1. Supply Chain Management
SYST 4050 Slides
Supply Chain Management
Lecture 20
Chapter 3

2. Outline Today Thursday Friday Chapter 11 Homework 4 due before class
SYST 4050 Slides
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
Chapter 3

3. Email: Ann.Richmond@colorado.edu
SYST 4050 Slides
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
Chapter 3

4. Effective inventory management is key to running a profitable business
SYST 4050 Slides
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
Chapter 3

5. Apple beats competitors at inventory turn over
SYST 4050 Slides
Inventory Management
Apple beats competitors at inventory turn over
Source: The Mac Observer, March 5, 2009
Chapter 3

6. Summary Lot sizing for a single product
SYST 4050 Slides
Summary
Lot sizing for a single product
Economic order quantity
Lot sizing with multiple products (complete aggregation)
Find order frequency (same for all products)
Calculate order quantity for each product Q = D/n
Chapter 3

7. Safety Inventory Inventory Demand (D) Order quantity/lot size (Q)
SYST 4050 Slides
Safety Inventory
Inventory
Demand (D)
Order quantity/lot size (Q)
Cycle Inventory
Average Inventory
Safety Inventory
Time
Cycle
Chapter 3

8. Example 11-1: Evaluating safety inventory given an inventory policy
SYST 4050 Slides
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
Chapter 3

9. Demand during lead time DL = LD
SYST 4050 Slides
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
Chapter 3

10. Example 11-1: Evaluating safety inventory given an inventory policy
SYST 4050 Slides
Example 11-1: Evaluating safety inventory given an inventory policy
Inventory
11,000
Order quantity/Lot size
6,000
Reorder point
Demand during lead time
Safety Inventory
1,000
Time
Lead time
Cycle
Chapter 3

11. Example 11-1: Evaluating safety inventory given an inventory policy
SYST 4050 Slides
Example 11-1: Evaluating safety inventory given an inventory policy
Reorder point (ROP) = demand during lead time + safety inventory = DL + ss
Average flow time = (avg. inventory) / (avg. demand)
ROP = DL + ss
Chapter 3

12. Role of Safety Inventory
SYST 4050 Slides
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
Chapter 3

13. Measuring Product Availability
SYST 4050 Slides
Measuring Product Availability
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
Product fill rate (fr)
Fraction of demand that is satisfied from product in inventory
Probability that product demand is supplied from available inventory
Order fill rate
Fraction of orders that are filled from available inventory
Product availability reflects a firm’s ability to fill a customer order out of available inventory. A stockout results if a customer order arrives when product is not available.
Chapter 3

14. CSL and fr are different!
SYST 4050 Slides
CSL and fr are different!
inventory
CSL is 0%, fill rate is almost 100%
time
CSL is 0%, fill rate is almost 0%
inventory
time
Chapter 3

15. SYST 4050 Slides
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
Chapter 3

16. = Prob(demand during lead time  ROP)
SYST 4050 Slides
Example 11-2: Evaluating cycle service level given a replenishment policy
CSL = Prob(of not stocking out in a cycle)
Inventory
= Prob(demand during lead time  ROP)
11,000
6,000
Reorder point
1,000
Time
Lead time
Chapter 3

17. Measuring Demand Uncertainty
SYST 4050 Slides
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
Chapter 3

18. SYST 4050 Slides
Example 11-2: Evaluating cycle service level given a replenishment policy
mean
D = 500
D = 2500
stdev
DL = LD = 2 x 2500 = 5000
L = L D = 2 x 500 = 707
mean
stdev
CSL = Prob(demand during lead time  ROP)
Chapter 3

19. SYST 4050 Slides
Example 11-2: Evaluating cycle service level given a replenishment policy
mean
D = 500
D = 2500
stdev
DL = LD = 2 x 2500 = 5000
L = L D = 2 x 500 = 707
mean
stdev
CSL = Prob(demand during lead time  ROP)
CSL = F(ROP,DL,L)
Chapter 3

20. F(ROP, DL, L) = NORMDIST(ROP, DL, L, 1)
SYST 4050 Slides
Example 11-4: Evaluating safety inventory given a desired service level
Average demand during lead time
DL =
Standard dev. of demand during lead time
L =
Cycle service level
CSL =
LD = 2*2,500 = 5,000
SQRT(L)D = SQRT(2)*500 = 707
F(ROP, DL, L) = F(6000, 5000, 707) = 0.92
F(ROP, DL, L) = NORMDIST(ROP, DL, L, 1)
Chapter 3

