1. inventory management - shared
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Inventory Management
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Lecture Outline
• Elements of Inventory Management• Inventory Control Systems• Economic Order Quantity Models• Quantity Discounts• Reorder Point• Order Quantity for a Periodic Inventory System
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What Is Inventory?
• Stock of items kept to meet future demand• Purpose of inventory management
• how many units to order• when to order
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Importance of Inventory
• Balance the advantages and disadvantages of small and large inventories
• Pressures for small inventories– Inventory holding cost– Cost of capital– Storage and handling costs– Taxes, insurance, and shrinkage
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Importance of Inventory
• Pressures for large inventories– Customer service– Ordering cost– Setup cost– Labor and equipment utilization– Transportation cost– Payments to suppliers
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Reasons for Holding Inventory
• To meet anticipated customer demand• To protect against stock outs• To take advantage of economic order cycles• To maintain independence of operations• To allow for smooth and flexible production
operations• To guard against price increases
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In Short,
Buffer against uncertainty in…..
Supply (Raw material inventories)
Production process ( Work in process inventories)&Demand (Finished good inventories)
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Supply Chain Management
• Bullwhip effect• demand information is distorted as it moves away
from the end-use customer• higher safety stock inventories to are stored to
compensate• Seasonal or cyclical demand• Inventory provides independence from vendors• Take advantage of price discounts• Inventory provides independence between
stages and avoids work stoppages
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Inventory ManagementTo have the correct inventory at the right place at the right time to minimize system costs while satisfying customer service requirements•Raw material/WIP/Finished goods
Inventory PolicyThe strategy, approach, or set of techniques used to determine how to manage inventory
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Quality Management in the Supply Chain
• Customers usually perceive quality service as availability of goods they want when they want them
• Inventory must be sufficient to provide high-quality customer service in QM
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Type of Inventory
Process stage
Demand Type Others
Raw Materials WIP Finished Goods
Independent Dependent
Spares Consumable
Purpose
CycleSafetySeasonalPipeline
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Independent Demand(demand for item is independent of demand for any other item)
Dependent Demand(demand for item is dependent upon the demand for some other item)
Independent vs. Dependent Demand
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Independent vs. Dependent Demand..
Item Materials WithIndependent Demand
Materials WithDependent Demand
DemandSource Company Customers Parent Items
MaterialType Finished Goods WIP & Raw Materials
Method ofEstimatingDemand
Forecast & BookedCustomer Orders
Calculated
PlanningMethod EOQ & ROP MRP
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Inventory Type : Purpose • Seasonal stocks
– These are accumulated to absorb seasonal fluctuations in supply or demand.
• Cycle stocks– Due to fixed transportation and handling charges or set up
requirements, it is economical to order or produce large quantities at a time.
• Safety stocks– These are built as a hedge against uncertainties in supply or
demand.
• Pipeline stocks– Inventories in-transit.
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Inventory Costs
• Carrying cost• cost of holding an item in inventory
• Ordering cost• cost of replenishing inventory
• Shortage cost• temporary or permanent loss of sales when
demand cannot be met
What are these costs made of? How to estimate these?
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Terms used in Inventory• Material cost = C (per unit of product)
• Fixed ordering cost = S (a fixed cost of receiving one order)
• Holding cost = H (% of C) – carrying one unit in inventory for a specified period of time i.e. Rs. H/Unit/Year
• Quantity in a lot or batch size = Q – Quantity is either produced or purchased at a time
• Demand per unit time = D – Demand in one 1 year, d = average demand per week, So, D = d *52 / years
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Inventory Cost Holding Costs
(H)
• Obsolescence• Insurance• Extra staffing• Interest• Pilferage• Damage• Warehousing• etc.
Ordering Costs (S)
• Supplies• Forms• Order processing• Clerical support• etc.
• Clean-up costs• Re-tooling costs• Adjustment costs• etc.
Setup Costs (S)
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Holding cost (H)
• Cost of Capital
• Obsolescence cost
• Handling cost Vary with quantity of product received , ZERO otherwise
• Occupancy cost Vary with quantity of product stored, ZERO otherwise
• Miscellaneous costs
Theft, security, damage, tax, insurance
Inventory Cost
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Ordering cost (S)
• Buyer time Time of buyer for placing extra order, ZERO otherwise Internet and communication has reduced this cost significantly
• Receiving costs Administrative work such as purchase order matching with updating
inventory records Quantity dependent should not be included here
• Transportation costs Fixed cost should be included here
Inventory Cost
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Shortage Costs
When occurs, company faces two possibilities…..
