Transcript Lecture 20

Supply Chain Management
Lecture 20
Outline
• Today
– Chapter 11
• Sections 1, 2, 3, 7, 8
– Skipping 11.2 “Evaluating Safety Inventory Given Desired Fill rate”
• Thursday
– Homework 4 due before class
– Chapter 12
• Sections 12.1, 12.2 up to and including Example 12.2, 12.3
• Friday
– Homework 5 online
• Due Thursday April 8 before class
Staples Visit
• Date
– Friday April 2, 10:30am – 2:30pm
• (11:30am – 1:30pm on site, the rest in transit)
• Free transportation
• Location
– Staples fulfillment Center, Brighton, CO
• What
– Lunch and Learn
Email: [email protected]
Summary
• Inventory is an asset, but it's also a liability until
it has been sold
– Inventory is cash in-transit
• Inventory does not improve with time. Inventory
becomes less valuable with every passing day
– It takes space, heat, light, power, handling, insurance,
interest to carry, …
Effective inventory management is
key to running a profitable business
Inventory Management
Apple beats competitors at inventory
turn over
Company Days of inventory
Apple
5 days
Dell
7 days
Lenovo
15 days
HP
32 days
Intel
89 days
D-Link
131 days
Source: The Mac Observer, March 5, 2009
Summary
• Lot sizing for a single product
– Economic order quantity
2 DS
Q* 
hC
• Lot sizing with multiple products (complete aggregation)
– Find order frequency (same for all products)
n* 

