate inventory records can be maintained

A B C Analysis (1 of 4)

Divides inventory into three classes based on annual dollar volume

Class A – high annual dollar volume

Items may represent 15% of the total items

Represent 70%-80% of the total dollar volume

Class B - medium annual dollar volume

Items may represent 30% of the total items

Represent 15%-25% of the total dollar volume

Class C - low annual dollar volume

Items may represent 55% of the total items

Represent 5% of the total dollar volume

ABC categories need not be exact.

Used to establish policies that focus on the few critical parts and not the many trivial ones

A B C Analysis (2 of 4)

Figure 12.2

Class A – 15% of the total items

70%-80% of the total dollar volume

Class B - 30% of the total items

15%-25% of the total dollar volume

Class C - 55% of the total items

5% of the total dollar volume

A B C Analysis (3 of 4)

A B C Analysis (4 of 4)

Other criteria than annual dollar volume may be used

High shortage or holding cost

Anticipated engineering changes

Delivery problems

Quality problems

Policies employed may include

More emphasis on supplier development for A items

Tighter physical inventory control for A items

More care in forecasting A items

Exercise

Your company has compiled the following data on the small set of products that comprise the specialty repair parts division.

Perform ABC analysis on the data.

Over which product do you suggest the firm keep the tightest control?

SKU	Annual Demand	Unit Cost
R11	125	$25
S22	55	$90
T33	100	$500
U44	150	$550
V55	2000	$4

Answer: D

A) R11

B) S22

C) T33

D) U44

E) V55

Exercise

Your company has compiled the following data on the small set of products that comprise the specialty repair parts division. Perform ABC analysis on the data. Over which products do you suggest the firm keep the tightest control? Explain.

SKU	Annual Demand	Unit Cost
R11	125	$25
S22	55	$90
T33	100	$800
U44	150	$150
V55	100	$45

Answer

T33 and U44 represent almost 90% of the firm's volume in this area.

T33 is classified A, U44 is classified B, and all others are C.

The tightest controls go to T33, then U44 because of their high percentage of sales volume.

SKU	Volume	Unit cost		Dollar volume	% Dollar volume	Cumulative $-vol %	Class
T33	100	$800		$80,000	69.52%	69.52%	A
U44	150	$150		$22,500	19.55%	89.07%	B
S22	55	$90		$4,950	4.30%	93.37%	C
V55	100	$45		$4,500	3.91%	97.28%	C
R11	125	$25		$3,125	2.72%	100.00%	C
			Total	$115,075

Group discussion: Have you once tried to use ABC analysis in your work or life?

Cycle Counting

Items are counted and records updated on a periodic basis

Often used with A B C analysis

Has several advantages

Eliminates shutdowns and interruptions

Eliminates annual inventory adjustment

Trained personnel audit inventory accuracy

Allows causes of errors to be identified and corrected

Maintains accurate inventory records

Cycle Counting Example

5,000 items in inventory

500 A items, 1,750 B items, 2,750 C items

ITEM CLASS	QUANTITY	CYCLE COUNTING POLICY	NUMBER OF ITEMS COUNTED PER DAY
A	500	Each month	500/20 = 25/day
B	1,750	Each quarter	1,750/60 = 29/day
C	2,750	Every 6 months	2,750/120 = 23/day
blank	blank	blank	77/day

Policy is to count

A items every month (20 working days),

B items every quarter (60 days), and

C items every six months (120 days)

Control of Service Inventories

Can be a critical component of profitability

Losses may come from shrinkage or pilferage

Applicable techniques include

Good personnel selection, training, and discipline

Tight control of incoming shipments

Effective control of all goods leaving facility

Inventory Models

Independent demand - the demand for item is independent of the demand for any other item in inventory

Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory

Holding costs - the costs of holding or “carrying” inventory over time

Ordering cost - the costs of placing an order and receiving goods

Setup cost - cost to prepare a machine or process for manufacturing an order

May be highly correlated with setup time

Holding Costs (1 of 2)

