Inventory BA 339 Mellie Pullman

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Inventory BA 339Mellie Pullman
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Inventory Definitions

• Inventory vs. Inventory system
• Dependent vs. Independent environments
• Types
• Safety Stock
• Anticipation Inventory
• Hedge inventory (unusual events)
• Transportation or Pipeline Inventory

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Purposes of Inventory

• 1. Independence of operations.
• 2. Variation
• Product demand
• Material Delivery Time
• 3. Scheduling flexibility
• 4. Volume Discounts
• 5. Material price fluctuations

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Inventory Costs

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

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Inventory Systems

• Rules to manage inventory, specifically
• timing (when to order)
• sizing (how much to order)
• Continuous Review or Fixed-Order Quantity Models
  (Q)
• Event triggered (Example running out of stock)
• Periodic Review or Fixed-Time Period Models (P)
• Time triggered (Example Monthly sales call by
  sales representative)

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Comparison of Periodic and Continuous Review
Systems

• Periodic Review
• Fixed order intervals
• Variable order sizes
• Convenient to administer
• Inventory position only required at review

• Continuous Review
• Varying order intervals
• Fixed order sizes (Q)
• Allows individual review frequencies
• Possible quantity discounts
• Lower, less-expensive safety stocks

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Inventory costs

• C Unit cost or production cost the additional
  cost for each unit purchased or produced.
• H Holding costs cost of keeping items in
  inventory(cost of lost capital, taxes and
  insurance for storage, breakage, etc., handling
  and storing)
• S Setup or ordering costs a fixed cost
  incurred every time you place an order or a batch
  is produced.

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Total costs of carrying inventory

• Assumptions
• demand is constant and uniform throughout the
  period for your products (5 cases per day)
• Price per unit is constant for the period
  (16/case)
• Inventory holding cost is based on an average
  cost.
• Total Inventory Policy Cost annually annual
  purchase cost annual order cost annual
  holding cost

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Total cost of Inventory Policy

• annual purchase cost (annual demand
  Cost/item) annual order cost (annual orders
  Cost to order) annual holding cost (average
  units heldcost to carry one unit)

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Total Inventory Cost Equation
D yearly demand of units C cost of each
unit Q quantity ordered S cost to place
order H average yearly holding cost for each
unit storageinterestC D/Q number of
orders per year Q/2 average inventory held
during a given period assuming with
start with Q and drop to zero before
next order arrives (cycle inventory).
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Deriving the EOQ Economic Order Quantity

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

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EOQ Model--Basic Fixed-Order Quantity Model (Q)
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The Reorder Point
Reorder point (average period demand)Lead Time
periods d L
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Another EOQ Example
Annual Demand 1,000 units Days per year
considered in average daily demand 365 Cost to
place an order 10 Holding cost per unit per
year 2.50 Lead time 7 days Cost per unit
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Determine the economic order quantity reorder
point.
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Minor Deviations Here

• What causes minor deviations from the ideal order
  size?
• Assumptions behind the regular EOQ Model?

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Variations in lead time

• If we have variations in lead time, how should we
  change the reorder point so we rarely run out?
  Reorder Point Average demand during lead
  time(dL) safety stock (Z sL)
• where d average daily (or weekly) demandL
  Lead time (matching days or weeks)sL standard
  deviation of demand during lead time. sD
  standard deviation of demand (days or weeks).

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Service Level or of time inventory will meet
demand during lead time
Z Value Resulting Service Level
1.28 90
1.65 95
2.33 99
3.08 99.9
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Example

• Annual Demand 1000 units
• 250 work days in the yeard1000/250 4
  units/day
• Q 200 unitsL9 days sL 3 units
• z2 (97.7 likelihood that we wont run out
  during lead time)Reorder point dL zsL
  (49) (23) 42 units

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P Method (periodic review)

• You have a predetermined time (P) between orders
  (sales rep comes by every 10 days) or the average
  time between orders from EOQ Q/D
• How much should you order to bring inventory
  level up to some predetermined level, R where
• R restocking level
• Current Inventory position IP
• Order Quantity R-IP

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Restocking Level

• Needs to meet most demand situations
• R Restocking level Average demand during
  lead time review period safety stock mPL
  z sPLwheremPL average demand during lead
  time and review period z of standard dev
  from mean above the average demand (higher z is
  lower probability of running out). sRPL
  standard deviation of demand during lead time
  review period

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ABC Inventory Management

• Based on Pareto concept (80/20 rule) and total
  usage in dollars of each item.
• Classification of items as A, B, or C based on
  usage.
• Purpose is to set priorities on effort used to
  manage different SKUs, i.e. to allocate scarce
  management resources.
• SKU Stock Keeping Unit

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ABC Inventory Management

• A items 20 of SKUs, 80 of dollars
• B items 30 of SKUs, 15 of dollars
• C items 50 of SKUs, 5 of dollars
• Three classes is arbitrary could be any number.
• Percents are approximate.
• Danger dollar use may not reflect importance of
  any given SKU!

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Example of SKU list for 10 items
Item Annual Usage in Units Unit Cost Dollar Usage Percentage of Total Dollar Usage
1 5,000 1.50 7,500 2.9
2 1,500 8.00 12,000 4.7
3 10,000 10.50 105,000 41.2
4 6,000 2.00 12,000 4.7
5 7,500 0.50 3,750 1.5
6 6,000 13.60 81,600 32.0
7 5,000 0.75 3,750 1.5
8 4,500 1.25 5,625 2.2
9 7,000 2.50 17,500 6.9
10 3,000 2.00 6,000 2.4
Total     254,725 100.0
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ABC Chart for SKU List
A
B
C
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ABC Application

• Jewelry Store
• Fine Dining Restaurant
• Outdoor Retailer
• Large Department Store