inventory management: cycle inventory-ii 【本著作除另有註明外，採取創用 cc...

Inventory Management: Cycle Inventory-II

Inventory Management: Cycle Inventory-II

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第五單元： Inventory Management: Cycle Inventory-II

郭瑞祥教授

1

http://creativecommons.org/licenses/by-nc-sa/3.0/tw/



http://get.nccu.edu.tw:8080/getcdb/handle/getcdb/127023



Lessons From Aggregation

Aggregation allows firm to lower lot size without increasing cost

Tailored aggregation is effective if product specific fixed cost is a large fraction of joint fixed cost

Complete aggregation is effective if product specific fixed cost is a

small fraction of joint fixed cost

2

Holding Cycle Inventory for Economies of Scale


► Fixed costs associated with lots

► Quantity discounts

► Trade Promotions

3

Quantity Discounts

► Lot size based

► Volume based

How should buyer react? How does this decision affect the supply chain

in terms of lot sizes, cycle inventory, and flow time?

What are appropriate discounting schemes that suppliers should offer?

》Based on total quantity purchased over a given period

》Based on the quantity ordered in a single lot

Total Material Cost

C0

C1

C2

q1 q2 q3

Average Cost per Unit

Quantity Purchased Order Quantityq1 q2 q3

> All units> Marginal unit

4

Evaluate EOQ for price in range qi to qi+1 ,

》Case 1:If qi Qi < qi+1 , evaluate cost of ordering Qi

》Case 2:If Qi < qi, evaluate cost of ordering qi

》Case 3:If Qi qi+1 , evaluate cost of ordering qi+1

Choose the lot size that minimizes the total cost over all price ranges.

Evaluate EOQ for All Unit Quantity Discounts

hCi

DSQi

2

DCihCiQiSD

TCi

2Qi

DCi+1hCiSD

TCi

qi+12

qi+1

DCihCiqiSD

TCi

2qi

5

Marginal Unit Quantity Discounts

C0

C1

C2

q1 q2 q3

Marginal Cost per Unit

Quantity Purchased Order Quantity

q1 q2 q3

Total Material Cost

If an order of size q is placed, the first q1-q0 units are priced at C0, the next q2-q1 are priced at C1, and so on.

6

Optimal lot size

2D(S+Vi-qiCi)

hCi

Qi=

► Evaluate EOQ for each marginal price Ci (or lot size between qi and qi+1)

Evaluate EOQ for Marginal Unit Discounts

》 Let Vi be the cost of order qi units. Define V0 = 0 and

Vi=C0(q1-q0)+C1(q2-q1)+ +C‧‧‧ i-1(qi-qi-1)

》 Consider an order size Q in the range qi to qi+1

Total annual cost = ( D/Q )S (Annual order cost)

+[Vi+(Q-qi)Ci] h/2 (Annual holding cost)

+ ( D/Q ) [Vi+(Q-qi)Ci] (Annual material cost)

7

》 Evaluate EOQ for each marginal price Ci

– Case 1 :If qi Qi < qi+1 , calculate cost of ordering Qi

– Case 2 and 3 : If Qi < qi or Qi > qi+1 , the lot size in this range

is either qi or qi+1 depending on which has the lower total cost

》 Choose the lot size that minimizes the total cost over all price ranges.

Evaluate EOQ for Marginal Unit Discounts

2D(S+Vi-qiCi)

hCi

Qi=► Evaluate EOQ for each marginal price Ci,

DSD

TCi+[ Vi+(Qi-qi)Ci] + [ Vi+(Qi-qi)Ci]

QiQi

h2

11

11 2

,2

Min ii

ii

ii

ii

i Vq

DhVS

q

DV

q

DhVS

q

DTC

8

The Comparison between All Unit and Marginal Unit Quantity

Discounts

The order quantity of all unit quantity discounts is less than the order quantity of marginal unit quantity discounts.

The marginal unit quantity discounts will further enlarge the cycle inventory and average flow time.

9

► Coordination: max total profits of suppliers and retailers

Why Quantity Discounts?

