What is Inventory?

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What is Inventory?

• Definition--The stock of any item or resource
  used in an organization
• Raw materials
• Finished products
• Component parts
• Supplies
• Work in process

2
Inventory System Purpose

• The set of policies and controls that determine
  what inventory levels should be maintained, when
  stock should be replenished, and how large orders
  should be

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Purposes of Inventory

• 1. To maintain independence of operations
• 2. To meet variation in product demand
• 3. To allow flexibility in production scheduling
• 4. To provide a safeguard for variation in raw
  material delivery time
• 5. To take advantage of economic purchase-order
  size

4
Inventory Costs

• Holding (or carrying) costs
• Setup (or production change) costs
• Ordering costs
• Shortage (or backlog) costs

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Independent vs. Dependent Demand
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Classifying Inventory Models

• Fixed-Order Quantity Models
• Event triggered
• Make exactly the same amount
• Use re-order point to determine timing
• Fixed-Time Period Models
• Time triggered
• Count the number needed to re-order

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Inventory Control
Inventory Models
Inventory
Single Period Models
Fixed Time Period Models
Fixed Order Quantity Models
Constant Demand
Uncertainty in Demand
EOQ w/ Quantity Discounts
Simple EOQ
EOQ w/usage
Find the EOQ and R
Determine p and d
Calculate Total costs
Select Q and find R
Find the EOQ and R
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Fixed-Order Quantity ModelsAssumptions

• Demand for the product is constant and uniform
  throughout the period
• Lead time (time from ordering to receipt) is
  constant
• Price per unit of product is constant
• Inventory holding cost is based on average
  inventory
• Ordering or setup costs are constant
• All demands for the product will be satisfied
  (No back orders are allowed)

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EOQ Model--BasicFixed-Order Quantity Model
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Basic Fixed-Order Quantity Model
Derive the Total annual Cost Equation, where TC
- Total annual cost D - Annual demand (and d-bar
average daily demand D/365) C - Cost per
unit Q - Order quantity S - Cost of placing an
order or setup cost R - Reorder point L - Lead
time H - Annual holding and storage cost per unit
of inventory
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Cost Minimization Goal
Total Cost
Holding Costs
Annual Cost of Items (DC)
Ordering Costs
QOPT
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Deriving the EOQ

• Using calculus, we take the derivative of the
  total cost function and set the derivative
  (slope) equal to zero

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EOQ Example
Annual Demand (D) 1,000 units Days per year
considered in average daily demand 365 Cost to
place an order (S) 10 Holding cost per unit
per year (H) 2.40 Lead time (L) 7 days Cost
per unit (C) 15
Determine the economic order quantity and the
reorder point.
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Solution
91 or 92 units???
When the inventory level reaches 20, order 91
units.
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Problem

• Retailer of Satellite Dishes
• D 1000 units
• S 25
• H 100
• How much should we order?
• What are the Total Annual Stocking Costs?

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EOQ with Quantity Discounts

• What if we get a price break for buying a larger
  quantity?
• To find the lowest cost order quantity
• Since C changes for each price-break, HiC
• Where, i percentage of unit cost attributed
  to carrying inventory
• and , C cost (or price) per unit
• Find the EOQ at each price break.
• Identify relevant and feasible order quantities.
• Compare total annual costs
• The lowest cost wins.

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EOQ with Quantity Discounts Example

• Copper may be purchased for
• .82 per pound for up to 2,499 pounds
• .81 per pound for 2,500 to 5,000 pounds
• .80 per pound for orders greater than 5,000
  pounds
• Demand (D) 50,000 pounds per year
• Holding costs (H) are 20 of the purchase price
  per unit
• Ordering costs (S) 30
• How much should the company order to minimize
  total costs?

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Problem 28
44
43
Feasible
(Costs in ,000)
lt2500
42
lt2500 - 4999
gt5000
41
40
0
20
40
60
80
100
(Order Quantity 100's of units)
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Inventory Control
Inventory Models
Inventory
Single Period Models
Fixed Time Period Models
Fixed Order Quantity Models
Constant Demand
Uncertainty in Demand
Find the ?L
Find Z
Safety Stock
Find the EOQ and R
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What if demand is not Certain?