k
i 1
Di hi Ci
2S *
– Calculate order quantity for each product Q = D/n
Safety Inventory
Inventory
Demand (D)
Order quantity/lot size (Q)
Cycle
Inventory
Average
Inventory
Safety
Inventory
Time
Cycle
Example 11-1: Evaluating safety
inventory given an inventory policy
• Assume that weekly demand for Palms at B&M
Computer World is normally distributed, with a
mean of 2,500 and a standard deviation of 500.
The manufacturer takes two weeks to fill an
order placed by the B&M manager. The store
manager currently orders 10,000 Palms when
the inventory drops to 6,000. Evaluate the safety
inventory carried by B&M and the average
inventory carried by B&M. Also evaluate the
average time spent by a Palm at B&M
Safety Inventory
Inventory
Demand (D)
Order quantity/lot size (Q)
Reorder point (ROP)
Cycle
Inventory
Average
Inventory
Safety
Inventory
Time
Lead time (L)
Cycle
Demand during lead time DL = LD
Example 11-1: Evaluating safety
inventory given an inventory policy
Inventory
11,000
Order quantity/Lot size
Reorder point
6,000
Demand during lead time
1,000
Safety Inventory
0
Time
Lead time
Cycle
Example 11-1: Evaluating safety
inventory given an inventory policy
• Reorder point (ROP)
= demand during lead time + safety inventory
= DL + ss
ROP = DL + ss
• Average flow time
= (avg. inventory) / (avg. demand)
Role of Safety Inventory
• There is a fundamental tradeoff
– Raising the level of safety inventory provides higher
levels of product availability and customer service
– Raising the level of safety inventory also raises the
level of average inventory and therefore increases
holding costs
Product availability reflects a firm’s ability to
fill a customer order out of available inventory
Measuring Product Availability
1. Cycle service level (CSL)
•
•
Fraction of replenishment cycles that end with all customer
demand met
Probability of not having a stockout in a replenishment cycle
2. Product fill rate (fr)
•
•
Fraction of demand that is satisfied from product in inventory
Probability that product demand is supplied from available
inventory
3. Order fill rate
•
Fraction of orders that are filled from available inventory
CSL and fr are different!
inventory
CSL is 0%, fill rate is almost 100%
0
inventory
0
time
CSL is 0%, fill rate is almost 0%
time
Example 11-2: Evaluating cycle service
level given a replenishment policy
• Weekly demand for Palms is normally
distributed, with a mean of 2,500 and a standard
deviation of 500. The replenishment lead time is
two weeks. Assume that the demand is
independent from one week to the next.
Evaluate the CSL resulting from a policy of
ordering 10,000 Palms when there are 6,000
Palms in inventory
Example 11-2: Evaluating cycle service
level given a replenishment policy
CSL = Prob(of not stocking out in a cycle)
= Prob(demand during lead time  ROP)
Inventory
11,000
Reorder point
6,000
1,000
0
Time
Lead time
Measuring Demand Uncertainty
Inventory
Demand (D)
Order quantity/lot size (Q)
Reorder point (ROP)
Cycle
Inventory
Average
Inventory
Safety
Inventory
Time
Lead time (L)
Cycle
Demand during lead time DL = LD
Standard deviation of demand over lead time L = (L)D
Example 11-2: Evaluating cycle service
level given a replenishment policy
stdev
D = 500
mean
D = 2500
stdev
L = L D = 2 x 500 = 707
mean
DL = LD = 2 x 2500 = 5000
CSL = Prob(demand during lead time  ROP)
Example 11-2: Evaluating cycle service
level given a replenishment policy
stdev
D = 500
mean
D = 2500
stdev
L = L D = 2 x 500 = 707
mean
DL = LD = 2 x 2500 = 5000
CSL = Prob(demand during lead time  ROP)
CSL = F(ROP,DL,L)
Example 11-4: Evaluating safety
inventory given a desired service level
Average demand during
lead time
Standard dev. of demand
during lead time
DL =
LD = 2*2,500 = 5,000
L =
SQRT(L)D =
SQRT(2)*500 = 707
Cycle service level
CSL = F(ROP, DL, L) =
F(6000, 5000, 707) = 0.92
F(ROP, DL, L) = NORMDIST(ROP, DL, L, 1)
Example 11-4: Evaluating safety
inventory given a desired service level
• Weekly demand for Lego at a Wal-Mart store is
normally distributed, with a mean of 2,500 boxes
and a standard deviation of 500. The
replenishment lead time is two weeks. Assuming
a continuous-review replenishment policy,
evaluate the safety inventory that the store
should carry to achieve a CSL of 90 percent.
Example 11-4: Evaluating safety
inventory given a desired service level
stdev
D = 500
mean
D = 2500
stdev
L = L D = 2 x 500 = 707
mean
DL = LD = 2 x 2500 = 5000
CSL = Prob(demand during lead time  ROP)
CSL = F(ROP,DL,L)
ROP = F-1(CSL,DL,L)
Example 11-4: Evaluating safety
inventory given a desired service level
Average demand during
lead time
Standard dev. of demand
during lead time
DL =
LD = 2*2,500 = 5,000
L =
SQRT(L)D =
SQRT(2)*500 = 707
Desired cycle service
level
Safety inventory
CSL = 0.90
ss =
Option 1:
ROP = F-1(CSL, DL, L) =
F-1(0.90, 5000, 707) = 5,906
ss = ROP – DL = 5906 – 5000 =
906
F-1(CSL, DL, L) = NORMINV(CSL, DL, L)
Ethical Dilemma
Wayne Hills Hospital in Wayne, Nebraska, faces a problem common
to large urban hospitals, as well as to small remote ones as itself.
That problem is deciding how much of each type of whole blood to
keep in stock. Because blood is expensive and has a limited shelf
life, Wayne Hills naturally wants to keep its stocks as low as
possible. Unfortunately, past disasters such as a major tornado and
a train wreck demonstrated that lives would be lost when not enough
blood was available to handle massive needs.
Source: Operations Management, J. Heizer and B. Render
Summary
L: Lead time for
replenishment
D: Average demand per unit
time
D:Standard deviation of
demand per period
DL: Average demand during
lead time
L: Standard deviation of
demand during lead time
CSL: Cycle service level
ss: Safety inventory
ROP: Reorder point
L
 LD
L
 L D
D

