Inventory Management

1
Chapter 12

• Inventory Management

2
Types of Inventories

• Raw materials purchased parts
• Partially completed goods called work in
  progress
• Finished-goods inventories
• manufacturing firms or merchandise (retail
  stores)

3
Types of Inventories (Contd)

• Replacement parts, tools, supplies
• Goods-in-transit to warehouses or customers

4
Functions of Inventory

• To meet anticipated demand
• To smooth production requirements
• To decouple components of the production-distribut
  ion system
• To protect against stock-outs

5
Functions of Inventory (Contd)

• To take advantage of order cycles
• To help hedge against price increases or to take
  advantage of quantity discounts
• To permit smooth operations

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Effective Inventory Management

• A system to keep track of inventory
• A reliable forecast of demand
• Knowledge of lead times
• Reasonable estimates of
• Holding costs
• Ordering costs
• Shortage costs
• A classification system

7
Inventory Counting Systems

• Periodic System
• Physical count of items made at periodic
  intervals.
• Perpetual Inventory System System that keeps
  track of removals from inventory continuously,
  thus automatically monitoringcurrent levels of
  each item (JIT).

8
Inventory Counting Systems (Contd)

• Two-Bin System - Two containers of inventory
  reorder when the first is empty.
• Universal Bar Code - Bar code printed on a label
  that hasinformation about the item to which it
  is attached.

9
Key Inventory Terms

• Lead time time interval between ordering and
  receiving the order.
• Holding (carrying) costs cost to carry an item
  in inventory for a length of time, usually a
  year.
• Ordering costs costs of ordering and receiving
  inventory.
• Shortage costs costs when demand exceeds supply.
  Loss of business and goodwill.

10
ABC Classification System

• Classifying inventory according to some measure
  of importance and allocating control efforts
  accordingly.
• A - very important
• B - mod. important
• C - least important

11
Economic Order Quantity Models

• Economic Order Quantity model (EOQ)
• Economic Production Quantity model (EPQ) or
  Economic Production Lot Size (EPLS)
• Quantity discount model

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Assumptions of EOQ Model

• Only one product is involved
• Annual demand requirements known
• Demand is even (linear) throughout the year
• Lead time does not vary
• Each order is received in a single delivery
• There are no quantity discounts

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The Inventory Cycle
Q
Usage rate
Reorder point
Average Quantity
Q/2
Place order
Time
Receive order
Receive order
Lead time
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The Inventory Cycle (Example)
Order size, Q 350 units Usage rate 50 units
per day Lead time 2 days Reorder point 100
units (2 days supply) Cycle time 7 days
Q 350
Usage rate 50 units per day
Cycle time 7 days
Q/2 175
Reorder Point 100 units
5
7
0
12
14
Place order
Time, Days
Place order
Receive order
Receive order
Lead time 2 days
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Total Cost

• Where Q Quantity of run

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Length of Order Cycle

• Length of order cycle (time between orders)
• where Q0 Optimum run or order size
• Example Q 10,000 units, D 1000 units per
  day, then Q0/D 10,000 units/1000 units/day
  10 days

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Cost Minimization Goal
Annual carrying cost, (Q/2)H
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Minimum Total Cost

• The total cost curve reaches its minimum where
  the carrying and ordering costs are equal.

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The minimum order quantity occurs when the
holding cost equals the ordering cost, and when
the derivative (slope) of the total cost equation
equals zero.
Note The second derivative is positive,
indicting that this is a minimum.
20
Economic Production Quantity (EPQ)Or Economic
Production Lot Size (EPLS)

• Production done in batches or lots
• Capacity to produce a part exceeds the parts
  usage or demand rate
• Assumptions of EPQ are similar to EOQ except
  orders are received incrementally during
  production

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Economic Production Quantity Assumptions

• Only one item is involved
• Annual demand is known
• Usage rate is constant
• Usage occurs continually
• Production rate is constant
• Lead time does not vary
• No quantity discounts

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Economic Production Quantity (EPQ)
Inventory level
Maximum Inventory level
Non-production phase
Production phase
Average Inventory level
Called lead time in EOQ
Production run
Time
0
Set-up time
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EPQ Formulas

• Optimal run on order size
• Total Cost
• Number of runs
• Cycle time
• Run time
• Maximum inventory level

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EPQ Formulas (Contd)

• where
• p Production or delivery rate (generally
  per day)
• u Usage rate (generally per day)
• Imax Maximum inventory level
• Q0 Optimum run or order size
• S Ordering cost

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Total Costs with Purchasing Cost (PD)(Quantity
Discounts)
Where P Unit price
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Total Costs with PD
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Total Cost with Constant Carrying Costs
Note When carrying costs (CC) are constant, all
curves have their minimum points at the same
quantity
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When to Reorder with EOQ Ordering

• Reorder Point - When the quantity on hand of an
  item drops to this amount, the item is reordered.
• Safety Stock - Stock that is held in excess of
  expected demand due to variable demand rate
  and/or lead time.
• Service Level - Probability that demand will not
  exceed supply during lead time.

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Safety Stock
30
Reorder Point
ROP ReOrder Point, quantity
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Reorder Points

• Reorder point under constant demand and lead time
• Reorder point under variable demand rate
• Reorder point under variable lead time
• Reorder point under variable lead time and demand
• Safety Stock
• SS ROP Average Demand

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Reorder Points (Contd)

• Where
• ROP Quantity on hand at reorder point
• d Demand rate
• LT Lead Time
• Average demand rate
• ?d Standard deviation of the demand
  rate
• z Standard normal deviation
• Average Lead Time
• Standard deviation of lead time

33
Fixed-Order-Interval Model

• Orders are placed at fixed time intervals
• Order quantity for next interval?
• Suppliers might encourage fixed intervals
• May require only periodic checks of inventory
  levels

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Fixed-Interval Benefits

• Tight control of type A items
• Items from same supplier may yield savings in
• Ordering
• Packing
• Shipping costs
• May be practical when inventories cannot be
  closely monitored

35
Fixed-Interval Disadvantages

• Requires a larger safety stock
• Increases carrying cost
• Costs of periodic reviews

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Single Period Model

• Single period model model for ordering of
  perishables and other items with limited useful
  lives
• Shortage cost generally the unrealized profits
  per unit
• Excess cost difference between purchase cost and
  salvage value of items left over at the end of a
  period

37
Single Period Model

• Continuous stocking levels
• Identifies optimal stocking levels
• Optimal stocking level balances unit shortage and
  excess cost
• Discrete stocking levels
• Service levels are discrete rather than
  continuous
• Desired service level is equaled or exceeded

38
Operations Strategy

• Too much inventory
• Tends to hide problems
• Easier to live with problems than to eliminate
  them
• Costly to maintain
• Wise strategy
• Reduce lot sizes
• Reduce safety stock