Determining Inventory Holding Costs

CATEGORY	Cost (and range) as a percentage of inventory value
Housing costs (building rent or depreciation, operating costs, taxes, insurance)	6% (3 - 10%)
Material handling costs (equipment lease or depreciation, power, operating cost)	3% (1 - 3.5%)
Labor cost (receiving, warehousing, security)	3% (3 - 5%)
Investment costs (borrowing costs, taxes, and insurance on inventory)	11% (6 - 24%)
Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like tablets and smart phones)	3% (2 - 5%)
Overall carrying cost	26%

Holding Costs (2 of 2)

Determining Inventory Holding Costs

CATEGORY	COST (AND RANGE) AS A PERCENTAGE OF INVENTORY VALUE
Housing costs (building rent or depreciation, operating costs, taxes, insurance)	6% (3 - 10%)
Material handling costs (equipment lease or depreciation, power, operating cost)	3% (1 - 3.5%)
Labor cost (receiving, warehousing, security)	3% (3 - 5%)
Investment costs (borrowing costs, taxes, and insurance on inventory)	11% (6 - 24%)
Pilferage, space, and obsolescence (much higher in industries undergoing rapid change like tablets and smart phones)	3% (2 - 5%)
Overall carrying cost	26%

Holding costs vary considerably depending on the business, location, and interest rates. Generally greater than 15%, some high tech and fashion items have holding costs greater than 40%.

Inventory Models for Independent Demand

Need to determine when and how much to order

Basic economic order quantity (E O Q) model

Production order quantity model

Quantity discount model

Important assumptions

Demand is known, constant, and independent

Lead time is known and constant

Receipt of inventory is instantaneous and complete

Quantity discounts are not possible

Only variable costs are setup (or ordering) and holding

Stockouts can be completely avoided

Basic E O Q Model

Inventory Usage Over Time

Minimizing Costs

Objective is to minimize total costs

Minimizing Costs (annual setup cost)

Q = Number of pieces per order

Q* = Optimal number of pieces per order (E O Q)

D = Annual demand in units for the inventory item

S = Setup or ordering cost for each order

H = Holding or carrying cost per unit per year

Minimizing Costs (annual holding cost)

Q = Number of pieces per order

Q* = Optimal number of pieces per order (E O Q)

D = Annual demand in units for the inventory item

S = Setup or ordering cost for each order

H = Holding or carrying cost per unit per year

Minimizing Costs (Economic order quantity)

Q = Number of pieces per order

Q* = Optimal number of pieces per order (EOQ)

D = Annual demand in units for the inventory item

S = Setup or ordering cost for each order

H = Holding or carrying cost per unit per year

Optimal order quantity is found when annual setup cost equals annual holding cost

Solving for Q*

E O Q-Determine optimal number of order

D = 1,000 units

S = $10 per order

H = $.50 per unit per year

E O Q –Determine expected number of orders

D = 1,000 units Q* = 200 units

S = $10 per order

H = $.50 per unit per year

EOQ—Determine optimal time between orders

D = 1,000 units Q* = 200 units

S = $10 per order N = 5 orders/year

H = $.50 per unit per year

E O Q—Determine the total annual cost

D = 1,000 units Q* = 200 units

S = $10 per order N = 5 orders/year

H = $.50 per unit per year T = 50 days

The E O Q Model

When including actual cost of material P

Robust Model

The E O Q model is robust

It works even if all parameters and assumptions are not met

The total cost curve is relatively flat in the area of the E O Q

E O Q model is robust

Only 2% less than the total cost of $125 when the order quantity was 200

Ordering old Q*

Ordering new Q*

If the demand is actually 1500 units rather than 1000 units, but EOQ of 200 is still used, how about TC?

Exercise

If Demand remains at 1000, Holding cost per unit per year is still $0.5. We order 200 needles at a time.

