Narrative Information Processing in Electronic Medical Report
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Transcript Narrative Information Processing in Electronic Medical Report
Managing Economies of Scale in the
Supply Chain: Cycle Inventory
Spring, 2014
Supply Chain Management:
Strategy, Planning, and Operation
Chapter 10
Byung-Hyun Ha
Contents
Introduction
Economies of scale to exploit fixed costs
Economies of scale to exploit quantity discount
Short-term discounting: trade promotions
Managing multiechelon cycle inventory
1
Introduction
Cycle inventory
inventory
level
time
Notation
D: demand per unit time
Q: quantity in a lot or batch size (order quantity)
Cycle inventory management (basic)
Determining order quantity Q that minimizes total inventory cost
with demand D given
2
Introduction
Analysis of cycle
Average inventory level (cycle inventory) = Q/2
Average flow time = Q/2D
Little’s law: (arrival rate) = (avg. number in system)/(avg. flow time)
Example
• D = 2 units/day, Q = 8 units
• Average inventory level
• (7 + 5 + 3 + 1)/4 = 4 = Q/2
• Average flow time
• (0.25 + 0.75 + 1.25 + 1.75 + 2.25 + 2.75 + 3.25 + 3.75)/8 = 2 = Q/2D
3
Introduction
Costs that are influenced by order quantity
C: (unit) material cost ($/unit)
• Average price paid per unit purchased
Quantity discount
H: holding cost ($/unit/year)
• Cost of carrying one unit in inventory for a specific period of time
• Cost of capital, obsolescence, handling, occupancy, etc.
• H = hC
Related to average flow time
S: ordering cost ($/order)
• Cost incurred per order
• Assuming fixed cost regardless of order quantity
• Cost of buyer time, transportation, receiving, etc.
10.2 Estimating cycle inventory-related costs in practice
SKIP!
4
Introduction
Assumptions
Constant (stable) demand, fixed lead time, infinite time horizon
Cycle optimality regarding total cost
Order arrival at zero inventory level is optimal.
Identical order quantities are optimal.
?
?
5
Introduction
Determining optimal order quantity Q*
Economy of scale vs. diseconomy of scale, or
Tradeoff between total fixed cost and total variable cost
Q1
D
?
Q2
D
6
Economies of Scale to Exploit Fixed Costs
Lot sizing for a single product
Economic order quantity (EOQ)
Economic production quantity (EPQ)
• Production lot sizing
Lot sizing for multiple products
Aggregating multiple products in a single order
Lot sizing with multiple products or customers
7
Economic Order Quantity (EOQ)
Assumption
Same price regardless of order quantity
Input
D: demand per unit time,
S: ordering cost,
C: unit material cost
H = hC: holding cost
Decision
Q: order quantity
• D/Q: average number of orders per unit time
• Q/D: order interval
• Q/2: average inventory level
Total inventory cost per unit time (TC)
TC TO TH (TM )
D
Q
S hC
Q
2
TO: total order cost
TH: total holding cost
TM: total material cost
8
Economic Order Quantity (EOQ)
Total cost by order quantity Q
TC
D
Q
S hC
Q
2
Optimal order quantity Q* that minimizes total cost
Q*
2 DS
hC
TC
TC * 2hCDS
Opt. order frequency
n*
D
Q
DhC
2S
Avg. flow time
Q*
S
2D
2DhC
Q*
Q
9
Economic Order Quantity (EOQ)
Robustness around optimal order quantity (KEY POINT)
Using order quantity Q' = Q* instead of Q*
D
Q
1
1
TC S hC TC *
Q
2
2
0.5
1/2( + 1/)
0.6
0.7
0.8
0.9
1.25 1.133 1.064 1.025 1.006
0
1.0
1.2
1.4
1.6
1.8
1.00 1.017 1.057 1.113
0
2.0
1.17 1.250
8
TC' = 1.25TC*
TC*
0.5
1
2
10
Economic Order Quantity (EOQ)
Robustness regarding input parameters
Mistake in indentifying ordering cost S' = S instead of real S
• Misleading to
2DS
2DβS
Q
βQ*
hC
hC
0.5
1/2( + 1/)
0.6
0.7
0.8
0.9
1.06 1.033 1.016 1.006 1.001
1
1.0
1.2
1
1
TC
β
TC *
2
β
1.4
1.6
1.00 1.004 1.014 1.028
0
1.8
2.0
1.04 1.061
3
TC' = 1.061TC*
TC*
What does mean
by robust?
