Inventory Management

1
Chapter 13

• Inventory Management

2
Independent Demand (Chapter 13)
Dependent Demand (Chapter 14)
A
C(2)
B(4)
D(2)
E(1)
D(3)
F(2)
Independent demand is uncertain. Dependent
demand is certain.
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Types of Inventories (1 of 2)

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

4
Types of Inventories (2 of 2)

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

5
Supplier Production Distribution System
Supplier
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Functions of Inventory

• Meet anticipated demand
• Smooth production requirements
• Decouple components (areas) of the
  production-distribution
• Protect against stock-outs
• Take advantage of order cycles
• Help hedge against price increases or to take
  advantage of quantity discounts
• Permit operations (operation lead time)

7
Concerns of Inventory Control

• Level of customer service
• have the right goods, in sufficient quantities,
  in the right place, at the right time
• in other words, the customer gets what ever
  he/she wants when he/she wants it
• Inventory-related costs
• ordering costs
• carrying costs

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Objectives of Inventory Management (1 of 2)

• Achieve satisfactory levels of customer service
  while keeping inventory costs within reasonable
  bounds
• Two fundamental decisions
• how much to order
• when to place the order

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Objectives of Inventory Management (2 of 2)

• Possible performance measures
• customer satisfaction
• number of backorders/lost sales
• number of customer complaints
• inventory turnover
• ratio of annual cost of goods sold to average
  inventory investment
• days of inventory
• expected number of days of sales that can be
  supplied from existing inventory

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Requirements forEffective Inventory Management

• A system to keep track of the inventory on hand
  and on order
• A classification system for inventory items
• A reliable forecast of demand that includes an
  measure of forecast error
• Reasonable estimates of inventory holding costs,
  ordering costs, and shortage costs
• Knowledge of lead times and lead time variability

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Inventory Counting Systems (1 of 2)

• Perpetual Inventory (Continual) System
• Keeps track of removals from and receipts into
  inventory continuously
• Cycle counting - taking physical counts of items
  and reconciling
• with records on a continual
• rotating basis

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Inventory Counting Systems (2 of 2)

• Universal Product Code - Bar code printed on a
  label that hasinformation about the item to
  which it is attached
• Periodic System
• Physical count of items made at periodic intervals

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ABC Classification System
Figure 13-1

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

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Demand Forecast andLead Time Information

• Reliable estimates of the amount and timing of
  demand
• Lead time - time interval between ordering and
  receiving the order
• Extent of variability in demand and lead time

15
The Typical Procurement Cycle
Internal Order Cycle Order Request/Requisition Aut
horization signatures obtained Verification by
inventory control Purchasing researches vendors,
obtains quotes, etc. Order transferred to vendor
Vendor Cycle Receives and enters
order Manufactures or picks order Ships order
Internal Receiving Cycle Receiving Incoming
inspection Inventory control receives order,
updates records, and notifies department
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Cost Information

• Holding or carrying costs
• Ordering costs

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Holding or Carrying Costs

• Cost to carry a unit in inventory for a length of
  time
• Includes interest (opportunity cost), insurance,
  taxes, depreciation, obsolescence, deterioration
• May be expressed as a percentage of unit price or
  as a dollar amount per unit

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Ordering Costs

• Cost of ordering and receiving inventory
• Include determining how much is needed, preparing
  invoices, shipping costs, inspecting goods upon
  receipt for quantity and quality
• Generally expressed as a fixed dollar amount,
  regardless of order size

19
Shortage Costs

• Result when demand exceeds the inventory on hand
• Include the opportunity cost of not making a
  sales, loss of customer goodwill, late charges,
  and in the case of internal customers, the cost
  of lost production or downtime
• Difficult to measure, thus may have be
  subjectively estimated

20
Basic Systems for Independent Demand

• Fixed-order-quantity systems
• basic economic order quantity (EOQ) model
  purchasing model
• basic economic order quantity model with
  incremental or noninstantaneous replenishment
  production order quantity
• quantity discount model
• Fixed-order-interval systems

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Basic EOQ ModelAssumptions

• Only one product is involved
• Annual demand requirements are known
• Demand is spread evenly throughout the year so
  that the demand rate is reasonable constant
• Lead time does not vary
• Each order is received in a single delivery
• There are no quantity discounts, i.e., the price
  is constant

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How the Basic Fixed-Order-Quantity Model Works
Figure 13-2
Profile of Inventory Level Over Time
Quantity on hand
Time
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Total Annual Cost
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Cost Minimization Goal
Figure 13-4
Annual Cost
Order Quantity (Q)
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Minimum Total Cost

• The total cost curve reaches its minimum where
  the carrying and ordering costs are equal.
• Alternatively we can use calculus by taking the
  first derivative of the total cost function and
  set the derivative (slope) equal to zero and
  solve for Q.