► Quantity discounts are valuable only if they result in:

► Coordination in the supply chain

► Use price discrimination to max supplier’s profits》Quantity discounts for commodity products (in the perfect competition market, price is fixed)

》Quantity discounts for products for which the firm has market power (in the oligopoly market, the determined price can influence demand)

》 Improved coordination in the supply chain

》 Extraction of surplus through price discrimination

>Two-part tariffs > Volume discounts

10

► Assume the following data.– Retailer: D =120,000/year , SR=$100 , hR=0.2 , CR=$3– Suplier: SS =$250 , hS =0.2 , CS =$2

► Retailer cost

► Supplier’s cost is based on retailer’s optimal order size.

》Supply chain total cost = 3,795+6,009=$9,804

Coordination for Commodity Products

6,32430.2

100120,0002Q *

xxx

$3,79530.22

6,3246,324

120,000100TC xxx

$6,00920.22

6,3246,324

120,000250TC xxx

11


► Consider a coordinated order size=9,165.

► Coordination through all unit quantity discounts.

– $3 for lots below 9,165

$2.9978 for lots of 9,165 or higher– Increase in retailer’s holding cost and order cost can be compensated

by the reduction in material cost. 120,000(3-2.9978)=$264– Decrease in supplier’s cost = supply chain savings = 903–264=$639

(can be further shared between two parties)

》Supply chain total cost=4,059+5,106 =$9,165(decreased by $639)

29,165

9,165120,000Suppler's TC=250x + x0.2x2 =$5,106

29,165

9,165120,000Suppler's TC=100x + x0.2x3 =$4,059 (Increased by $264)

$3,795

(decreased by $903)

$6,009

12


Since the price is determined by the market, supplier can use lot-

size based quantity discounts to achieve coordination in supply

chain and decrease supply chain cost.

In practice, the cycle inventory does not decrease in the supply

chain because in most firms, marketing and sales department

design quantity discounts independent of operations department

who works on reducing the order cost.

In theory, if supplier reduces its setup or order cost, the discount it

offers will change and the cycle inventory is expected to decrease.

Lot size-based quantity discounts will increase cycle inventory.

13

Quantity Discounts When Firm has Market Power

RetailerSupplierpCRCS =$2

Demand=360,000-60,000p

► No inventory related costs.

► Assume the following data

Demand curve = 360,000-60,000p (p is retailer’s sale price)

CS = $2 (cost of supplier).

► Need to determine CR (Suppler’s charge on retailer) and p.

14

► Maximize individual profits and make pricing decision independently

► Demand = 360,000-60,000(5)=60,000

Profit for retailer = (5-4)(60,000)=$60,000

Profit for supplier = (4-2)(60,000)=$120,000

Profit for supply chain = 60,000+120,000=$180,000

RetailerSupplierpCRCS =$2

Demand=360,000-60,000p

Scenario 1: No Coordination

ProfitR

CR=4; p=5

2

CRp

=(p-CR)

0p

(ProfitR)

0CR

(ProfitS)

ProfitS=

(360,000-60,000p)

2

CR=(CR-2)[360,000-60,000( 3+ )](CR-2)(360,000-60,000p)

15

Quantity Discounts When Firm has Market Power

Demand=360,000-60,000p

► No inventory related costs.

► Assume the following data

Demand curve = 360,000-60,000p (p is retailer’s sale price)

CS = $2 (cost of supplier).

► Need to determine CR (Suppler’s charge on retailer) and p.

CR

Variation

p

Fix

CS =$2RetailerSupplier

16

How to increase the total profit through coordination ?

► Profit for supply chain

► Demand = 360,000-60,000(4)=120,000► Profit for supple chain = (4-2)(120,000)=$240,000 > $180,000

Maximize Supply Chain Profits

p=4

=(p-Cs) (360,000-60,000p)

=(p-2) (360,000-60,000p)

0p

(Profit)

Microsoft。

Microsoft。

Microsoft。

17

Scenario 2: Coordination through Two-Part Tariff -I

► Supplier charges his entire profit as an up-front franchise fee.

Supplier sells to the retailer at production cost (CS).