• It can meet the shortage with some type of rush, special handling or priority shipment
• It cannot meet the shortage at all
So…. It depends on How company handles the problem
?
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• Permanent– Lost profits due to unsatisfied demand– Lost profits of future sales
• Temporary (CB)– Backordered, so not necessarily lost– Special clerical & paperwork costs– Extraordinary transportation cost to customer
Shortage Costs
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Inventory policy considerations:
• Customer demand: known/random• Replenishment lead time: known/random• Product variety (# of SKUs)• Length of planning horizon• Costs: Order costs Vs Inventory costs• Service level requirements
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Inventory management policies/ control systems:
• Periodic review policy• No tracking of inventory position on a regular basis. • Inventory position is reviewed after a fixed period,• Based on a pre-specified order up to level the firm decides the
order size. • Continuous review policy
• As soon as the inventory position goes down a certain pre-specified level the order is placed.
Since most firms have real time inventory information systems in place, the continuous review policy would be the focus.
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ABC Analysis
• Stock-keeping units (SKU) • Identify the classes so management can
control inventory levels• A Pareto chart
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ABC Classification
• Class A• 5 – 15 % of units• 70 – 80 % of value
• Class B• 30 % of units• 15 % of value
• Class C• 50 – 60 % of units• 5 – 10 % of value
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ABC Classification
1 $ 60 90 (60 * 90) 54002 350 403 30 1304 80 605 30 1006 20 1807 10 1708 320 509 510 60
10 20 120
PART UNIT COST ANNUAL USAGE TOTAL VALUE
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ABC Classification
9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0
TOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE
A
B
C
$85,400
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ABC Classification
% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0
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ABC Problem
Booker’s Book Bindery divides SKUs into three classes, according to their dollar usage.Calculate the usage values of the following SKUs and determine which is most likely to be classified as class A.
SKU Number Description Quantity Used per Year
Unit Value ($)
1 Boxes 500 3.002 Cardboard
(square feet)18,000 0.02
3 Cover stock 10,000 0.754 Glue (gallons) 75 40.005 Inside covers 20,000 0.056 Reinforcing tape
(meters)3,000 0.15
7 Signatures 150,000 0.45
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Seating arrangement (E)
11
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1 1 1 11
1 11
1
1
1
111
2
2
2
2
2
2
22
2
2
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Seating arrangement (F)
1 1
1
1
1
1
1
1
1
1 1
1
1
1
1 1 1
111 1
11 1
1 1
1
1
1
1
1
1
1
1
1
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Top margin:
Name: Roll No.: Group#: (1 or 2)-------------------------------------------------------------------
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Economic Order Quantity (EOQ) Models
• EOQ• optimal order quantity that will minimize
total inventory costs• Basic EOQ model• Production quantity model
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Assumptions of Basic EOQ Model
• Demand is known with certainty and is constant over time
• No shortages are allowed• Lead time for the receipt of orders is constant• Order quantity is received all at once
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Inventory Order Cycle
Demand rate
TimeLead time
Lead time
Order placed
Order placed
Order receipt
Order receipt
Inve
ntor
y Le
vel
Reorder point, R
Order quantity, Q
0
Average inventory
Q2
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EOQ Cost Model
S - cost of placing order D - annual demandH - annual per-unit carrying cost Q - order quantity
Annual ordering cost =SDQ
Annual carrying cost =HQ2
Total cost = +SDQ
HQ2
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EOQ Cost Model
TC = +SDQ
HQ2
= – +SDQ2
H2
TCQ
0 = – +SDQ2
H2
Qopt =2SD
H
Deriving Qopt Proving equality of costs at optimal point
=SDQ
HQ2
Q2 =2SD
H
Qopt =2SD
H
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EOQ Cost Model
Order Quantity, Q
Annual cost ($) Total Cost
Carrying Cost =HQ2
Slope = 0
Minimum total cost
Optimal order Qopt
Ordering Cost =SDQ
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EOQ Example
H = $0.75 per gallon S = $150 D = 10,000 gallons
Qopt =2SD
H
Qopt =2(150)(10,000)
(0.75)
Qopt = 2,000 gallons
TCmin = +SDQ
HQ2
