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Lecture5

Project ManagementChapter 17

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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

Probabilistic/Uncertain Activity TimesProbabilistic/Uncertain Activity Times

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ActivityImmediate

PredecessorOptimisticTime (a)

Most LikelyTime (m)

PessimisticTime (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

ExampleExample

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Management Scientist SolutionManagement Scientist Solution

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Lecture5

Inventory ManagementChapter 11

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Types of InventoriesTypes 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

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Functions of InventoryFunctions 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

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Objective of Inventory ControlObjective 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

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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

Key Inventory TermsKey Inventory Terms

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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

Inventory Classification SystemsInventory Classification SystemsABC AnalysisABC Analysis

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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% A

#12760 1,550 17.00 $ 26,350 11.3% B

#10867 30% 350 42.86 15,001 6.4% 23% B

#10500 1,000 12.50 12,500 5.4% B

ABC Analysis ExampleABC Analysis Example

#12572 600 $ 14.17 $ 8,502 3.7% C

#14075 2,000 .60 1,200 .5% C

#01036 50% 100 8.50 850 .4% 5% C

#01307 1,200 .42 504 .2% C

#10572 250 .60 150 .1% C

$232,057

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Economic order quantity (EOQ) model

Economic production model (EPQ)

Quantity discount model

Economic Order Quantity ModelsEconomic Order Quantity Models

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The Inventory CycleThe Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

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Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

Q2H D

QSTC = +

Formula (11-1)

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Cost Minimization GoalCost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

SQ

DH

QTC

2

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Deriving the EOQ & Minimum Total Deriving the EOQ & Minimum Total CostCost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = QOPT

Number of orders per year = D/Q0

Length of order cycle = Q0/D

Formula (11-2)

Formula (11-3)

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Inventory Management – In-class ExampleInventory 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?

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Management Scientist SolutionsManagement Scientist Solutions

(a)

(b)(c)

(d)

(e)

(f)

(g)

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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

Assumptions of EOQ ModelAssumptions of EOQ Model

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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.

Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)

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EPQ = EOQ with Incremental Inventory EPQ = EOQ with Incremental Inventory ReplenishmentReplenishment

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EPQ Model AssumptionsEPQ 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.

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EPQ Model FormulaeEPQ Model Formulae Optimal production lot-size (formula 11-5 of book)

Run time: Q */p

Time between set-ups (cycle time): Q */u years

QDS

H

p

p u0

2

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Example: Non-Slip Tile Co.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

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Management Scientist SolutionsManagement 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

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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

Economic Production Quantity AssumptionsEconomic Production Quantity Assumptions

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EOQ with Quantity DiscountsEOQ 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.

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EOQ with Quantity DiscountsEOQ 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)

PDSQ

DH

QTC .

2 *

*

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Example – EOQ with Quantity DiscountExample – 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 more7% discount on orders of 400 rolls or more 10% discount for 900 rolls or more, and10% discount for 900 rolls or more, and 15% discount for 2000 rolls or more15% discount for 2000 rolls or more

Determine Walgreen’s optimal order quantityDetermine Walgreen’s optimal order quantity

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Management Scientist SolutionsManagement Scientist Solutions

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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

Operations StrategyOperations Strategy

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28-Jan-00 29-Jan-99 Change Percent

Current assets:Cash $3,809 $1,726 $2,083 121%Short-term investments 323 923 (600) -65%Account receivables, net 2,608 2,094 514 25%Inventories 391 273 118 43%Other 550 791 (241) -30% Total current assets 7,681 5,807 1,874 32%

Property, plant, and equipment, net 765 523 242 46%Long-term investments 1,048 532 516 97%Equity securities and other investments 1,673 --- 1,673Goodwill and others 304 15 289 1927%

Total assets $11,471 $6,877 $4,594 67%

LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:Accounts payable $3,538 $2,397 $1,141 48%Accrued and other 1,654 1,298 356 27% Total current liabilities 5,192 3,695 1,497 41%

Long-term debt 508 512 (4) -1%Other 463 349 114 33%

Total liabilities 6,163 4,556 1,607 35%Stockholders' equity:

Preferred stock --- ---Common stock and capitalin excess of $0.01 per value 3,583 1,781 1,802 101%Retained earnings 1,260 606 654 108%Other 465 (66) 531 Total stockholders' equity 5,308 2,321 2,987 129% Total liabilities and stockholders' equity $11,471 $6,877 $4,594 67%

The Balance Sheet – Dell Computer Co.

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Income Statement – Dell Computer Co.(in millions, except per share amount)

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

Fiscal Year Ended

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

Debt ratio =Total debt

Total assets

$6,

$11,

.

163

471

53 73%

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Inventory Turnover RatioInventory 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 =

times

balanceinventoryAverage

Sales

10.762/)391$273($

265,25$