Inventory Control
Inventory Control
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Inventory Control is everywhere.
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Fuel for the Car
Milk to Drink
Milk to Sell
MotherBoards to
Assemble Computers
Production with Setups
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Some youtube videos
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http://es.youtube.com/watch?v=qkZQxXJuqKo
http://es.youtube.com/watch?v=_VrBKF6SUCA
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Why we do store?
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Unplanned shocks (labor strikes, natural
disasters, surges in demand, etc.)
To maintain independence of supply chain
Economies of production
Improve customer service
Economies of purchasing
Transportation savings
Hedge against future
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Costs Related with Inventory Control
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Inventory deteriorates, becomes obsolete, lost, stolen, etc.
Order processing
 Shipping
 Handling
Carrying Costs
 Capital (opportunity) costs
 Inventory risk costs
 Space costs
 Inventory service costs
Out-of- Stock Costs
 Lost sales cost
 Back-order cost
Complacency
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Nature of Inventory: Adding Value
through Inventory
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Speed
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Cost
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direct: purchasing, delivery, manufacturing
indirect: holding, stockout.
Quality
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location of inventory has gigantic effect on speed
inventory can be a “buffer” against poor quality; conversely,
low inventory levels may force high quality
Flexibility
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location, level of anticipatory inventory both have effects
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Nature of Inventory:Functional Roles
of Inventory
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Transit
Buffer
Seasonal
Decoupling
Speculative
Lot Sizing or Cycle
Mistakes
Promotional
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Logistics Costs
Categoría de
Coste
Costes
Totales
% sobre
Ventas
% Costes
Logísticos
Transporte
636
5,4%
(5.9%)
62,7%
Almacenamiento
82
0,7%
(0.8%)
8,1%
Costes de
Inventarios
250
2,1%
(3%)
24,6%
Administración
47
0,4%
(0.4%)
4,6%
1015
8,6%
(10.1%)
100%
Total
Source: 16th Annual State of Logistics Report, 2004
(Entre parentesis los datos del 2001)
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http://www.loanational.org/documents/cscmp/17th_Annual_State_of_Logistics_Report.pdf
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Sectores diferentes tienen diferentes perfiles de coste
Pero
además la logística
además también impacta en:
Costes Logísticos como
Porcentaje de ventas
20%
Maquinaría
Aerospacial
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Otros costes en la Cadena
de suministro como los de
fabricación materia prima o
gestión de clientes.
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La cantidad de capital en
el negocio.
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Y una elevada proporción
del riesgo global del
negocio.
Automovil
15%
Comida&Bebida
Electronica
Sanidad
Químicas
10%
Gas y Petrol
Distribución
Banca
5%
0%
Source: ILT, McKinsey, LCP Consulting analysis
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Visión general
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Which are the main factors
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Main Factors defining an Inventory Policy
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Demand
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Setup
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Cost
Time
Storage
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Average Forecasted Demand
Error on Forecasted Demand
Cost
Capacity
Expiration
Time
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Lead Time
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Lead Time (LT)
Basic Period
Period of Forecasting
Horizon
Finite and Infinite Horizon
Finite or Infinite Production Rate
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EOQ Formula
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Why to do it with Formulae what has
always been done by head?
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Reduce Cost
Number of Different units
Time to do Added Value tasks
Computer Aid Management
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Assumptions to derive the EOQ
formula
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Production is Instantaneous.
Delivery is inmediate
Demand is deterministic
Demand is constant over time
A production run incurs a fixed setup cost
Products can be analyzed individually
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Inventory Order Cycle
Order quantity, Q
Inventory Level
Demand
rate
Reorder point, R
0
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Lead
time
Order Order
placed receipt
Lead
time
Order Order
placed receipt
Time
EOQ Cost Model
Co - cost of placing order
Cc - annual per-unit carrying cost
Annual ordering cost =
Co D
Q
Annual carrying cost =
CcQ
2
Total cost =
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D - annual demand
Q - order quantity
CoD
+
Q
CcQ
2
EOQ Cost Model
Proving equality of
costs at optimal point
Deriving Qopt
CoD
CcQ
TC =
+
Q
2
CoD
Cc
TC
=
2 +
Q
2
Q
C0D
Cc
0=
+
Q2
2
Qopt =
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2CoD
Cc
CoD
CcQ
=
Q
2
Q2
2CoD
=
Cc
Qopt =
2CoD
Cc
EOQ Cost Model (cont.)