TCmin = +(150)(10,000)
2,000(0.75)(2,000)
2
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5= 62.2 store days
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Production Quantity Model
• Order is received gradually, as inventory is simultaneously being depleted• AKA non-instantaneous receipt model• assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over time, a.k.a. production rate
• d - daily rate at which inventory is demanded
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Production Quantity Model
Q(1-d/p)
Inventorylevel
(1-d/p)Q2
Time0
Orderreceipt period
Beginorder
receipt
Endorder
receipt
Maximuminventory level
Averageinventory level
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Production Quantity Model
p = production rate d = demand rate
Maximum inventory level = Q - d
= Q 1 -
Qp
dp
Average inventory level = 1 - Q2
dp
TC = + 1 -dp
SDQ
HQ2
Qopt =2SD
H 1 - dp
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Production Quantity Model
S = $0.75 per gallon H = $150 D = 10,000 gallonsd = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = = = 2,256.8 gallons2SD
H 1 - dp
2(150)(10,000)
0.75 1 - 32.2150
TC = + 1 - = $1,329dp
SDQ
HQ2
Production run = = = 15.05 days per orderQp
2,256.8150
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Production Quantity Model
Number of production runs = = = 4.43 runs/yearDQ
10,0002,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 gallons
dp
32.2150
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Quantity Discounts
Price per unit decreases as order quantity increases
TC = + + PDHDQ
SQ2
whereP = per unit price of the itemD = annual demand
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Quantity Discount Model
Qopt=72.5
Carrying cost
Ordering cost
Inve
ntor
y co
st ($
)
Q1 = 49 Q2= 90
TC ($900)
TC ($1100)
TC = ($1400) ORDER SIZE PRICE1 - 49 $140050 – 89 $110090+ $900
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Quantity Discount
QUANTITY PRICE
1 - 49 $1,40050 - 89 1,100
90+ 900
S = $2,500 H = $190 per TV D = 200 TVs per year
Qopt = = = 72.5 TVs2SDH
2(2500)(200)190
TC = + + PD = $233,784 SDQopt
HQopt
2
For Q = 72.5
TC = + + PD = $194,105SDQ
HQ2
For Q = 90
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Reorder Point
• Inventory level at which a new order is placed
R = dLwhere
d = demand rate per periodL = lead time
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Reorder Point
Demand = 10,000 gallons/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 gallons/dayLead time = L = 10 days
R = dL = (32.154)(10) = 321.54 gallons
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Safety Stock
• Safety stock• buffer added to on hand inventory during lead time
• Stockout • an inventory shortage
• Service level • probability that the inventory available during lead
time will meet demand• P(Demand during lead time <= Reorder Point)
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Variable Demand With Reorder Point
Reorderpoint, R
Q
LTTime
LT
Inve
ntor
y le
vel
0
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Reorder Point With Safety Stock
Reorderpoint, R
Q
LTTime
LT
Inve
ntor
y le
vel
0Safety Stock
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Reorder Point With Variable Demand
R = dL + zd L
where
d = average daily demandL = lead time
d = the standard deviation of daily demand z = number of standard deviations
corresponding to the service levelprobability
zd L = safety stock
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Reorder Point For a Service Level
Probability of meeting demand during lead time = service level
Probability of a stockout
R
Safety stock
dLDemand
zd L
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Reorder Point For Variable Demand
The paint store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 gallons per dayL = 10 days
d = 5 gallons per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= 326.1 gallons
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 gallons
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Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd tb + L - I
where
d = average demand ratetb = the fixed time between ordersL = lead time
d = standard deviation of demand
zd tb + L = safety stockI = inventory level
Fixed periodicity between two orders, T = tb + L
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Derivation of optimal ordering frequency (N)
To determine optimum N (or T):
We know that minimum cost occurs at,
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Periodic Inventory System
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Fixed-Period Model With Variable Demand
d = 6 packages per dayd = 1.2 packagestb = 60 daysL = 5 daysI = 8 packagesz = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 packages