► Proof:Assume demand function = a-bp (a, b are constants)

Then retailer’s profit = (p-cR)(a-bp)-F (F: franchise fee)

The supply chain’s profit = (p-cS)(a-bp)Maximize both profits will obtain

18

Scenario 2: Coordination through Two-Part Tariff-II






19

Scenario 2: Coordination through Two-Part Tariff-III

CR= CS






P = + = +2ba

2ba

2CR

2CS

In our example, CR =CS =2 , p =4, demand=120,000Assume a franchise fee of 180,000Retailer’s profit =(4-2)(120,000)-180,000=$60,000 (same as before) Supplier’s profit = F = $180,000 Supply chain’s profit = 60,000+180,000=$240,000

20

Scenario 3: Coordination through Volume- based Quantity Discounts

In our example, design the volume discounts

CR =$4 (for volume < 120,000)

CR =$3.5 (for volume 120,000)

To sell 120,000, the retailer sets price at p = 4.(from the demand function)

Retailer’s profit =(4-3.5)(120,000)=$60,000 (same as before)

Supplier’s profit = (3.5-2)(120,000) = $180,000

Supply chain’s profit = 60,000+180,000=$240,000

► The two-part tariff is really a volume-based quantity discounts.

► Supplier offers the volume discounts at the break point of optimal demand.

► Supplier offers the discount price so that the retailer will have a profit the profit of no coordination and no discount.

21

Lessons From Discounting Schemes

Lot size-based discounts increase lot size and cycle inventory in the supply chain.

Volume-based discounts with some fixed cost passed on to retailer

are more effective in general

Lot size-based discounts are justified to achieve coordination for

commodity products.

Volume-based discounts are better using rolling horizon to avoid the

“hockey stick phenomenon”.

22

Price Discrimination to Max Supplier Profits

► Price discrimination is the practice which a firm charges differential prices to maximize profits.

► Price discrimination is also a volume-based discount scheme.► Consider an example

Demand curve (supplier sells to retailer)=200,000-50,000CR

CS =2

Profit of supplier = (CR-2)(200,000-50,000CR)

► What is the optimal “ fixed ” price CR to maximize profit ?

CR $0CR

(Profit)

Demand=200,000-50,000(3)=50,000

Profit =(3-2)(50,000)=$50,000

23

Demand Curve and Demand at Price of $3

Price p=4

p=3

p=2

100,000 200,000 Demand

Marginal cost = $2

► The fixed price of $3 does not maximize profits for the supplier. The profit is only the shaded area in the following figure.► The supplier could obtain the entire area under the demand curve above his marginal cost of $2 (the triangle within the solid lines) by pricing each unit differently.

50,000

24

An Equivalent Two-Part Tariff to Price Discrimination

► The entire triangle under the demand curve (above the marginal

cost of $2) = franchise fee = 1/2(4-2)(100,000)=$100,000

► The selling price to retailer: CR =CS =2.

► Demand = 200,000-50,000(2)=100,000

Profit of supplier = F = $100,000Price p=4

p=3

p=2

100,000 200,000 Demand

Marginal cost = $2

50,000

Price p=4

p=3

p=2

100,000 200,000 Demand

Marginal cost = $2

50,000

50,000

50,000

25

Demand Curve and Demand at Price of $3

► The fixed price of $3 does not maximize profits for the supplier. The profit is only the shaded area in the following figure.► The supplier could obtain the entire area under the demand curve above his marginal cost of $2 (the triangle within the solid lines) by pricing each unit differently.

Price p=4

p=3

p=2

100,000 200,000 Demand

Marginal cost = $2

50,000

50,000

50,000

26



► Fixed costs associated with lots

► Quantity discounts

► Trade Promotions

27

Trade Promotion

► Goals:

– Induce retailers to spur sales

– Shift inventory from manufacture to retailer and the customer

– Defend a brand against competition

► Retailer options:

– Pass through some or all of the promotion to customers to

spur sales

– Pass through very little of the promotion to customers but purchase in greater quantity to exploit temporary reduction

in price (forward buying)

28

Inventory Profile for Forward Buying

t

I(t)

Q* Q* Q* Q* Q*

Qd

Qd: lot size ordered at the discount price Q* : EOQ at normal price

29

Forward Buying Decisions

► Goal:

► Assumptions:

– Discount will only be offered once.– Order quantity Qd is a multiple of Q*.– The retailer takes no action to influence the demand.