ROP  D L  ss
CSL  F ( ROP , D L , L )
ROP  F (CSL, D L , L )
1
Average Inventory = Q/2 + ss
Safety Inventory
What actions can be taken to improve product
availability without hurting safety inventory?
ROP = F-1(CSL,DL,L)
ROP – DL = F-1(CSL,0,L)
(ROP – DL)/L = F-1(CSL,0,1)
ss/L = Fs-1(CSL)
ss = Fs-1(CSL)L
Safety Inventory
Why is it that successful retailers and
manufacturers (i.e. Wal-Mart, Seven-Eleven
Japan, Dell) carry only little inventory but
still have high levels of product availability?
Measuring Product Availability
1. Cycle service level (CSL)
•
•
Fraction of replenishment cycles that end with all customer
demand met
Probability of not having a stockout in a replenishment cycle
2. Product fill rate (fr)
•
•
Fraction of demand that is satisfied from product in inventory
Probability that product demand is supplied from available
inventory
3. Order fill rate
•
Fraction of orders that are filled from available inventory
Product Fill Rate
inventory
fr = 1 – 10/1000 = 1 – 0.01 = 0.99
Q = 1000
0
ESC = 10
inventory
0
time
fr = 1 – 970/1000 = 1 – 0.97 = 0.03
time
Q = 1000
ESC = 970
Expected Shortage per
Replenishment Cycle
• Expected shortage during the lead time

ESC 
 ( x  ROP ) f ( x)dx
where f(x) is pdf of DL
x  ROP
• If demand is normally distributed

 ss 
 ss 
   L f s 

ESC   ss 1  Fs 
  L 
L 

Does ESC decrease or increase with ss?
Does ESC decrease or increase with L?
Product Fill Rate
• fr: is the proportion of customer
demand satisfied from stock.
Probability that product
demand
is supplied from inventory.
• ESC: is the expected shortage
per replenishment cycle (is
the demand not satisfied from
inventory in stock per
replenishment cycle)
• ss: is the safety inventory
• Q: is the order quantity
ESC
fr  1 
Q
 ss 
ESC   ss{1  F S  }
 L 
 ss 
  L f S  
 L 
Example 11-3: Evaluating fill rate
given a replenishment policy
• Recall that weekly demand for Palms at B&M is
normally distributed, with a mean of 2,500 and a
standard deviation of 500. The replenishment
lea time is two weeks. Assume that the demand
is independent from one week to the next.
Evaluate the fill rate resulting from the policy of
ordering 10,000 Palms when there are 6,000
Palms in inventory.
Example 11-3: Evaluating fill rate
given a replenishment policy
Lot size
Average demand during
lead time
Standard dev. of demand
during lead time
Expected shortage per
replenishment cycle
Q=
DL =
10,000
LD = 2*2,500 = 5,000
L =
SQRT(L)D =
SQRT(2)*500 = 707
ESC = -ss(1-Fs(ss/L))+Lfs(ss/L) =
-1000*(1-Fs(1,000/707) +
707fs(1,000/707) =
25.13
Product fill rate
fr =
1 – ESC/Q =
1 – 25.13/10,000 = 0.9975
Cycle Service Level versus Fill
Rate
What happens to CSL and fr when the safety
inventory (ss) increases?
What happens to CSL and fr when the lot
size (Q) increases?
Managing Inventory in Practice
• India’s retail market
– Retail market (not inventory) projected to reach
almost $308 billion by 2010
– Due to its infrastructure (many mom-and-pop stores
and often poor distribution networks) lead times are
long
ss = Fs-1(CSL)L
Managing Inventory in Practice
• Department of Defense
– DOD reported (1995) that it had a secondary
inventory (spare and repair parts, clothing, medical
supplies, and other items) to support its operating
forces valued at $69.6 billion
– About half of the inventory includes items that are not
needed to be on hand to support DOD war reserve or
current operating requirements