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Managing Facilitating Goods. Replenishment order. Replenishment order. Customer order. Replenishment order. Factory. Wholesaler. Distributor. Retailer. Customer. Production Delay. Shipping Delay. Shipping Delay. Item Withdrawn. Wholesaler

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managing facilitating goods

Managing Facilitating Goods

Replenishment

order

Replenishment

order

Customer

order

Replenishment

order

Factory

Wholesaler

Distributor

Retailer

Customer

Production

Delay

Shipping

Delay

Shipping

Delay

Item Withdrawn

Wholesaler

Inventory

Distributor

Inventory

Retailer

Inventory

learning objectives
Learning Objectives
  • Discuss the role of information technology in managing inventories.
  • Describe the functions and costs of an inventory system.
  • Determine the order quantity.
  • Determine the reorder point and safety stock for inventory systems with uncertain demand.
  • Design a continuous or periodic review inventory-control system.
  • Conduct an ABC analysis of inventory items.
  • Determine the order quantity for the single-period inventory case.
  • Describe the rationale behind the retail discounting model.
role of inventory in services
Role of Inventory in Services
  • Decoupling inventories
  • Seasonal inventories
  • Speculative inventories
  • Cyclical inventories
  • In-transit inventories
  • Safety stocks
considerations in inventory systems
Considerations in Inventory Systems
  • Type of customer demand
  • Planning time horizon
  • Replenishment lead time
  • Constraints and relevant costs
relevant inventory costs
Relevant Inventory Costs
  • Ordering costs
  • Receiving and inspections costs
  • Holding or carrying costs
  • Shortage costs
inventory management questions
Inventory Management Questions
  • What should be the order quantity (Q)?
  • When should an order be placed, called a reorder point (ROP)?
  • How much safety stock (SS) should be maintained?
inventory models
Inventory Models
  • Economic Order Quantity (EOQ)
  • Special Inventory Models With Quantity Discounts Planned Shortages
  • Demand Uncertainty - Safety Stocks
  • Inventory Control Systems Continuous-Review (Q,r) Periodic-Review (order-up-to)
  • Single Period Inventory Model
inventory levels for eoq model
Inventory Levels For EOQ Model

Units on Hand

Q

0

Q

Time

D

eoq formula
EOQ Formula
  • NotationD = demand in units per yearH = holding cost in dollars/unit/yearS = cost of placing an order in dollarsQ = order quantity in units
  • Total Annual Cost for Purchase Lots
  • EOQ
annual costs for quantity discount model
Annual Costs for Quantity Discount Model

22,000

21000

20000

2000

1000

C = $20.00

C = $19.50

C = $18.75

Annual Cost, $

0 100 200 300 400 500 600 700

Order quantity, Q

formulas for special models
Formulas for Special Models
  • Quantity Discount Total Cost Model
  • Model with Planned Shortages
values for q and k as a function of backorder cost
Values for Q* and K* as AFunction of Backorder Cost

B Q* K* Inventory Levels

0

0

0

undefined

Q*

0

demand during lead time example
Demand During Lead Time Example

=

+

+

+

u=3

u=3

u=3

u=3

ROP

s s

Demand During Lead time

Four Days Lead Time

safety stock ss
Safety Stock (SS)
  • Demand During Lead Time (LT) has Normal Distribution with - -
  • SS with r% service level
  • Reorder Point
continuous review system q r
Continuous Review System (Q,r)

Amount used during first lead time

Inventory on hand

EOQ

Reorder point, ROP

Order quantity, EOQ

d3

Average lead time usage, dL

d1

d2

EOQ

Safety stock, SS

First lead

time, LT1

LT2

LT3

Time

Order 1 placed

Order 3 placed

Order 2 placed

Shipment 1 received

Shipment 2 received

Shipment 3 received

periodic review system order up to
Periodic Review System(order-up-to)

Inventory on Hand

Review period

RP

RP

RP

Target inventory level, TIL

First order quantity, Q1

Q3

Q2

d3

d1

Amount used during

first lead time

d2

Safety stock, SS

First lead time, LT1

LT2

LT3

Time

Order 3 placed

Order 2 placed

Order 1 placed

Shipment 3 received

Shipment 1 received

Shipment 2 received

inventory control systems
Inventory Control Systems
  • Continuous Review System
  • Periodic Review System
inventory items listed in descending order of dollar volume
Inventory Items Listed in Descending Order of Dollar Volume

Monthly Percent of

Unit cost Sales Dollar Dollar Percent of

Inventory Item ($) (units) Volume ($) Volume SKUs Class

Computers 3000 50 150,000 74 20 A

Entertainment center 2500 30 75,000

Television sets 400 60 24,000

Refrigerators 1000 15 15,000 16 30 B

Monitors 200 50 10,000

Stereos 150 60 9,000

Cameras 200 40 8,000

Software 50 100 5,000 10 50 C

Computer disks 5 1000 5,000

CDs 20 200 4,000

Totals 305,000 100 100

single period inventory model newsvendor problem example
Single Period Inventory ModelNewsvendor Problem Example

D = newspapers demanded

p(D) = probability of demand

Q = newspapers stocked

P = selling price of newspaper, $10

C = cost of newspaper, $4

S = salvage value of newspaper, $2

Cu = unit contribution: P-C = $6

Co = unit loss: C-S = $2

single period inventory model expected value analysis
Single Period Inventory Model Expected Value Analysis

Stock Q

p(D) D 6 7 8 9 10

.028 2 4 2 0 -2 -4

.055 3 12 10 8 6 4

.083 4 20 18 16 14 12

.111 5 28 26 24 22 20

.139 6 36 34 32 30 28

.167 7 36 42 40 38 36

.139 8 36 42 48 46 44

.111 9 36 42 48 54 52

.083 10 36 42 48 54 60

.055 11 36 42 48 54 60

.028 12 36 42 48 54 60

Expected Profit $31.54 $34.43 $35.77 $35.99 $35.33

single period inventory model incremental analysis
Single Period Inventory Model Incremental Analysis

E (revenue on last sale) E (loss on last sale)

P ( revenue) (unit revenue) P (loss) (unit loss)

(Critical Fractile)

where:

Cu = unit contribution from newspaper sale ( opportunity cost of underestimating demand)

Co = unit loss from not selling newspaper (cost of overestimating demand)

D = demand

Q = newspaper stocked

critical fractile for the newsvendor problem
Critical fractile for the newsvendor problem

P(D<Q)

(Co applies)

P(D>Q)

(Cu applies)

0.722

retail discounting model
Retail Discounting Model
  • S = current selling price
  • D = discount price
  • P = profit margin on cost (% markup as decimal)
  • Y = average number of years to sell entire stock of “dogs” at current price (total years to clear stock divided by 2)
  • N = inventory turns (number of times stock turns in one year)

Loss per item = Gain from revenue

S – D = D(PNY)

topics for discussion
Topics for Discussion
  • Discuss the functions of inventory for different organizations in the supply chain.
  • How would one find values for inventory costs?
  • How can information technology create a competitive advantage through inventory management?
  • How valid are the assumptions for the EOQ model?
  • How is a service level determined for inventory items?
  • What inventory model would apply to service capacity such as seats on an aircraft?
interactive exercise
Interactive Exercise

The class engages in an estimation of the cost of a 12-ounce serving of Coke in various situations (e.g., supermarket, convenience store, fast-food restaurant, sit-down restaurant, and ballpark). What explains the differences?