Managing Inventory throughout the Supply Chain

Chapter ObjectivesBe able to: Describe the various roles of inventory, including the different types of

inventory and inventory drivers. Distinguish between independent demand and dependent demand

inventory. Calculate the restocking level for a periodic review system. Calculate the economic order quantity (EOQ) and reorder point (ROP) for

a continuous review system. Determine the best order quantity when volume discounts are available. Calculate the target service level and target stocking point for a single-

period inventory system. Describe how inventory decisions affect other areas of the supply chain.

In particular, be able to describe the bullwhip effect, inventory positioning issues, and the impact of transportation, packaging, and material handling considerations.

Inventory Management

• Functions, forms, and drivers of inventory

• Inventory cost issues

• Tools:Economic order quantity (EOQ)Reorder point (ROP) and safety

stock Dealing with quantity discounts

Types of Inventory

• Cycle stock• Safety stock (buffer inventory)• Anticipation inventory• Others

– Hedge inventories– Transportation inventory (pipeline)– Smoothing inventories

Four Inventory Drivers

1. Demand and Supply Uncertainties Safety stock, hedge inventory

2. Demand and Process Volume Mismatches Cycle stock

3. Demand and Capacity Mismatches Smoothing inventory

4. Demand and Supply Lead-Time Mismatches Anticipation inventory, transportation inventory

Independent Demand

• Demand from outside the organization• Unpredictable usually forecasted

Demand for tables . . .

Dependent Demand

• Tied to the production of another item• Relevant mostly to manufacturers

Once we decide how many tables we want tomake, how many legs do we need?

Two “Classic” Systems for Independent Demand Items

• Periodic review systems

• Continuous (perpetual) review systems

Factors– Order quantity (Q) – Restocking level (R)– Inventory level when reviewed (I)

Restocking Levels

• Periodic Review

• Continuous Review

LRPLRP zR

dLR

Periodic Review System(Orders at regular intervals)

Inventorylevel

Time2 4 6

Continuous Review System(Orders when inventory drops to R)

L-T

Q

R

How is the reorder point ROP established?

Inventorylevel

Timelead time to get a new order in

Comparison of Periodic and Continuous Review Systems

Periodic Review• Fixed order intervals• Variable order sizes• Convenient to administer• Orders may be combined• Inventory position only

required at review

Continuous Review• Varying order intervals• Fixed order sizes (Q)• Allows individual review

frequencies• Possible quantity discounts• Lower, less-expensive safety

stocks

Order Quantity Q and Average Inventory Level

As the order quantity doublesso does the average inventory (= Q/2)

Q1

Q2

Q22

Q12

What is the “Best” Order Size Q?

Determined by:• Inventory related costs

– Order preparation costs and setup costs– Inventory carrying costs– Shortage and customer service costs

• Other considerations– Out of pocket or opportunity cost?– Fixed, variable, or some mix of the two?

Economic Order Quantity (EOQ) Model

• Cost Minimizing “Q”

• Assumptions:Uniform and known demand rate

Fixed item cost

Fixed ordering cost

Constant lead time

What are the Total Relevant Annual Inventory Costs?

Consider:D = Total demand for the yearS = Cost to place a single orderH = Cost to hold one unit in inventory for a yearQ = Order quantity

Then: Total Cost = Annual Holding Cost + Annual Ordering Cost

= [(Q/2) × H] + [(D/Q) × S]

How do these costs vary as Q varies?Why isn’t item cost for the year included?

Holding Cost

$

Q

Holding cost increasesas Q increases . . .

(Q/2)×H

Ordering Costs

$

Q

Ordering costs per yeardecrease as Q increases

(why?)(Q/2)×H

(D/Q)×S

Total Annual Costs and EOQ

0

500

1000

1500

2000

10 50 90 130

170

210

250

290

330

370

410

Order Quantity Q

Inve

ntor

y Co

st ($

)

Holding Cost Ordering Cost Total Cost

EOQ at minimum total cost

EOQ Solution

HDSQEOQ 2*

When the order quantity = EOQ, the holding and setup costs are equal

Sample Problems• Pam runs a mail-order business for gym equipment.

Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit is $2.50 and the cost to place an order is $50. What is the economic order quantity?

• Using the same holding and ordering costs as above, suppose demand for TricoFlexers doubles to 32,000. Does the EOQ also double? Explain what happens.

EOQ tells us how much to order...

…but when should we order?

Reorder point and safety stock analysis

Safety Stock

When both lead time and demand are constant, you know exactly when your reorder point is ...

Q

L

R

Safety Stock II Under these assumptions:

Reorder point = total demand during the lead time between placement of the order and its receipt.

ROP = d × L, where

d = demand per unit time, and

L = lead time in the same time units

Safety Stock III(Uncertainties)

But what happens when either demand or lead time varies?

Q

L1

R

L2

Safety Stock IV

What causesthis variance?

Average demandduring lead time Ld

Uncertainty Drivers

1) The variability of demand2) The variability of lead time3) The average length of lead time4) The desired service level

2) and 3) are determined by a company’s choice of supply chain partners

Safety Stock

• Additional inventory beyond amount needed to meet “average” demand during lead time

• Protects against uncertainties in demand or lead time

• Balances the costs of stockouts against the cost of holding extra inventory

Shown Graphically …

Now, what is thechance of a stockout?