0.5
1
2
11
Economic Order Quantity (EOQ)
Sensitivity regarding demand (KEY POINT)
Demand change from D to D1 = kD
2 D1S
hC
Q
*
1
2kDS
2 DS
k
k Q*
hC
hC
TC1* 2hCD1S 2hCkDS k 2hCDS k TC *
Opt. order frequency
n1*
D1
D1hC
*
k
n
Q1*
2S
Avg. flow time
Q1*
2 D1
S
1 Q*
2 D1hC
k 2D
12
Economic Order Quantity (EOQ)
Reducing flow time by reducing ordering cost (KEY POINT)
Efforts on reducing S to S1 = S
Hoping Q1* = kQ*
How much should S be reduced? (What is ?)
2DS1
2DγS
2DS
Q
γ
γ Q* k Q*
hC
hC
hC
*
1
= k2 (ordering cost must be reduced by a factor of k2)
13
Economic Production Quantity (EPQ)
Production of lot instead of ordering
P: production per unit time
Total cost by production lot size Q
TC
D
DQ
S 1 hC
Q
P 2
Optimal production quantity Q*
When P goes to infinite, Q* goes to EOQ.
2 DS
Q
1 D P hC
*
Q
x
D
(P – D)
Q/P
Q/D – Q/P = Q(1/D – 1/P)
1/(D/Q) = Q/D
14
Aggregating Products in a Single Order
Multiple products
m products
D: demand of each product
S: ordering cost regardless of aggregation level
All the other parameters across products are the same.
All-separate ordering
Q
*
i
2 DS
hC
TCi* 2hCDS
All-aggregate ordering
ASQ*
2DS
SSQ m
hC
*
SSTC* m 2hCDS
2m DS
2DS
m
hC
hC
ASTC* 2hCm DS m 2hCDS
Impractical supposition for analysis purpose
15
Lot Sizing with Multiple Products
Multiple products with different parameters
m products
Di, Ci, hi: demand, price, holding cost fraction of product i
S: ordering cost each time an order is placed
• Independent of the variety of products
si: additional ordering cost incurred if product i is included in order
Ordering each products independently?
Ordering all products jointly
Decision
• n: number of orders placed per unit time
• Qi = Di /n: order quantity of item i
Total cost and optimal number of orders
m
m
TC S si n Di hi Ci 2n
i 1
i 1
n
*
m
DhC
i 1
i i
i
m
2 S si
i 1
16
Lot Sizing with Multiple Products
Example 10-3 and 10-4
i LE22B
Input
• Common transportation cost, S = $4,000
• Holding cost fraction, h = 0.2
Ordering each products independently
• ITC* = $155,140
i
LE22B
LE19B
Di
Ci
si
12,000
$500
$1,000
LE19B
LE19A
1,200
$500
$1,000
120
$500
$1,000
200,000
LE19A
180,000
160,000
Qi*
ni *
TCi*
1,095
11.0
$109,544
346
3.5
$34,642
110
1.1
$10,954
LE19B
100,000
60,000
• n* = 9.75
• JTC* = $155,140
LE22B
120,000
80,000
Ordering jointly
i
140,000
40,000
20,000
0
LE19A
LE22B
Qi*
1,230
123
LE19B
LE19A
12.3
17
Lot Sizing with Multiple Products
How does joint ordering work?
Reducing fixed cost by enjoying robustness around optimal order
quantity
Is joint ordering is always good?
No!
Then, possible other approaches?
Partially joint
• NP-hard problem (i.e., difficult)
A heuristic algorithm
• Subsection: “Lots are ordered and delivered jointly for a
selected subset of the products”
• SKIP!
