Lecture
5
Project Management
Chapter 17
1
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
2
Example
Immediate
Activity Predecessor
Optimistic
Time (a)
Most Likely
Time (m)
Pessimistic
Time (b)
A
--
4
6
8
B
--
1
4.5
5
C
A
3
3
3
D
A
4
5
6
E
A
0.5
1
1.5
F
B,C
3
4
5
G
B,C
1
1.5
5
H
E,F
5
6
7
I
E,F
2
5
8
J
D,H
2.5
2.75
4.5
K
G,I
3
5
7
3
Management Scientist Solution
4
Lecture
5
Inventory Management
Chapter 11
5
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
6
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
7
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
8
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
9
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
10
ABC Analysis Example
Item
Stock
Number
#10286
Percent of
Number of
Items
Stocked
x
Unit Cost
=
Annual
Dollar
Volume
Class
1,000
$ 90.00
$ 90,000
38.8%
#11526
500
154.00
77,000
33.2%
A
#12760
1,550
17.00
$ 26,350
11.3%
B
350
42.86
15,001
6.4%
#10500
1,000
12.50
12,500
5.4%
B
#12572
600
$ 14.17
$ 8,502
3.7%
C
#14075
2,000
.60
1,200
.5%
C
100
8.50
850
.4%
#01307
1,200
.42
504
.2%
C
#10572
250
.60
150
.1%
C
#10867
#01036
20%
Annual
Volume
(units)
Percent of
Annual
Dollar
Volume
30%
50%
$232,057
72%
23%
5%
A
B
C
11
Economic Order Quantity Models

Economic order quantity (EOQ) model

Economic production model (EPQ)

Quantity discount model
12
The Inventory Cycle
Profile of Inventory Level Over Time
Q
Quantity
on hand
Usage
rate
Reorder
point
Receive
order
Place Receive
order order
Place Receive
order order
Time
Lead time
13
Total Cost
Annual
Annual
Total cost = carrying + ordering
cost
cost
TC =
Q
H
2
+
DS
Q
Formula (11-1)
14
Cost Minimization Goal
Annual Cost
The Total-Cost Curve is U-Shaped
Q
D
TC  H  S
2
Q
Ordering Costs
QO (optimal order quantity)
Order Quantity
(Q)
15
Deriving the EOQ & Minimum Total Cost
The total cost curve reaches its minimum
where the carrying and ordering costs are
equal.
Q OPT =
2DS
2(Annual Demand)(Or der or Setup Cost)
=
H
Annual Holding Cost
Formula (11-2)
Number of orders per year = D/Q0
Length of order cycle = Q0/D
Formula (11-3)
16
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?
17
Management Scientist Solutions
(a)
(d)
(e)
(f)
(g)
(b)
(c)
18
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
19
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


This model's variable costs are



hence requires the production rate to be greater than the
demand rate
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.
20
EPQ = EOQ with Incremental Inventory
Replenishment
21
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.
22
EPQ Model Formulae

Optimal production lot-size (formula 11-5 of book)
Q0 
2DS
H
p
p u

Run time: Q */p

Time between set-ups (cycle time): Q */u years
23
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
24
Management Scientist Solutions



Optimal TC = $28,868
Current TC = .04167(100,000) + 5,000,000,000/100,000
= $54,167
LOSS
= 54,167 - 28,868 = $25,299
25
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 

26
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.
27
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)
Q*
D
TC 
H 
S  D.P
*
2
Q
(holding + ordering + purchase)
28
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
29
Management Scientist Solutions
30
Operations Strategy

Too much inventory

Tends to hide problems
 Easier to live with problems than to eliminate
them
 Costly to maintain

Wise strategy

Reduce lot sizes
 Reduce safety stock
31
The Balance Sheet – Dell Computer Co.
28-Jan-00 29-Jan-99
Current assets:
Cash
Short-term investments
Account receivables, net
Inventories
Other
Total current assets
Property, plant, and equipment, net
Long-term investments
Equity securities and other
investments
Goodwill and others
Total assets
Change
Percent
$3,809
323
2,608
391
550
7,681
765
1,048
$1,726
923
2,094
273
791
5,807
523
532
$2,083
(600)
514
118
(241)
1,874
242
516
121%
-65%
25%
43%
-30%
32%
46%
97%
1,673
304
$11,471
--15
$6,877
1,673
289
$4,594
1927%
67%
$3,538
1,654
5,192
508
463
6,163
$2,397
1,298
3,695
512
349
4,556
$1,141
356
1,497
(4)
114
1,607
48%
27%
41%
-1%
33%
35%
---
---
3,583
1,260
465
5,308
1,781
606
(66)
2,321
1,802
654
531
2,987
101%
108%
$11,471
$6,877
$4,594
67%
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
Accounts payable
Accrued and other
Total current liabilities
Long-term debt
Other
Total liabilities
Stockholders' equity:
Preferred stock
Common stock and capital
in excess of $0.01 per value
Retained earnings
Other
Total stockholders' equity
Total liabilities and
stockholders' equity
129%
32
Income Statement – Dell Computer Co.
(in millions, except per share amount)
Net revenue
Cost of revenue
Gross margin
Operating expenses:
Selling, general and administrative
Research, development, and engineering
Total operating expenses
Operating income
Other income
Income before income taxes
Provision for income taxes
Net income
Earnings per common share:
Basic
Diluted
Weighted average shares outstanding:
Basic
Diluted
Retained Earnings:
Balances at beginning of period
Net income
Repurchase of common stocks
Balances at end of period
Fiscal Year Ended
28-Jan-00 29-Jan-99
$25,265 $18,243
20,047
14,137
5,218
4,106
2,387
568
2,955
2,263
188
2,451
785
$1,666
1,788
272
2,060
2,046
38
2,084
624
$1,460
$0.66
$0.61
$0.58
$0.53
2,536
2,728
2,531
2,772
606
1,666
(1,012)
$1,260
607
1,460
(1,461)
$606
33
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
Total debt
Debt ratio =
Total assets
$6,163

$11,471
 53.73%
34
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 =
Sales
Average inventory balance
$25,265

 76.10 times
($273  $391) / 2
35