If the true order cost=$15 (rather than $10), what is the annual cost?

Reorder Points

E O Q answers the “how much” question

The reorder point (R O P) tells “when” to order

Lead time (L) is the time between placing and receiving an order

Reorder Point Curve

Reorder Point Example

Demand = 8,000 iPhones per year

250 working day year

Lead time for orders is 3 working days, may take 4

Production Order Quantity Model (1 of 5)

Used when inventory builds up over a period of time after an order is placed

Used when units are produced and sold simultaneously

Production Order Quantity Model (2 of 5)

Q = Number of units per order p = Daily production rate

H = Holding cost per unit per year d = Daily demand (usage) rate

t = Length of the production run in days

Production Order Quantity Model (3 of 5)

Q = Number of units per order p = Daily production rate

H = Holding cost per unit per year d = Daily demand (usage) rate

t = Length of the production run in days

However, Q = total produced = pt ; thus t = Q/p

Production Order Quantity Model (4 of 5)

Q = Number of units per order p = Daily production rate

H = Holding cost per unit per year d = Daily demand (usage) rate

t = Length of the production run in days

Comparing with

Production Order Quantity Example

D = 1,000 units p = 8 units per day

S = $10 d = 4 units per day

H = $0.50 per unit per year

Production Order Quantity Model (5 of 5)

Note:

When annual data are used the equation becomes:

Exercise

For a certain item, the cost-minimizing order quantity obtained with the basic EOQ model is 200 units, and the total annual inventory (carrying and setup) cost is $400. What is the inventory carrying cost per unit per year for this item?

A product has a demand of 4000 units per year. Ordering cost is $20, and holding cost is $4 per unit per year. The EOQ model is appropriate. The cost-minimizing solution for this product will cost ________ per year in total annual inventory (holding and setup) costs.

The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, setup cost is $50, holding cost is $12 per unit per year, the daily demand rate is 20 and the daily production rate is 100. What is the production order quantity for this problem?

A production order quantity problem has a daily demand rate = 10 and a daily production rate = 50. The production order quantity for this problem is approximately 750 units. What is the average inventory for this problem?

Answers:

1. $2. 2. $800. 3. 195 4. 300

Questions?

Quantity Discount Models (1 of 5)

Reduced prices are often available when larger quantities are purchased

Trade-off is between reduced product cost and increased holding cost

Table 12.2 A Quantity Discount Schedule

Price range	Quantity ordered	Price per unit p
Initial price	0 to 119	$ 100
Discount price 1	120 to 1,499	$ 98
Discount price 2	1,500 and over	$ 96

Quantity Discount Models (2 of 5)

where Q = Quantity ordered P = Price per unit

D = Annual demand in units I = Holding cost per unit per year

S = Ordering or setup cost per order expressed as a percent of price P

Because unit price varies, holding cost is expressed as a percentage (I) of unit price (P)

Quantity Discount Models (3 of 5)

Steps in analyzing a quantity discount

Starting with the lowest possible purchase price, calculate Q* until the first feasible E O Q is found. This is a possible best order quantity, along with all price-break quantities for all lower prices.

Calculate the total annual cost for each possible order quantity determined in Step 1. Select the quantity that gives the lowest total cost.

Quantity Discount Models (4 of 5)

Figure 12.7

Quantity Discount Models (5 of 5)

Calculate Q* for every discount starting with the lowest price

Infeasible – calculate Q* for next-higher price

Feasible

Quantity Discount Example

Table 12.3 Total Cost Computations for Chris Beehner Electronics

Choose the price and quantity that gives the lowest total cost

Buy 275 drones at $98 per unit

Quantity Discount Variations

All-units discount is the most popular form

Incremental quantity discounts apply only to those units purchased beyond the price break quantity