21. SYST 4050 Slides
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.
Chapter 3

22. CSL = F(ROP,DL,L) ROP = F-1(CSL,DL,L)
SYST 4050 Slides
Example 11-4: Evaluating safety inventory given a desired service level
mean
D = 500
D = 2500
stdev
DL = LD = 2 x 2500 = 5000
L = L D = 2 x 500 = 707
mean
stdev
CSL = Prob(demand during lead time  ROP)
CSL = F(ROP,DL,L)
ROP = F-1(CSL,DL,L)
Chapter 3

23. F-1(CSL, DL, L) = NORMINV(CSL, DL, L)
SYST 4050 Slides
Example 11-4: Evaluating safety inventory given a desired service level
Average demand during lead time
DL =
Standard dev. of demand during lead time
L =
Desired cycle service level
CSL =
Safety inventory
ss =
LD = 2*2,500 = 5,000
SQRT(L)D = SQRT(2)*500 = 707
0.90
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)
Chapter 3

24. Source: Operations Management, J. Heizer and B. Render
SYST 4050 Slides
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
Chapter 3

25. Summary Average Inventory = Q/2 + ss L: Lead time for replenishment
SYST 4050 Slides
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
Notes:
Average Inventory = Q/2 + ss
Chapter 3

26. Safety Inventory ROP = F-1(CSL,DL,L) ROP – DL = F-1(CSL,0,L)
SYST 4050 Slides
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
Chapter 3

27. SYST 4050 Slides
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?
Chapter 3

28. Measuring Product Availability
SYST 4050 Slides
Measuring Product Availability
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
Product fill rate (fr)
Fraction of demand that is satisfied from product in inventory
Probability that product demand is supplied from available inventory
Order fill rate
Fraction of orders that are filled from available inventory
Product availability reflects a firm’s ability to fill a customer order out of available inventory. A stockout results if a customer order arrives when product is not available.
Chapter 3

29. Product Fill Rate fr = 1 – 10/1000 = 1 – 0.01 = 0.99 Q = 1000 ESC = 10
SYST 4050 Slides
Product Fill Rate
inventory
fr = 1 – 10/1000 = 1 – 0.01 = 0.99
Q = 1000
time
ESC = 10
inventory
fr = 1 – 970/1000 = 1 – 0.97 = 0.03
time
Q = 1000
ESC = 970
Chapter 3

30. Expected Shortage per Replenishment Cycle
SYST 4050 Slides
Expected Shortage per Replenishment Cycle
Expected shortage during the lead time
If demand is normally distributed
Does ESC decrease or increase with ss?
Does ESC decrease or increase with L?
Chapter 3

31. SYST 4050 Slides
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 is expressed in number of products (not a probability) that is not satisfied from inventory.
Hence, ESC/Q is the fraction of demand (Q = the average demand per replenishment cycle) that is not satisfied from inventory/stock.
Fill rate is the opposite, hence fr = 1 – ESC/Q.
Chapter 3

32. Example 11-3: Evaluating fill rate given a replenishment policy
SYST 4050 Slides
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.
Chapter 3

33. Example 11-3: Evaluating fill rate given a replenishment policy
SYST 4050 Slides
Example 11-3: Evaluating fill rate given a replenishment policy
Lot size
Q =
Average demand during lead time
DL =
Standard dev. of demand during lead time
L =
Expected shortage per replenishment cycle
ESC =
Product fill rate
fr =
10,000
LD = 2*2,500 = 5,000
SQRT(L)D = SQRT(2)*500 = 707
-ss(1-Fs(ss/L))+Lfs(ss/L) = -1000*(1-Fs(1,000/707) + 707fs(1,000/707) =
1 – ESC/Q = 1 – 25.13/10,000 =
Chapter 3

34. Cycle Service Level versus Fill Rate
SYST 4050 Slides
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?
Chapter 3

35. Managing Inventory in Practice
SYST 4050 Slides
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
Chapter 3

36. Managing Inventory in Practice
SYST 4050 Slides
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
MRO Maintenance Repair and Operations
DoD mandates RFID
Chapter 3