slide 1. slide 2 slide 3 slide 4 demand distribution

27
Slide 1 Basic Inventory D ecisions H ow m uch? W hen? Lotsizing decision Determ ination ofthequantity to be ordered. Lottim ing decision Determ ination ofthe tim ing forthe orders.

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Page 1: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 1

Basic Inventory Decisions

How much? When?

Lot sizing decision

Determination of the quantity to be ordered.

Lot timing decision Determination of the timing for the orders.

Page 2: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 2

Page 3: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 3

Page 4: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 4

Demand Distribution

Page 5: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 5

Ideal depletion

Page 6: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 6

Without Safety Stock

Page 7: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 7

With Safety Stock

Page 8: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 8

Inventory/Time with ROP

Page 9: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 9

Lead Time Variability

Page 10: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 10

Reorder Point With Variable Demand

RR = = dLdL + + zzdd L L

wherewhere

dd == average daily demandaverage daily demandLL == lead timelead time

dd == the standard deviation of daily demand the standard deviation of daily demand

zz == number of standard deviationsnumber of standard deviationscorresponding to the service levelcorresponding to the service levelprobabilityprobability

zzdd L L == safety stocksafety stock

Page 11: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 11

Reorder Point for a Service Level

Probability of Probability of meeting demand during meeting demand during lead time = service levellead time = service level

Probability of Probability of a stockouta stockout

RR

Safety stock

ddLLDemandDemand

zd L

Page 12: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 12

Economic Order Quantity (EOQ) ModelEconomic Order Quantity (EOQ) Model

Page 13: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 13

200

400

0

Days 10 20 30 40 50 60

Inventory

Orderplaced

Orderarrival

Orderplaced Average

cycleinventory

A. Order quantity of 400 units

Orderarrival

The Effect of Reorder Quantity on Average Inventory Investment with Constant Demand and Lead Time

4 4

Demand = 20 units/day

Page 14: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 14

Inventory

Orderplaced

Orderarrival

Averagecycle

inventory

Days 10 20 30 40 50 60

0

100

200

B. Order quantity of 200 units

The Effect of Reorder Quantity on Average Inventory Investment with Constant Demand and Lead Time

45

Demand = 20 units/day

Page 15: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 15

Averagecycle

inventory

Orderarrival

Orderplaced

C. Order quantity of 600 units

Days 10 20 30 40 50 60

Inventory

0

300

600

The Effect of Reorder Quantity on Average Inventory Investment with Constant Demand and Lead Time

46

Demand = 20 units/day

Page 16: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 16

Size of order

Annual cost(dollars)

Lowest total cost(EOQ)

Total cost

Inventorycarrying

cost

Ordering cost

Cost Trade-offs Required to Determine the Most Economic Order Quantity

48

Page 17: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Inventory Carrying Inventory Carrying Costing: based on % of Product ValueCosting: based on % of Product Value

CostPercentage of Product

Value

Opportunity 12 %

Shrinkage 8

Tax/Insurance 3

Storage/Handling 2

Total 25 %

Page 18: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 18

EOQ Cost Model

CCoo - cost of placing order - cost of placing order DD - annual demand - annual demand

CCcc - annual per-unit carrying cost - annual per-unit carrying cost QQ - order quantity - order quantity

Annual ordering cost =Annual ordering cost =CCooDD

QQ

Annual carrying cost =Annual carrying cost =CCccQQ

22

Total cost = +Total cost = +CCooDD

QQ

CCccQQ

22

Page 19: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 19

EOQ Cost Model

TC = +CoD

Q

CcQ

2

= +CoD

Q2

Cc

2

TC

Q

0 = +C0D

Q2

Cc

2

Qopt =2CoD

Cc

Deriving Qopt Proving equality of costs at optimal point

=CoD

Q

CcQ

2

Q2 =2CoD

Cc

Qopt =2CoD

Cc

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Slide 20

EOQ Example

CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards

QQoptopt = =22CCooDD

CCcc

QQoptopt = =2(150)(10,000)2(150)(10,000)

(0.75)(0.75)

QQoptopt = 2,000 yards = 2,000 yards

TCTCminmin = + = +CCooDD

QQ

CCccQQ

22

TCTCminmin = + = +(150)(10,000)(150)(10,000)

2,0002,000

(0.75)(2,000)(0.75)(2,000)

22

TCTCminmin = $750 + $750 = $1,500 = $750 + $750 = $1,500

Orders per year =Orders per year = DD//QQoptopt

== 10,000/2,00010,000/2,000

== 5 orders/year5 orders/year

Order cycle time =Order cycle time = 311 days/(311 days/(DD//QQoptopt))

== 311/5311/5

== 62.2 store days62.2 store days

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Economic Order Quantity (EOQ) ModelsEconomic Order Quantity (EOQ) Models

Orders arrive in a single shipment No quantity discounts (i.e., single price) Demand rate is constant No constraints on order size relevant costs include only holding and

ordering/setup Ordering decisions for items are independent from

other items. No uncertainty in lead time or supply

Basic EOQ Model: assumptions

Page 22: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 22

OrderQuantity

Numberof Orders

(D/Q)

OrderingCost

P*(D/Q)

InventoryCarrying

Cost1/2 (Q*C*V)

TotalCost

406080

100120140160200300400

120806048403530241812

$ 4,800 3,200 2,400 1,920 1,600 1,400 1,200

960 720 480

$ 500 750

1,000 1,250 1,500 1,750 2,000 2,500 3,750 5,000

$ 5,300 3,950 3,400 3,170 3,100 3,150 3,200 4,460 4,470 5,480

Cost Trade-offs Required to Determine the Most Economic Order Quantity

49

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Slide 23

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Slide 24

Inventory Control Systems

Continuous system (fixed-Continuous system (fixed-order-quantity)order-quantity)

constant amount ordered when constant amount ordered when inventory declines to inventory declines to predetermined levelpredetermined level

Periodic system (fixed-time-Periodic system (fixed-time-period)period)

order placed for variable order placed for variable amount after fixed passage of amount after fixed passage of timetime

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Slide 25

Objednávání fixního množství k proměnlivému okamžiku Continuous system - označení (B,Q) nebo (s,Q)

s

q0

q0

q0

S1

S2

s

S3

Čas

Stav

t1 t2 t3

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Slide 26

Objednávání variabilního množství k pevně stanovenému okamžiku označení Periodic system - (s,S) nebo (R,S)

S

q1

q2q3

Stav

Čas

t0 t0 t0

Page 27: Slide 1. Slide 2 Slide 3 Slide 4 Demand Distribution

Slide 27

Two Forms of Demand

DependentDependent Demand for items used to produce final Demand for items used to produce final

products products Tires stored at a Goodyear plant are an

example of a dependent demand item

IndependentIndependent Demand for items used by external Demand for items used by external

customerscustomers Cars, appliances, computers, and

houses are examples of independent demand inventory