18
Exploiting Quantity Discount
Total cost with quantity discount
D
Q
TC TO TH TM S hC DC
Q
2
TO: total ordering cost
TH: total holding cost
TM: total material cost
Types of quantity discount
Lot size-based
• All unit quantity discount
• Marginal unit quantity discount
Volume-based
Decision making we consider
Optimal response of a retailer
Coordination of supply chain
19
All Unit Quantity Discount
Pricing schedule
Quantity break points: q0, q1, ..., qr , qr+1
• where q0 = 0 and qr+1 =
Unit cost Ci when qi Q qi+1, for i=0,...,r
• where C0 C1 Cr
Solution procedure
1. Evaluate the optimal lot size for each Ci.
Qi*
C0
C1
C2
...
It is possible that qiCi (qi + 1)Ci
average
cost
per unit
Cr
q0
...
q1
q2
q3 ... qr
2 DS
hC i
2. Determine lot size that minimizes the overall cost by the total
cost of the following cases for each i.
• Case 1: qi Qi* qi+1 , Case 2: Qi* qi , Case 3: qi+1 Qi*
20
All Unit Quantity Discount
Example 10-7
r = 2, D = 120,000/year
S = $100/lot, h = 0.2
Q* = 10,000
i
0
qi
Ci
0
$3.00
1
2
5,000 10,000
$2.96 $2.92
390,000
385,000
380,000
375,000
370,000
365,000
360,000
355,000
350,000
345,000
340,000
335,000
0
2000
4000
6000
8000
10000
12000
14000
16000
21
All Unit Quantity Discount
Example 10-7 (cont’d)
Sensitivity analysis
• Optimal order quantity Q* with regard to ordering cost
(no discount)
C = $3
(discount)
(original) S = $100/lot
6,324
10,000
(reduced) S' = $4/lot
1,256
10,000
22
Marginal Unit Quantity Discount
Pricing schedule
Quantity break points: q0, q1, ..., qr , qr+1
• where q0 = 0 and qr+1 =
Marginal unit cost Ci when qi Q qi+1, for i=0,...,r
• where C0 C1 Cr
Price of qi units
Vi = C0(q1 – q0) + C1(q2 – q1) + ... + Ci–1(qi – qi–1)
Ordering Q units
Suppose qi Q qi+1 .
C2
...
TC TO TH TM
V Q qi Ci
D
S i
h
Q
2
D
Vi Q qi Ci
Q
marginal
cost C0
per unit C1
Cr
q0
...
q1
q2
q3 ... qr
23
Marginal Unit Quantity Discount
Example 10-8
r = 2, D = 120,000/year
S = $100/lot, h = 0.2
Q* = 16,961
i
0
1
2
qi
Ci
Vi
0
$3.00
$0
5,000
$2.96
$15,000
10,000
$2.92
$29,800
395,000
390,000
385,000
380,000
375,000
370,000
365,000
360,000
355,000
350,000
0
4000
8000
12000
16000
20000
24000
28000
24
Marginal Unit Quantity Discount
Example 10-8 (cont’d)
Sensitivity analysis
• Optimal order quantity Q* with regard to ordering cost
(no discount)
C = $3
(discount)
(original) S = $100/lot
6,324
16,961
(reduced) S' = $4/lot
1,256
15,775
Higher inventory level (longer average flow time)?
25
Why Quantity Discount?
1. Improve coordination to increase total supply chain profit
Each stage’s independent decision making for its own profit
• Hard to maximize supply chain profit (i.e., hard to coordinate)
How can a manufacturer control a myopic retailer?
• Quantity discounts for commodity products
• Quantity discounts for products for which firm has market power
Manufacturer
(supplier)
Retailer
customers
supply chain
2. Extraction of surplus through price discrimination
Revenue management (Ch. 15)
Other factors such as marketing that motivates sellers
Munson and Rosenblatt (1998)
26
Coordination for Total Supply Chain Profit
Quantity discounts for commodity products
Assumption
• Fixed price and stable demand fixed total revenue
Max. profit min. total cost
Example case
• Two stages with a manufacture (supplier) and a retailer
Manufacturer
(supplier)
Retailer
customers
SS = 250
hS = 0.2
CS = 2
SR = 100
hR = 0.2
CR = 3
D = 120,000
27
Coordination for Total Supply Chain Profit
Quantity discounts for commodity products (cont’d)
No discount
• Retailer’s (local) optimal order quantity ( supply chain’s decision)
• Q1 = (212,000100/0.23)1/2 = 6,325
• Total cost (without material cost)
• TC1 = TC1S + TC1R = $6,008 + $3,795 = $9,803
Minimum total cost, TC*, regarding supply chain (coordination)
• Q* = 9,165
• TC* = TC*S + TC*R = $5,106 + $4,059 = $9,165
• Dilemma?