– Identify Qd that maximizes the reduction in total cost (material cost + order cost + holding cost)I(t)

Qd


t

Q* Q* Q* Q* Q*

30

Decision on Q*d

► Assume the following data Normal order quantity = EOQ = The discount = $d. The discounted material cost = $(C-d )

► Now estimate the total cost of ordering Qd in the discount period TC(Qd) = material cost + order cost + inventory cost

=(C-d)Qd

=(C-d)Qd + S + (Qd/D)2 (C-d)h / 2D

Note: Discount period =Qd/D

hC2DSQ* =

+ S + Qd/2 (C-d)h [ Qd/D ]

t

I(t)

Q* Q* Q* Q* Q*

Qd


31

Decision on Q*d

2hCDS=CD+=CD hC2DS+(D/ )S

► Now estimate the total cost of ordering Q* in the discount period

Annual TC(Q*) = material cost + order cost + inventory cost

hC2DS+hC/2

Discount period TC (Q*) = Qd/D [Annual TC(Q*) ]=Qd/D [CD+ 2hCDS ]

► Define the cost reduction in the discount period

F(Qd) = TC(Qd) – Discount period TC(Q*)

C-dF(Qd)

Qd=0 Qd= +

CQ*

[C-d]hdD

► Forward buy = Qd – Q*

32

Decision on Q*d




hC2DS+hC/2




C-dF(Qd)

Qd=0 Qd= +

CQ*

[C-d]hdD


33

Decision on Q*d




hC2DS+hC/2




C-dF(Qd)

Qd=0 Qd= +

CQ*

[C-d]hdD


34

Example

Assume the following data without promotion. D =120,000/year , C =$3 , h =0.2 , S =$100 then →Q* = 6,324 Cycle inventory = Q*/2 = 3,162 Average flow time = Q*/2D =

0.02635(year) = 0.3162 (month).

Qd = + =dD

[C-d]hCD*C-d

0.15X120,000[3-0.15][0.2]

+3(6,324)3-0.15

=38,236

► Assume a promotion is offered (d =$0.15)

Cycle inventory = Qd/2 = 19,118

Average flow time = Qd/2D = 0.1593(year) = 1.9118 (month).

► Forward buy = 38,236 – 6,324 =31,912

► Trade promotions generally result in reduced supply chain

profits unless the trade promotions reduce demand

fluctuations.

► Trade promotions lead to a significant increase in lot size

and cycle inventory because of forward buying by the

retailer.

35

► Assume demand function = a-bp (a, b are constants)

Then retailer’s profit = [p-CR][a-bp]

Maximizing retailer’s profits will obtain

If a discount d is offered, the new C R=CR-d

Then the new

► Retailer’s optimal response to a discount is to pass only 50% of the discount to the customers.

Promotion Pass through to Customers

2

CR

2ba P =

p

2dp

2d

2CR

2bap

36

Demand curve at retailer: 300,000 – 60,000p

► Normal supplier price, CR = $3.00

► Promotion discount = $0.15

► Retailer only passes through half the promotion discount

Example-I

》Optimal retail price = $4.00

》Customer demand = 60,000

37





Example-II



38





Example-III





》Demand increases by only 7.5%》Cycle inventory increases significantly

39

Counter measures

Trade Promotions

Goal is to discourage forward buying in the supply chain

– EDLP– Scan based promotions– Customer coupons

Wikipedia

Microsoft。

Microsoft。

40

Levers to Reduce Lot Sizes Without Hurting Costs

Cycle Inventory Reduction

► Reduce transfer and production lot sizes

► Are quantity discounts consistent with manufacturing and logistics operations?

► Are trade promotions essential?

》Aggregate fixed cost across multiple products, supply points, or delivery points.

》Volume discounts on rolling horizon》Two-part tariff

》EDLP》Base on sell-thru rather than sell-in

41

頁碼作品授權條件作者 /來源

17 本作品轉載自Microsoft Office 2007多媒體藝廊，依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。

40 本作品轉載自WIKIPEDIA (http://en.wikipedia.org/wiki/File:Wal-Mart_logo.svg)，瀏覽日期 2012/2/20。



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