Fixed fees may encourage larger purchases

Aggregation over items or time

Truckload discounts, buy-one-get-one-free offers, one-time-only sales

Probabilistic Models and Safety Stock

Used when demand is not constant or certain

Use safety stock to achieve a desired service level and avoid stockouts

Annual stockout costs = The sum of the units short for each demand level × The probability of that demand level × The stockout cost/unit × The number of orders per year

Safety Stock Example (1 of 2)

ROP = 50 units Stockout cost = $40 per frame

Orders per year = 6 Carrying cost = $5 per frame per year

NUMBER OF UNITS	PROBABILITY
30	.2
40	.2
ROP  50	.3
60	.2
70	.1
blank	1.0

Safety Stock Example (2 of 2)

ROP = 50 units Stockout cost = $40 per frame

Orders per year = 6 Carrying cost = $5 per frame per year

A safety stock of 20 frames gives the lowest total cost

ROP = 50 + 20 = 70 frames

Probabilistic Demand (1 of 3)

Probabilistic Demand (2 of 3)

Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined

where

Probabilistic Demand (3 of 3)

Probabilistic Example (1 of 3)

μ = Average demand = 350 kits

σdLT = Standard deviation of demand during lead time = 10 kits

Stockout policy = 5% (service level = 95%)

Using Appendix I, for an area under the curve of 95%, the Z = 1.645

Safety stock = ZσdLT = 1.645(10) = 16.5 kits

Reorder point = Expected demand during lead time + Safety stock

= 350 kits + 16.5 kits of safety stock

= 366.5 or 367 kits

Other Probabilistic Models (1 of 4)

When data on demand during lead time are not available, there are other models available

When demand is variable and lead time is constant

When lead time is variable and demand is constant

When both demand and lead time are variable

Other Probabilistic Models (2 of 4)

Demand is variable and lead time is constant

where

Probabilistic Example (2 of 3)

Average daily demand (normally distributed) = 15

Lead time in days (constant) = 2

Standard deviation of daily demand = 5

Service level = 90%

Z for 90% = 1.28

From Appendix I

Safety stock is about 9 computers

Other Probabilistic Models (3 of 4)

Lead time is variable and demand is constant

where

Probabilistic Example (3 of 3)

Daily demand (constant) = 10

Average lead time = 6 days

Standard deviation of lead time = σLT = 1

Service level = 98%, so Z (from Appendix I) = 2.055

Reorder point is about 81 cameras

Other Probabilistic Models (4 of 4)

Both demand and lead time are variable

where

Probabilistic Example

Average daily demand (normally distributed) = 150

Standard deviation = σd = 16

Average lead time 5 days (normally distributed)

Standard deviation = σLT = 1 day

Service level = 95%, so Z = 1.645 (from Appendix I)

Single-Period Model

Only one order is placed for a product

Units have little or no value at the end of the sales period

Single-Period Example (1 of 2)

Average demand = μ = 120 papers/day

Standard deviation = σ = 15 papers

Cs = cost of shortage = $1.25 − $.70 = $.55

Co = cost of overage = $.70 − $.30 = $.40

Single-Period Example (2 of 2)

From Appendix I, for the area .579, Z ≅ .199

The optimal stocking level

= 120 copies + (.199)(σ)

= 120 + (.199)(15) = 120 + 3 = 123 papers

The stockout risk = 1 − Service level

= 1 − .579 = .421 = 42.1%

Fixed-Period (P) Systems (1 of 3)

Fixed-quantity models require continuous monitoring using perpetual inventory systems

In fixed-period systems orders placed at the end of a fixed period

Periodic review, P system

Fixed-Period (P) Systems (2 of 3)

Inventory counted only at end of period

Order brings inventory up to target level

Only relevant costs are ordering and holding

Lead times are known and constant

Items are independent of one another

Fixed-Period (P) Systems (3 of 3)

Figure 12.9

Fixed-Period Systems

Inventory is only counted at each review period

May be scheduled at convenient times

Appropriate in routine situations

May result in stockouts between periods

May require increased safety stock

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