• Manufacturer saving by $902, but retailer cost increase by $264
• How to coordinate (decision maker is the retailer)?
D
Q
D
Q
SS hSCS S R hR CR
Q
2
Q
2
D
Q
SS S R hSCS hR CR
Q
2
TC TCS TCR
Q*
2 DSS S R
9,165
hSCS hR CR
28
Coordination for Total Supply Chain Profit
Quantity discounts for commodity products (cont’d)
Lot size-based quantity discount offering by manufacturer
• q1 = 9,165, C0 = $3, C1 = $2.9978
• Retailer’s (local) optimal order quantity (considering material cost)
• Q2 = 9,165
• Total cost (without material cost)
• TC2 = TC2S + TC2R = $5,106 + $4,057 = $9,163
• Savings (compared to no discount)
• Manufacturer: $902
• Retailer: $264 (material cost) – $262 (inventory cost) = $2
KEY POINT
• For commodity products for which price is set by the market,
manufacturers with large fixed cost per lot can use lot size-based
quantity discounts to maximize total supply chain profit.
• Lot size-based discount, however, increase cycle inventory in the
supply chain.
29
Coordination for Total Supply Chain Profit
Quantity discounts for commodity products (cont’d)
Other approach: setup cost reduction by manufacturer
Manufacturer
(supplier)
Retailer
customers
S'S = 100
hS = 0.2
CS = 2
SR = 100
hR = 0.2
CR = 3
D = 120,000
• Retailer’s (local) optimal order quantity
• Q3 = Q1 = 6,325
• Total cost (without material cost): no need to discount!
• TC3 = TC3S + TC3R = $3,162 + $3,795 = $6,957
Same with optimal supply chain cost when material cost is
considered
Expanding scope of strategic fit
• Operations and marketing departments should be cooperate!
30
Coordination for Total Supply Chain Profit
Quantity discounts for products with market power
Assumption
• Manufacturer’s cost, CS = $2
• Customer demand depending on price, p, set by retailer
• D = 360,000 – 60,000p
Profit depends on price.
D = 360,000 – 60,000p
Manufacturer
(supplier)
CS = 2
Retailer
CR = ?
customers
p=?
31
Coordination for Total Supply Chain Profit
Quantity discounts for products with market power (cont’d)
No coordination (deciding independently)
• Manufacturer’s decision on CR
• Expected retailer’s profit, ProfR
» ProfR = (p – CR)(360 – 60p)
• Retailer’s optimal price setting (behavior) when CR is given
» p1 = 3 + 0.5CR
• Demand by p1 (supplier’s order quantity)
» D = 360 – 60p1 = 180 – 30CR
• Expected manufacturer’s profit, ProfS
» ProfS = (CR – CS)(180 – 30CR)
CR1 that maximizes ProfR (manufacturer’s decision)
» CR1 = $4
• Retailer’s decision on p1 with given CR1
• p1 = $5 (D1 = 360,000 – 60,000p1 = 60,000)
• Supply chain profit, Prof01
• Prof01 = ProfR1 + ProfS1 = $120,000 + $60,000 = $180,000
32
Coordination for Total Supply Chain Profit
Quantity discounts for products with market power (cont’d)
Coordinating supply chain
• Optimal supply chain profit, Prof0*
• Prof0 = (p – CS)(360 – 60p)
• p* = $4
• D* = 120,000
• Prof0* = $240,000
Double marginalization problem (local optimization)
• But how to coordinate?
• i.e., ProfS* = ?, ProfR* = ?