93%

SSLd

7%

Recalculating the Reorder Point to include Safety Stock

timeleadduringdemandaveragetheabovedeviationsdardtansofnumberz

timeleadofvarianceperiodtimeduringdemandofvariance

timeleadaverageLperiodtimeperdemandaveraged

wheredLzLdSSLdROP

L

d

Ld

2

2

222

:

Determining “z”

z = number of standard deviations above the average demand during lead time

The higher z is: The lower the risk of stocking out The higher the average inventory level

What is the average inventory level when we include safety stock?

Determining “z”

Typical choices for z: z

= 1.28 90% service level z = 1.65 95% service level z = 2.33 99% service level

What do we mean by “service level”?

Reorder Point + Safety Stock Formula:

What happens if lead time is constant? What happens if the demand rate is constant? What happens if both are constant? If you wanted to reduce the amount of safety stock

you hold, what is your best option?

222Ld dLzLdROP

Problems IOne of the products stocked by Sam’s Club is SamsCola.

During the slow season, the demand rate is approximately 650 cases a month, which is the same as a yearly demand rate of 650×12 = 7,800 cases.

During the busy season, the demand rate is approximately 1,300 cases a month, or 15,600 cases a year.

The cost to place an order is $5, and the yearly holding cost for a case of SamsCola is $12.

Problems II

According to the EOQ formula: How many cases of SamsCola should be

ordered at a time during the slow season? How many cases of SamsCola should be

ordered during the busy season?

Problems IIIDuring the busy season, the store manager has decided

that 98 percent of the time, he does not want to run out of SamsCola before the next order arrives. Use the following data to calculate the reorder point for SamsCola.

• Weekly demand during the busy season: 325 cases per week• Lead-time: 0.5 weeks• Standard deviation of weekly demand: 5.25• Standard deviation of lead-time: 0 (lead-time is

constant)• Number of standard deviations above the

mean needed to provide a 98% service level (z): 2.05

Quantity Discounts IWhat effect will quantity discounts have on EOQ?

D = 1,200 units (100×12 months)H = $10 per unit per yearS = $30.00 ordering cost

Order Size Price0 - 89 $35.0090 and up $32.50

Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way.

Quantity Discounts II

1. Calculate the EOQ for the non discount price:

2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...

8510$

30$12002 EOQ

Quantity Discounts III

Compare total holding, carrying, AND item cost for the year at: Each price break

The first feasible EOQ quantity

Do you understand why we must now look at item cost for the year?

Quantity Discounts IV

Total costs at an order quantity of 85:

(85/2)×$10 + (1200/85)×$30 + 1200×$35.00 =

$425 + $423.53 + $42,000 = ??

Total costs at an order quantity of 90:

(90/2)×$10 + (1200/90)×$30 + 1200×$32.50 =

$450 + $400 + $39,000 = ??

Conclusions:• When all costs are considered, it is cheaper to

order 90 at a time and take the price discount.

• When there are volume discounts, the EOQ calculation might be infeasible or might not result in lowest total cost.

• If holding cost is a percentage of the item value (a common practice for more expensive items), analysis is more complex, but done the same way

Single-Period Inventory(When safety stock is not an option)

• Inventory is perishable– Newspapers, periodicals– Fresh food, Christmas trees

• Must balance costs of – Being short = profit lost– Having excess = item cost + disposal cost – salvage value

• Requires a target service level that best balances shortage and excess costs

Target Service Level

Sets expected shortage cost = expected excess cost

Or (1–p) × Cshortage = p × Cexcess

Where p = probability of enough units to meet demand, (1–p) = probability of shortage

Hence solving for p where the top equation is true provides the target service level

SLT = Cshortage / (Cshortage + Cexcess)

Target Stocking Point

• Must know how demand is distributed– Is it roughly the same every day?– Are there different demand distributions?

• In all cases, develop the cumulative probability distribution for the demand levels in order of increasing demand and select demand level whose corresponding cumulative probability is nearest to the target service level.

Text Example for SLT = 65%

Inventory in the Supply Chain

• Bullwhip Effect– Small demand changes large order variations

• Inventory Positioning– Cost and value increases, flexibility decreases down the supply

chain where do we hold inventory?

• Transportation, Packaging, Material Handling– Physical size and quantity of lot, how it is packaged, handling

equipment needed,and disposal of packaging are all factors in choosing appropriate supplier and distribution process

Demand versus Order Size(Bullwhip Effect)

Case Study in Inventory Management

Northcutt Bikes: The Service Department

SupplementABC Classification Method

IDEA

Companies have thousands of items to track

Methods like EOQ only justifiable for most important items.

ABC Method

1. Determine annual $ usage for each item

2. Rank the items according to their annual $ usage

3. Let:

Top 20% “A” items roughly 80% of total $

Middle 30% “B” items roughly 15% of total $

Bottom “50% “C” item roughly 5% of total $

ABC Analysis Example

Total $ Usage = $98,500

Item Cost Demand $ UsageA1 $46 200 $9,200

B2 $40 10 $400

C3 $5 6680 $33,400

D4 $81 100 $8,100

E5 $22 50 $1,100

F6 $6 100 $600

G7 $176 250 $44,000

H8 $6 150 $900

I9 $10 10 $100

J10 $14 50 $700

Ranking by Annual $ Usage

Item $ UsageCumulative $

Usage% of Total $

Usage ClassG7 $44,000 $44,000 44.67% A

C3 $33,400 $77,400 78.58% A

A1 $9,200 $86,600 87.92% B

D4 $8,100 $94,700 96.14% B

E5 $1,100 $95,800 97.26% B

H8 $900 $96,700 98.17% C

J10 $700 $97,400 98.88% C

F6 $600 $98,000 99.49% C

B2 $400 $98,400 99.90% C

I9 $100 $98,500 100.00% C