1. Lecture 5
Decision Analysis
Chapter 14

2. Decision Environments
Certainty - Environment in which relevant parameters have known values
Risk - Environment in which certain future events have probabilistic outcomes
Uncertainty - Environment in which it is impossible to assess the likelihood of various future events

3. Decision Making under Uncertainty
Maximin - Choose the alternative with the best of the worst possible payoffs
Maximax - Choose the alternative with the best possible payoff
Minimax Regret - Choose the alternative that has the least of the worst regrets

4. Payoff Table: An Example
Possible Future Demand
Low
Moderate
High
Small facility
$10
Medium facility 7 12
Large facility
- 4 2 16
Values represent payoffs (profits)

5. Maximax Solution
Note: choose the “minimize the payoff” option if the numbers in the previous slide represent costs

6. Maximin Solution

7. Minimax Regret Solution

8. Decision Making Under Risk - Decision Trees
State of nature 1 B
Payoff 1
State of nature 2
Payoff 2
Payoff 3 2
Choose A’1
Choose A’2
Payoff 6
Payoff 4
Payoff 5
Choose A’3
Choose A’4
Choose A’ 1
Decision Point
Chance Event

9. Decision Making with Probabilities
Expected Value Approach
Useful if probabilistic information regarding the states of nature is available
Expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring
Decision yielding the best expected return is chosen.

10. Example: Burger Prince
Burger Prince Restaurant is considering opening a new restaurant on Main Street.
It has three different models, each with a different seating capacity.
Burger Prince estimates that the average number of customers per hour will be 80, 100, or 120 with a probability of 0.4, 0.2, and 0.4 respectively
The payoff (profit) table for the three models is as follows.
s1 = s2 = s3 = 120
Model A $10, $15, $14,000
Model B $ 8, $18, $12,000
Model C $ 6, $16, $21,000
Choose the alternative that maximizes expected payoff

11. Decision Tree Payoffs 10,000 2 15,000 d1 14,000 8,000 d2 1 3 18,000 d3.4
10,000 s2 .2 2
15,000 s3 .4 d1
14,000 .4 s1
8,000 d2 1 3 s2 .2
18,000 d3 s3 .4
12,000 s1 .4
6,000 4 s2 .2
16,000 s3 .4
21,000

12. Management Scientist Solutions
EVPI = expected payoff under certainty – expected payoff under risk

13. Lecture 5
Inventory Management
Chapter 11

14. Types of Inventories Raw materials & purchased parts
Partially completed goods called work in progress
Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers

15. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts

16. Objective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory

17. Key Inventory Terms
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply

18. Inventory Classification Systems ABC Analysis
Divides inventory into three classes based on annual dollar volume
Class A - high annual dollar volume
Class B - medium annual dollar volume
Class C - low annual dollar volume
Used to establish policies that focus on the few critical parts and not the many trivial ones
No “hard-and-fast” rule to classify into different categories

19. ABC Analysis Example $232,057 Item Stock Number
Percent of Number of Items Stocked
Annual Volume (units) x
Unit Cost =
Annual Dollar Volume
Percent of Annual Dollar Volume
Class
#10286
20%
1,000
$ 90.00
$ 90,000
38.8%
72% A
#11526
500
154.00
77,000
33.2%
#12760
1,550
17.00
$ 26,350
11.3% B
#10867
30%
350
42.86
15,001
6.4%
23%
#10500
12.50
12,500
5.4%
#12572
600
$ 14.17
$ 8,502
3.7% C
#14075
2,000
.60
1,200
.5%
#01036
50%
100
8.50
850
.4% 5%
#01307
.42
504
.2%
#10572
250
150
.1%
$232,057

20. Economic Order Quantity Models
Economic order quantity (EOQ) model
Quantity discount model
Economic production model (EPQ)

21. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time Q
Usage
rate
Quantity
on hand
Reorder
point
Time
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time

22. Total Cost Annual carrying cost ordering Total cost = + Q 2 Ch D Co
TC =
Formula (11-4)

23. Cost Minimization Goal
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q) QO
(optimal order quantity)

24. Deriving the EOQ & Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Formula (11-5)
Number of orders per year = D/Q0
Length of order cycle = Q0/D

25. Inventory Management – In-class Example
Number 2 pencils at the campus book-store are sold at a fairly steady rate of 60 per week.
It cost the bookstore $12 to initiate an order to its supplier.
Holding costs are $0.005 per pencil per year.
Determine
(a) The optimal number of pencils for the bookstore to purchase to minimize total annual inventory cost,
(b) Number of orders per year,
(c) The length of each order cycle,
(d) Annual holding cost,
(e) Annual ordering cost, and
(f) Total annual inventory cost.
(g) If the order lead time is 4 months, determine the reorder point.
Illustrate the inventory profile graphically.
What additional cost would the book-store incur if it orders in batches of 1000?

26. Management Scientist Solutions
(d)
(e)
(f)
(g)
(b)
(c)

27. Assumptions of EOQ Model
Only one product is involved
Annual demand requirements known/deterministic
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

28. EOQ with Quantity Discounts
EOQ with quantity discounts model
applicable where a supplier offers a lower purchase cost when an item is ordered in larger quantities
This model's variable costs are
Annual holding,
Ordering cost, and
Purchase costs
For the optimal order quantity, the annual holding and ordering costs are not necessarily equal

29. EOQ with Quantity Discounts
Formulae
Optimal order quantity: the procedure for determining Q * will be demonstrated
Number of orders per year: D/Q *
Time between orders (cycle time): Q */D years
Total annual cost: (formula of book)
(holding + ordering + purchase)

30. Example – EOQ with Quantity Discount
Walgreens carries Fuji 400X instant print film
The film normally costs Walgreens $3.20 per roll
Walgreens sells each roll for $5.25
Walgreens's average sales are 21 rolls per week
Walgreens’s annual inventory holding cost rate is 25%
It costs Walgreens $20 to place an order with Fujifilm, USA
Fujifilm offers the following discount scheme to Walgreens
7% discount on orders of 400 rolls or more
10% discount for 900 rolls or more, and
15% discount for 2000 rolls or more
Determine Walgreen’s optimal order quantity

31. Management Scientist Solutions