Annual
cost ($)
Total Cost
Slope = 0
Carrying Cost =
Minimum
total cost
CcQ
2
Ordering Cost =
CoD
Q
Optimal order
Qopt
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Order Quantity, Q
EOQ Example
Cc = $0.75 per yard
Qopt =
2CoD
Cc
Qopt =
2(150)(10,000)
(0.75)
Co = $150
Qopt = 2,000 yards
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
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D = 10,000 yards
CoD
CcQ
TCmin =
+
Q
2
TCmin
(150)(10,000) (0.75)(2,000)
=
+
2,000
2
TCmin = $750 + $750 = $1,500
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
Required Data to generate a Policy
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Time
 Forecast Period
 Horizon
 Lead Time
Demand for a given Period (average and Standard Deviation)
 Demand during Horizon
Cost
 holding Cost (€ per unit per year) =K·Cu
 Unit Cost (€ per unit)
 Setup Cost S (€)
 Total Cost =Holding Cost + Setup Cost
Service Level (max % of runouts that we are willing to afford)
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Policies
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Reorder Point:
if stock<ROP then Buy(Q)
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ROP=Level of inventory at which a new order is placed
ROP= Maximun demand that we want to serve during Lead
Time
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Average Demand during Lead Time
Standard deviation of demand
Safety Stock (ss)
R = dL+ss
where
d = demand rate per period
L = lead time
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Q: Quantity that minimizes Total Cost
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Safety Stocks. Basic Concepts
 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
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Variable Demand with
a Reorder Point
Inventory level
Q
Reorder
point, R
0
LT
LT
Time
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Inventory level
Reorder Point with
a Safety Stock
Q
Reorder
point, R
Safety Stock
0
LT
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LT
Time
Reorder Point With Variable Demand
R = dL + zd L
where
d = average daily demand
L = lead time
d = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
zd 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
Safety stock
zd L
dL
Demand
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R
Reorder Point for Variable Demand
The carpet store wants a reorder point with a 95%
service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L
Safety stock = z d L
= 30(10) + (1.65)(5)( 10)
= (1.65)(5)( 10)
= 326.1 yards
= 26.1 yards
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Periodic Review Policies:
if time then Buy(OUL-Stock)
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OUL: Max Demand we cover during next
Review Period + Lead Time
Time Review Period that minimizes Total
Cost
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Economic Order Period (T*)
Power of Two Policies
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Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd
tb + L - I
where
d
tb
L
d
zd
= average demand rate
= the fixed time between orders
= lead time
= standard deviation of demand
tb + L = safety stock
I = inventory level
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Fixed-Period Model with Variable Demand
d
d
tb
L
I
z
= 6 bottles per day
= 1.2 bottles
= 60 days
= 5 days
= 8 bottles
= 1.65 (for a 95% service level)
Q = d(tb + L) + zd
tb + L - I
= (6)(60 + 5) + (1.65)(1.2)
= 397.96 bottles
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60 + 5 - 8
Problem
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A toy manufacturer uses aproximately 32000 silicon chips
annually. The Chips are used at a steady rate during the 240
days a year that the plant operates. Annual holding cost is 60
cents per chip and ordering cost is 24$. A year has 288 days.
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How muchh should we order each time?
How many times per year are we to order?
What is the length of an order cycle.
What is the total cost?
If the supplier has a lead time of 20 days?
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Which is the reorder point?
Should do we have a safety stock? To prevent what?
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Problem
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Determine optimal number to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
The pack has 150 units each
Management underestimated demand by 50%
C = $5/unit
There is a discount of 5% per unit if you buy more
than 500 units
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Problem
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A company substitutes in a regular way a
component of a given machine to ensure quality
parameters of the product. Machine works during
the whole year and needs 40 parts per week. The
component supplier offers a price of 10 € per unit for
orders with less than 300 units, and a price of 9.70 €
per unit for bigger orders. The cost of setting each
order is stimated on 25 €, and the holding cost is of
0.26 €/ €/ year.
How many units should you request each time?
If the supplier wants you to make orders bigger than
500 units ¿which is maximum unit price that should
stablish for orders bigger than 500 units?
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Karbonicas JuPe
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Karbonicas JuPe is a company bottling drinks where you work. To simplify we are to
consider only one product. Our company has a warehouse where store product just
manufactured and from where we serve the three logistics platforms that our client holds.
The logistics platforms are cross-dock warehouses, where storing products has a high
cost, and from where there associated retail stores are served.
The lead time at the manufacturing side for Karbonicas JuPe is 7 days (i.e. it takes one
week from we have been asked to produce until the product is ready at the warehouse.
Each of the logistics platforms faces a demand (measured in pallets) that might be
approximated by a normal distribution. (Data can be found at Table I).
Each logistic platform knows the demand and the stock levels of each associated retail
store. It takes two (2) days since the platform asks for products until the product reaches
each retail store through the logistic platform. The inventory system is Reorder Point at
each echelon. (i.e. the platforms work with ROP logic to the central warehouse of
Karbonicas JuPe, and the central warehouse works with ROP to the manufacturing facility).
The relation between the logistic platform and the retail stores is not considere in this
problem.
You are considering the posibility of eliminate the central warehouse echelon. To do that
the three logistics platforms should agree a joint review period (considering all the costs)
with a power-of-two policy. The factory consolidates the three orders (that have been done
simultaneously) and will bottle them together. From the factory docks and without passing
through the central warehouse the product will be sent directly to each logistic platform.
Key questions are: how much does it cost now, how much will it cost the new system.
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Karbonicas JuPe (ctnd)
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Data
Almacen Plataf. 1 Plataf. 2 Plataf. 3
Average demand (pallets per day)
Standard Deviation
Setup Cost(€)
Fixed cost per truck(€)
Holding cost per pallet and month
Lead time
NSC
z
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3
1
2
0.5
3
0.5
150
32
2
99,99%
4
100
32
2
99,99%
4
150
32
2
99,99%
4
480
8
7
99,99%
4