Inventory Management

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Inventory Management
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• Amazon.com

• Amazon.com started as a virtual retailer no
  inventory, no warehouses, no overhead just
  computers taking orders to be filled by others
• Growth has forced Amazon.com to become a world
  leader in warehousing and inventory management

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What Is Inventory?

• Stock of items kept to meet future demand
• Working Capital
• Def. - A physical resource that a firm holds in
  stock with the intent of selling it or
  transforming it into a more valuable state.

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Inventory by Nature of Material

• Raw Materials
• Works-in-Process
• Finished Goods
• Maintenance, Repair and Operating (MRO)

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Inventory by Uses of Material

• Transaction Inventory
• Speculative Inventory
• Precautionary Inventory

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Functional Classification Of Inventory

• Based on utility, all inventory can be in one or
  more of the following categories
• Working stock
• Safety stock
• Anticipation stock
• Pipeline stock
• Decoupling stock
• Psychic stock

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Cost of Inventory
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1.Ordering /Procurement cost

• Cost of replenishing inventory
• Order processing
• Shipping
• Handling

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2.Carrying Costs

• Cost of holding an item in inventory
• Working Capital (opportunity) costs
• Inventory risk costs( spoilage, breakage,
  detoriation ,obsolescence)
• Space costs
• Inventory service costs
• Insurance Taxes

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3.Out-of-Stock Costs/Shortage Cost

• Lost sales cost
• Back-order cost

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Inventory Management

• If company holds too little Inventory
• too frequent ordering
• loss of quantity discount
• higher transportation charges
• likely shortage in future
• If company holds too much Inventory
• carrying/holding charges
• storage
• obsolescence, depreciation
• Involvement of working capital

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Objectives of Inventory Management

• 1) Maximize the level of customer service by
  avoiding under stocking.(How much to order?)
• 2) Promote efficiency in production and
  purchasing by minimizing the cost of providing an
  adequate level of customer service.(When to
  order?)

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Design of Inventory Mgmt. Systems Micro Issues

• Order Quantity
• Economic Order Quantity
• Order Timing
• Reorder Point

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Inventory Systems

• Single-Period Inventory Model
• One time purchasing decision (Example vendor
  selling t-shirts at a football game)
• Seeks to balance the costs of inventory overstock
  and under stock
• Multi-Period Inventory Models
• Fixed-Order Quantity Models
• Event triggered (Example running out of stock)

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Single-Period Inventory Model

• 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

• Our college 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 Rs100 on
  every shirt we sell at the game, but lose Rs50 on
  every shirt not sold. How many shirts should we
  make for the game?

Cu Rs100 and Co Rs50 P 100 / (100 50)
.667 Z.667 .432 (use NORMSDIST(.667) or
Appendix E) therefore we need 2,400 .432(350)
2,551 shirts
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Multi-Period Inventory Models Fixed Order
Quantity Systems

• Economic Order Quantity (EOQ) Systems

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Behavior of EOQ Systems

• As demand for the inventoried item occurs, the
  inventory level drops
• When the inventory level drops to a critical
  point, the order point, the ordering process is
  triggered
• The amount ordered each time an order is placed
  is fixed or constant
• When the ordered quantity is received, the
  inventory level increases

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• Basic Fixed-Order Quantity Model and Reorder
  Point Behavior

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Inventory Order Cycle
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Determining Order Quantities

• Basic EOQ
• EOQ for Production Lots
• EOQ with Quantity Discounts

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Assumptions of Basic EOQ Model

• Demand is known with certainty and is constant
  over time
• No shortages are allowed
• Lead time for the receipt of orders is constant
• Order quantity is received all at once
• Quantity Discount does not exist
• Average Invenory is half of total inventory

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EOQ Cost Model
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EOQ Cost Model
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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 Qopt inventory
  order point that minimizes total costs

• C
• O
• S
• T

• Holding
• Costs

• Ordering Costs

• Order Quantity (Q)

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ExampleElectronic Village stocks and sells a
particular brand of personal computer. It costs
the store Rs450 each time it places an order with
the manufacturer for the personal computers. The
annual cost of carrying the PCs in inventory is
Rs170. The store manager estimates that annual
demand for the PCs will be 1200 units. Determine
the optimal order quantity and the total minimum
inventory cost.
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Example Basic EOQ
Zartex Co. produces fertilizer to sell to
wholesalers. One raw material calcium nitrate
is purchased from a nearby supplier at 22.50
per ton. Zartex estimates it will need 5,750,000
tons of calcium nitrate next year. The annual
carrying cost for this material is 40 of the
acquisition cost, and the ordering cost is 595.
a) What is the most economical order
quantity? b) How many orders will be placed per
year? c) How much time will elapse between
orders?
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Example 10.2

• Electronic Village stocks and sells a particular
  brand of personal computer. It costs the store
  Rs450 each time it places an order with the
  manufacturer for the personal computers. The
  annual cost of carrying the PCs in inventory is
  Rs170. The store
• manager estimates that annual demand for the PCs
  will be 1200 units. Determine the optimal order
  quantity and the total minimum inventory cost.