33
Coordination for Total Supply Chain Profit
Quantity discounts for products with market power (cont’d)
Two pricing schemes that can be used by manufacturer
• Two-part tariff
• Up-front fee $180,000 (fixed) + material cost $2/unit (variable)
• Retailer’s decision
» ProfR = (p – CR)(360 – 60p)
» p2 = 3 + 0.5CR = $4
• Prof02 = ProfR2 + ProfS2 = $180,000 + $60,000 = $240,000
Retailer’s side: larger volume more discount
• Volume-based quantity discount
• q1 = 120,000, C0 = $4, C1 = $3.5
• p3 = $4
• Prof03 = ProfR3 + ProfS3 = $180,000 + $60,000 = $240,000
34
Coordination for Total Supply Chain Profit
Quantity discounts for products with market power (cont’d)
KEY POINT
• For products for which the firm has market power, two-part tariffs or
volume-based quantity discounts can be used to achieve coordination
in the supply chain and maximizing supply chain profits.
KEY POINT
• For those products, lot size-based discounts cannot coordinate the
supply chain even in the presence of inventory cost.
• In such a setting, either a two-part tariff or a volume-based quantity
discount, with the supplier passing on some of its fixed cost to the
retailer, is needed for the supply chain to be coordinated and
maximize profits.
Lot size-based vs. volume-based discount
Lot size-based: raising inventory level suitable for supplier’s
high setup cost
Hockey stick phenomenon & rolling horizon-based discount
35
Short-term Discounting: Trade Promotion
Trade promotion by manufacturers
Induce retailers to use price discount, displays, or advertising to
spur sales.
Shift inventory from manufactures to retailers and customers.
Defend a brand against competition.
Retailer’s reaction?
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 during the promotion period to
exploit the temporary reduction in price.
• Forward buy demand variability increase inventory & flow time
increase supply chain profit decrease
36
Short-term Discounting: Trade Promotion
Analysis
Determining order quantity with discount Qd
• Unit cost discounted by d (C' = C – d)
Assumptions
• Discount is offered only once.
• Customer demand remains unchanged.
• Retailer takes no action to influence customer demand.
Qd
Q*
Qd/D
1 – Qd/D
37
Short-term Discounting: Trade Promotion
Analysis (cont’d)
Optimal order quantity without discount Q* = (2DS/hC)1/2
Optimal total cost without discount TC* = CD + (2DShC)1/2
Total cost with Qd
Q
Q
Q
TC C d Qd S d hC d d TC * 1 d
2
D
D
dD
CQ*
*
Qd
hC d C d
Example 10-9
C = $3 Q* = 6,324
d = $0.15 Qd* = 38,236 (forward buy: 31,912 500%)
KEY POINT
Trade promotions lead to a significant increase in lot size and
cycle inventory, which results in reduced supply chain profits
unless the trade promotion reduces demand fluctuation.
38
Short-term Discounting: Trade Promotion
Retailer’s action of passing discount to customers
Example 10-10
Assumptions
• Customer demand: D = 300,000 – 60,000p
• Normal price: CR = $3
• Ignoring all inventory-related cost
Analysis
• Retailer’s profit, ProfR
• ProfR = (p – CR)(300 – 60p)
• Retailer’s optimal price setting with regard to CR
• p = 2.5 + 0.5CR
No discount (CR1 = $3)
• p1 = $4, D1 = 60,000
Discount (CR2 = $2.85)
• p2 = $3.925, D2 = 64,500 (p1 – p2 = 0.075 < 0.15 = CR1 – CR2)
39
Short-term Discounting: Trade Promotion
Retailer’ response to short-term discount
Insignificant efforts on trade promotion, but
High forward buying
• Not only by retailers but also by end customers
• Loss to total revenue because most inventory could be provided with
discounted price
KEY POINT
Trade promotions often lead to increase of cycle inventory in
supply chain without a significant increase in customer demand.
40
Short-term Discounting: Trade Promotion
Some implications
Motivation for every day low price (EDLP)
Suitable to
• high elasticity goods with high holding cost
• e.g., paper goods
• strong brands than weaker brand (Blattberg & Neslin, 1990)
Competitive reasons
Sometimes bad consequence for all competitors
Discount by not sell-in but sell-though
• Scanner-based promotion
41
Managing Multiechelon Cycle Inventory
Configuration
Multiple stages and many players at each stage
General policy -- synchronization
Integer multiple order frequency or order interval
Cross-docking
(Skip!)
42