• Use safety stock to cover uncertainty in demand.
• Given service probability which is the
  probability demand will NOT exceed some amount.
• The safety stock level is set by increasing the
  reorder point by the amount of safety stock.
• The safety stock equals z?L
• where,
• ?L the standard deviation of demand during the
  lead time.
• For example for a 5 chance of running out z
  ?1.65

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Problem

• Annual Demand 25,750 or 515/wk _at_ 50 wks/year
• Annual Holding costs 33 of item cost
  (10/unit)
• Ordering costs are 250.00
• ?d 25 per week Leadtime 1
  week
• Service Probability 95
• Find
• a.) the EOQ and R
• b.) annual holding costs and annual setup costs
• c.) Would you accept a price break of 50 per
  order for lot sizes that are larger than 2000?

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Inventory Control
Inventory Models
Inventory
Single Period Models
Fixed Time Period Models
Fixed Order Quantity Models
Current Inventory
Find the?TL
Find Z
Find order quantity (q)
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Fixed-Time Period Models

• Check the inventory every review period and then
  order a quantity that is large enough to cover
  demand until the next order will come in.
• The model assumes uncertainty in demand with
  safety stock added to the order quantity.
• More exposure to variability than fixed-order
  models

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Fixed-Time Period Model with Safety Stock Formula
q Average demand Safety stock - Inventory
currently on hand
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Determining the Value of sTL

• The standard deviation of a sequence of random
  events equals the square root of the sum of the
  variances.

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Example of the Fixed-Time Period Model
Given the information below, how many units
should be ordered?
Average daily demand for a product is 20
units. The review period is 30 days, and lead
time is 10 days. Management has set a policy of
satisfying 96 percent of demand from items in
stock. At the beginning of the review period
there are 200 units in inventory. The daily
demand standard deviation is 4 units.
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Example of the Fixed-Time Period Model Solution
So, to satisfy 96 percent of the demand, you
should place an order of 645 units at this review
period.
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Problem

• A pharmacy orders antibiotics every two
  weeks (14 days).
• the daily demand equals 2000
• the daily standard deviation of demand 800
• lead time is 5 days
• service level is 99
• present inventory level is 25,000 units
• What is the correct quantity to order to minimize
  costs?

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Inventory Control
Inventory Models
Inventory
Single Period Models
Fixed Time Period Models
Fixed Order Quantity Models
Constant Demand
Uncertainty in Demand
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Single Period Model for items w/obsolescence
(newsboy problem)

• For a single purchase
• Amount to order is when marginal profit (MP) is
  equal to marginal loss (ML).
• Adding probabilities
• (P probability of that unit being sold)
• for the last unit ordered we want
• P(MP)?(1-P)ML or P ? ML /(MPML)
• Increase order quantity as long as this holds.

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SinglePeriod Model (Text Prob. 21)

• Famous Alberts Cookie King

Demand (dozen) Probability of Demand
1,800 0.05
2,000 0.10
2,200 0.20
2,400 0.30
2,600 0.20
2,800 0.10
3,000 0.05
Each dozen sells for 0.69 and costs 0.49 with a
salvage value of 0.29.
How many cookies should he bake?
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ABC Classification System

• Items kept in inventory are not of equal
  importance in terms of
• dollars invested
• profit potential
• sales or usage volume
• stock-out penalties

60
of Value
A
30
B
0
C
30
of Use
60
So, identify inventory items based on percentage
of total dollar value, where A items are
roughly top 15 , B items as next 35 , and the
lower 50 are the C items.
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Inventory Accuracy and Cycle Counting

• Inventory accuracy
• Do inventory records agree with physical count?
• Cycle Counting
• Frequent counts
• When? (zero balance, backorder, specified level
  of activity, level of important item, etc.)