Chapter 15. Inventory Management

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Chapter 15. Inventory Management

• Inventory is the stock of any item or resource
  used in an organization and can include raw
  materials, finished products, component parts,
  supplies, and work-in-process
• An inventory system is the set of policies and
  controls that monitor levels of inventory and
  determines what levels should be maintained, when
  stock should be replenished, and how large orders
  should be
• Firms invest 25-35 percent of assets in inventory
  but many do not manage inventories well

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Purposes of Inventory

• To maintain independence of operations
• Provide optimal amount of cushion between work
  centers
• Ensure smooth work flow
• To allow flexibility in production scheduling
• To meet variation in product demand
• To provide a safeguard for variation in raw
  material or parts delivery time
• Protect against supply delivery problems
  (strikes, weather, natural disasters, war, etc.)
• To take advantage of economic purchase-order size

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Inventory Control (Management)

• Independent vs. Dependent Demand
• Inventory costs
• Single-Period Model
• Multi-Period Models Basic Fixed-Order Quantity
  Models
• Event triggered (Example running out of stock,
  or dropping below a reorder point)
• EOQ, EOQ with reorder point (ROP) , and with
  safety stock
• Multi-Period Models Basic Fixed-Time Period
  Model
• EOQ with Quantity Discounts
• ABC analysis

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Independent vs. Dependent Demand
Independent Demand (Demand not related to other
items or the final end-product)
Dependent Demand (Derived demand items for
component parts, subassemblies, raw materials,
etc.)
E(1)
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Inventory Costs

• Holding (or carrying) costs.
• Costs for capital, taxes, insurance, etc.
• (Dealing with storage and handling)
• Setup (or production change) costs.
  (manufacturing)
• Costs for arranging specific equipment setups,
  etc.
• Ordering costs (services manufacturing)
• Costs of someone placing an order, etc.
• Shortage (backordering) costs.
• Costs of canceling an order, customer goodwill,
  etc.

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A Single-Period Model

• Sometimes referred to as the newsboy problem
• Is used to handle ordering of perishables (fresh
  seafood, cut flowers, etc.) and items that have a
  limited useful life (newspaper, magazines, high
  fashion goods, some high tech components, etc)
• The optimal stocking level uses marginal analysis
  is where the expected profit (benefit from
  derived from carrying the next unit) is less than
  the expected cost of that unit (minus salvage
  value)
• Co Cost/unit of overestimated demand (excess
  demand)
• Co Cost per unit salvage value per unit
• Cu Cost/unit of underestimated demand
• Cu Price/unit cost/unit cost of loss
  of goodwill per unit
• Optimal order level is where P lt Cu /(Co Cu )
• This model states that we should continue to
  increase the size of the inventory so long as the
  probability of selling the last unit added is
  equal to or greater than the ratio of Cu/CoCu

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Single Period Model Example

• UNC Charlotte basketball team is playing in a
  tournament game this weekend. Based on our past
  experience we sell on average 2,400 shirts with a
  standard deviation of 350. We make 10 on every
  shirt we sell at the game, but lose 5 on every
  shirt not sold. How many shirts should we make
  for the game?
• Determine Cu 10 and Co 5 (this time,
  these were directly given)
• Compute P 10 / (10 5) 0.667 ? 66.7
• Order up to 66.7 of the demand
• How do you determine it?
• Normal distribution, Z transformation,
• Z0.667 0.432 (use NORMSDIST(.667) or Appendix
  E)
• Therefore we need 2,400 0.432(350) 2,551 shirts

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Single Period Model, Marginal Analysis

• Marginal analysis approach.
• Consider solved problem 1, p. 617
• Determine Cu 100-70 30 and Co
  70-20 50
• Compute P 30/(3050) ? 0.375
• Develop a full marginal analysis table (Excel
  time!)
• Assume we purchase 35 units, compute the expected
  total cost
• Repeat step 4, for 36,, 40
• The optimal order (purchase) size is the no. of
  units with the minimum expected total cost

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Fixed-Order Quantity Models Assumptions

• Demand for the product is constant and uniform
  throughout the period.
• 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.)
• Lead time (time from ordering to receipt) is
  constant (later, this assumption is relaxed with
  safety stocks).
• Price per unit of product is constant.

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Basic Fixed-Order Quantity Model and Reorder
Point Behavior
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Cost Minimization Goal
By adding the item, holding, and ordering costs
together, we determine the total cost curve,
which in turn is used to find the Qoptimal
(a.k.a. EOQ) inventory order point that
minimizes total costs.
C O S T
Holding Costs
Annual Cost of Items (DC)
Ordering Costs
QOPTIMAL
Order Quantity (Q)
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Basic Fixed-Order Quantity (EOQ) Model
Annual Holding Cost
A little bit of calculus
A little bit of common sense
ROP with safety stock
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Basic EOQ ROP Example
Given the information below, what are the EOQ,
reorder point, and total annual cost?
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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EOQ ? 89.44 ? 89 or 90 units ROP ? 2.747 ?
19.18 ? 19 or 20 units
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Another example
Days per year considered in average daily demand
360 Average daily demand is 3.5 units Standard
deviation of daily demand is 0.95 units Cost to
place an order 50 Holding cost per unit per
year 7.25 Lead time 4 days Compute the EOQ,
and ROP is the firm wants to maintain a 97
service level (probability of not stocking out)
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Fixed-Time Period Model with Safety Stock
q Average demand Safety stock Inventory
currently on hand
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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.
q 20(3010) 1.75(25.30) 200 ? 644.27
units
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A special purpose model

• Price-Break Model (Quantity discounts)
• Based on the same assumptions as the EOQ model,
  the price-break model has a similar EOQ (Qopt)
  formula
• Annual holding cost, H, is calculated using H
  iC where
• i percentage of unit cost attributed to
  carrying inventory
• C cost per unit
• Since C changes for each price-break, the
  formula above must be applied to each price-break
  cost value.
• Determine the total cost for each price break
• The lowest total cost suggests the optimal order
  size (EOQ)

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Price-Break Example
A company has a chance to reduce their inventory
ordering costs by placing larger quantity orders
using the price-break order quantity schedule
below. What should their optimal order quantity
be if this company purchases this single
inventory item with an e-mail ordering cost of
4, a carrying cost rate of 2 of the inventory
cost of the item, and an annual demand of 10,000
units?
Order Quantity(units) Price/unit() 0 to
2,499 1.20 2,500 to 3,999 1.00 4,000 or
more 0.98
Re-do the example with an order cost of 25 and
an inventory carrying cost rate of 45.
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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
• 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 65 are the C items

60
of Value
A
30
B
0
C
30
of Use
60
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Inventory Accuracy and Cycle Counting

• Inventory accuracy refers to how well the
  inventory records agree with physical count
• Lock the storeroom
• Hire the right personnel for as storeroom manager
  or employees
• Cycle Counting is a physical inventory-taking
  technique in which inventory is counted on a
  frequent basis rather than 1-2 times a year
• Easier to conduct when inventories are low
• Randomly (minimize predictability)
• Pay more attention to A items, then B, etc.
• Suggested problems 3, 6, 12, 14, 17, 18, 21, 24
• Case Hewlett-Packard