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Reorder Point

• Quantity to which inventory is allowed to drop
  before replenishment order is made
• Need to order EOQ at the Reorder Point
• ROP D X LT
• D Demand rate per period
• LT lead time in periods

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Example

• The I-75 Discount Carpet Store is open 311 days
  per year. If annual demand is 10,000 yards of
  Super Shag Carpet and the lead time to receive an
  order is 10 days, determine the reorder point for
  carpet.

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Example

• Item X is a standard item stocked in a companys
  inventory of component parts. Each year the firm,
  on a random basis, uses about 2000 of item X,
  which costs Rs25 each. Storage costs, which
  include insurance and cost of capital, amount to
  Rs5 per unit of average inventory. Every time an
  order is placed for more item X, it costs Rs10.
• (a) Whenever item X is ordered, what should the
  order size be?
• (b) What is the annual cost for ordering item X?
• (c) What is the annual cost for storing item X?

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Production Quantity Model(EOQ for lot)

• An inventory system in which an order is received
  gradually, as inventory is simultaneously being
  depleted
• Non-instantaneous receipt model
• assumption that Q is received all at once is
  relaxed
• p - daily rate at which an order is received over
  time, production rate
• d - daily rate at which inventory is demanded

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Assumptions of Production Quantity Model

• Demand is known with certainty and is constant
  over time
• No safety stock
• No shortages are allowed
• Lead time for the receipt of orders is constant
• Goods are supplied (p)at and consumed (d)at
  uniform rate,
• Supply rate is greater than usage rate.
• Quantity Discount does not exist

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Production Quantity Model (cont.)
d p
Q 2
Annual carrying cost 1 -
Cc
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Production Quantity Model (cont.)
CoD Q
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Production Quantity Model (cont.)
(p-d)
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Production Quantity Model Example
Cc 0.75 per yard Co 150 D 10,000 yards d
10,000/311 32.2 yards per day p 150 yards
per day
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Production Quantity Model Example (cont.)
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Example
I-75 Outlet Store has its own manufacturing
facility in which it produces Super Shag carpet.
The ordering cost is the cost of setting up the
production process to make Super Shag carpet.
Estimated annual demand is 10,000 meters of
carpet, and annual carrying cost is Rs0.75 per
meter. The manufacturing facility operates the
same days the store is open (i.e., 311 days) and
produces 150 meters of the carpet per day.
Determine the optimal order size, total inventory
cost, the length of time to receive an order, the
number of orders per year, and the maximum
inventory level.
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Example EOQ for Production Lots
Highland Electric Co. buys coal from Cedar
Creek Coal Co. to generate electricity. CCCC
can supply coal at the rate of 3,500 tons per day
for 10.50 per ton. HEC uses the coal at a rate
of 800 tons per day and operates 365 days per
year.HECs annual carrying cost for coal is 20
of the acquisition cost, and the ordering cost is
5,000. a) What is the economical production lot
size? b) What is HECs maximum inventory level
for coal?
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Quantity Discounts
Price per unit decreases as order quantity
increases
PO if Qltq1 P1 if q1ltQltq2 P2 if
q2ltQltq3 . . . P n-1 if Qgtqn
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Quantity Discounts
Price per unit decreases as order quantity
increases
Where Cc I Pi I carrying cost
2CoD Cc
Qoptm
PO if Qltq1 P1 if q1ltQltq2 P2 if
q2ltQltq3 . . . P n-1 if Qgtqn
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Quantity Discount Model (cont.)
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Price-Break Example Problem Data (Part 1)

• 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
  Rs4, 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(Rs)
• 0 to 2,499 Rs1.20
• 2,500 to 3,999 1.00
• 4,000 or more .98

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Price-Break Example Solution (Part 2)

• First, plug data into formula for each
  price-break value of C

• Annual Demand (D) 10,000 units
• Cost to place an order (S) Rs4

• Carrying cost of total cost (i) 2
• Cost per unit (C) 1.20, 1.00, 0.98

• Next, determine if the computed Qopt values are
  feasible or not

• Interval from 0 to 2499, the Qopt value is
  feasible

• Interval from 2500-3999, the Qopt value is not
  feasible

• Interval from 4000 more, the Qopt value is not
  feasible

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Price-Break Example Solution (Part 4)

• Next, we plug the true Qopt values into the total
  cost annual cost function to determine the total
  cost under each price-break

• TC(0-2499)(100001.20)(10000/1826)4(1826/2)(0.
  021.20)
• Rs12,043.82
• TC(2500-3999) Rs10,041
• TC(4000more) Rs9,949.20

• Finally, we select the least costly Qopt, which
  is this problem occurs in the 4000 more
  interval. In summary, our optimal order
  quantity is 4000 units

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Quantity Discount Example
A hardware store procures and sells hardware
items.Information on a item s give
here Expected annual sales8,000
units Ordering costRs.180 per order Holding
cost10 of the average inventory value. Items
can be purchased to the following
schedule LOT SIZE UNIT PRICE(In
Rs.) 1-999 Rs 22.00 1,000-1,499 Rs.20.00
1,500-1999 Rs.19.00 2,000 and above Rs.
18.50 We are require to determine the best order
size.