1. Lecture 5
Project Management
Chapter 17

2. Probabilistic/Uncertain Activity Times
In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution.
An activity’s mean completion time is:
t = (a + 4m + b)/6
a = the optimistic completion time estimate
b = the pessimistic completion time estimate
m = the most likely completion time estimate

3. Example Activity Immediate Predecessor Optimistic Time (a) Most Likely
Time (m)
Pessimistic
Time (b) A -- 4 6 8 B 1
4.5 5 C 3 D E
0.5
1.5 F
B,C G H
E,F 7 I 2 J
D,H
2.5
2.75 K
G,I

4. Management Scientist Solution

5. Lecture 5
Inventory Management
Chapter 11

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

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

13. 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

14. Total Cost Annual carrying cost ordering Total cost = + Q 2 H D S TC =
Formula (11-1)

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

16. Deriving the EOQ & Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Formula (11-2)
Number of orders per year = D/Q0
Length of order cycle = Q0/D
Formula (11-3)

17. 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 and 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?

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

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

20. Economic Production Quantity (EPQ)
Economic production quantity (EPQ) model: variant of basic EOQ model
Production done in batches or lots
Replenishment order not received in one lump sum unlike basic EOQ model
Inventory is replenished gradually as the order is produced
hence requires the production rate to be greater than the demand rate
This model's variable costs are
annual holding cost, and
annual set-up cost (equivalent to ordering cost).
For the optimal lot size,
annual holding and set-up costs are equal.

21. EPQ = EOQ with Incremental Inventory Replenishment

22. EPQ Model Assumptions
Demand occurs at a constant rate of D items per year.
Production rate is p items per year (and p > u ).
u = usage rate
Set-up cost: $S per run.
Holding cost: $H per item in inventory per year.
Purchase cost per unit is constant (no quantity discount).
Set-up time (lead time) is constant.
Planned shortages are not permitted.

23. EPQ Model Formulae Optimal production lot-size (formula 11-5 of book)
Run time: Q */p
Time between set-ups (cycle time): Q */u years

24. Example: Non-Slip Tile Co.
Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tile annually.
The set-up cost is $5,000 per run
Holding cost is estimated at 10% of the manufacturing cost of $1 per tile.
The production capacity of the machine is 500,000 tiles per month.
The factor is open 365 days per year.
Determine
Optimal production lot size
Annual holding and setup costs
Number of setups per year
Loss/profit that NST is incurring annually by using their present production schedule

25. Management Scientist Solutions
Optimal TC = $28,868
Current TC = (100,000) + 5,000,000,000/100,000
= $54,167
LOSS = 54, ,868 = $25,299

26. Economic Production Quantity Assumptions
Only one item is involved 
Annual demand is known 
Usage rate is constant 
Usage occurs continually
Production occurs periodically
Production rate is constant
Lead time does not vary 
No quantity discounts 

27. EOQ with Quantity Discounts
The EOQ with quantity discounts model is 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.

28. 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 11.9 of book)
(holding + ordering + purchase)

29. 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

30. Management Scientist Solutions

31. Operations Strategy Too much inventory Wise strategy
Tends to hide problems
Easier to live with problems than to eliminate them
Costly to maintain
Wise strategy
Reduce lot sizes
Reduce safety stock

32. The Balance Sheet – Dell Computer Co.

33. Income Statement – Dell Computer Co.
(in millions, except per share amount)
28-Jan-00
29-Jan-99
Net revenue
$25,265
$18,243
Cost of revenue
20,047
14,137
Gross margin
5,218
4,106
Operating expenses:
Selling, general and administrative
2,387
1,788
Research, development, and engineering
568
272
Total operating expenses
2,955
2,060
Operating income
2,263
2,046
Other income
188 38
Income before income taxes
2,451
2,084
Provision for income taxes
785
624
Net income
$1,666
$1,460
Earnings per common share:
Basic
$0.66
$0.58
Diluted
$0.61
$0.53
Weighted average shares outstanding:
2,536
2,531
2,728
2,772
Retained Earnings:
Balances at beginning of period
606
607
1,666
1,460
Repurchase of common stocks
(1,012)
(1,461)
Balances at end of period
$1,260
$606
Fiscal Year Ended

34. Debt Ratio
What It Measures: The extent to which a form uses debt financing
How You Compute: The ratio of total debt to total assets

35. Inventory Turnover Ratio
What It Measures: How effectively a firm is managing its inventories.
How You Compute: This ratio is computed by dividing sales by inventories
Inventory turnover ratio =