26
Basic Fixed Order Quantity ModelWith Incremental
Replenishment

• Used to determine the order size, production lot,
  if an item is produced at one stage of production
  and then sent to the next stage or the customer
• Differs from the basic model because orders are
  assumed to be supplied or produced at a uniform
  rate (p) rather than the order being received all
  at once

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Basic Fixed Order Quantity ModelWith
Incremental Replenishment
Profile of Inventory Level Over Time
Production rate - usage rate
Q
Quantity on hand
Usage rate
Reorder point
Time
Place order
Place order
Receive order
Start to receive order
Start to receive order
Finish receiving order
Lead time
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Basic Fixed Order Quantity ModelWith
Incremental Replenishment
Profile of Inventory Level Over Time
Production rate - usage rate
Q
Quantity on hand
Usage rate
Reorder point
Time
Place order
Place order
Receive order
Start to receive order
Start to receive order
Finish receiving order
Lead time
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Basic Fixed Order Quantity ModelWith Incremental
Replenishment

• It is also assumed that the supply rate, p, is
  greater than the usage rate, u
• Figure 13-6, page 573, shows the difference
  between the basic EOQ model and this model
• The change in maximum inventory level requires
  modification of the TC equation

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Basic Fixed Order Quantity ModelWith Incremental
Replenishment

• The optimization results in

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Quantity Discount Model (1 of 4)

• This model differs from the basic model because
  the price per unit (P) may vary with the quantity
  ordered
• The supplier offers a lower unit price if larger
  quantities are ordered at one time
• This is presented as a price or discount
  schedule, i.e., a certain unit price covers a
  certain order quantity range

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Quantity Discount (2 of 4)

• Under this condition, annual product cost becomes
  an incremental cost and must be considered in the
  determination of the EOQ
• The total annual costs (TC) Annual holding cost
  annual setup cost annual product cost
• TC (Q/2)H (D/Q)S DP

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Costs FunctionsUnder Quantity Discount
cost
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Quantity Discount (3 of 4)

• To find the EOQ, the following procedure is used
• Compute the basic EOQ using the lowest unit price
  and HIP where I is an interest rate. If the
  resulting EOQ is feasible, i.e., that quantity
  can be purchased at the price used, it is
  optimal. Otherwise, go on to Step 2

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Quantity Discount (4 of 4)

• Using the EOQ from Step 1 and the discount
  schedule, find the price that should have been
  used and compute a new EOQ using this price. This
  new EOQ should be feasible.
• Compute the TC for the EOQ found in Step 2
• Compute the TC for all quantities greater than
  Step 2s EOQ where a discount begins. Select the
  quantity with the lowest TC as the EOQ

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Basis for Setting the Reorder Point

• In the fixed quantity system, the ordering
  process is triggered when the inventory level
  drops to a critical point, the reorder point
  (ROP)
• This starts all activities associated with
  placing, filling and receiving the order, or the
  lead time for the item

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Basis for Setting the Reorder Point

• During the lead time, customers continue to draw
  down the inventory level
• It is during this period that the inventory is
  vulnerable to stockout (run out of inventory)
• When the demand during the lead time is not known
  or not constant, a certain amount of inventory
  above the average or expected demand is carried
  this is safety stock

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Reorder Point
Quantity
Maximum probable demand during lead time
Expected demand during lead time
ROP
Safety stock
Time
LT
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Basis for Setting the Reorder Point

• Determinants of the reorder point
• The rate and distribution of demand
• The distribution of lead time
• The degree of stockout risk acceptable to
  management, customer service level
• Reorder point (ROP) Expected demand during
  lead time safety stock

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Basis for Setting the Reorder Point

• Customer service level
• order cycle service level is the probability that
  demand will not exceed supply during the lead
  time
• annual service level is the percentage of demand
  filled directly from inventory

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Reorder Point
Quantity
Maximum probable demand during lead time
Expected demand during lead time
ROP
Safety stock
Time
LT
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Lead Time Demand
Risk of shortage
ROP
Service level
safety stock
Distribution of lead time demand
Place order
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Distribution of Lead Time Demand
Figure 13-13
Service level
Risk of a stockout
Probability of no stockout
Quantity
ROP
Mean or expected demand
Safety stock
Standard deviation
0
z
z-scale
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Distribution of Lead Time Demand
Service level
Risk of a stockout
Probability of no stockout
Quantity
Mean or expected demand
Safety stock
Standard deviation
ROP
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Administration of the System

• Using the perpetual counting system, a signal is
  given when the records indicate that the
  inventory reaches the ROP
• Using the periodic counting system, a two-bin
  system could be used
• two bins of inventory
• bin A holds an amount equal to the reorder point
• bin B holds the remainder of the order
• customers are supplied out of bin B
• when bin B is empty, it is time to reorder
• customers are then supplied out of bin A until
  the order arrives

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Fixed-Order-Interval Model
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Basic Fixed-Order-Interval SystemInventory Level
Over Time
Target Maximum
How much to order
Inventory Level
Minimum Inventory
Time
When to order
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Operation of Fixed-Order-Interval Systems

• As demand for the inventoried item occurs, the
  inventory level drops
• When a prescribed period of time has elapsed, the
  ordering process is triggered, i.e., the time
  between orders is fixed or constant
• At that time the order quantity is determined
  using order quantity target maximum level -
  current inventory level

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Operation of Fixed-Order-Interval Systems

• After the lead time elapses, the ordered quantity
  is received, and the inventory level increases
• The maximum inventory level is expected demand
  during protection interval safety stock, or

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Administration of the System

• Using the periodic counting system, the inventory
  is reviewed (counted) at the end of each order
  interval
• Using the perpetual counting system, an items
  inventory level is checked in the inventory at
  the end of each order internal

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Reasons to Use

• Suppliers policy might encourage use
• Some situations do not lend themselves to
  continuous monitoring
• Used where it is desirable to physically count
  inventory each time an order is placed

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Benefits/Advantages

• Benefits
• results in tight control needed for A items in a
  A-B-C classification
• grouping ordering to one supplier may result in
  savings
• Disadvantages
• larger amount of safety stock needed for the same
  service level
• cost of periodic reviews

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Single-Period Model
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Single-Period Model

• Used to handle ordering of perishables and items
  with a limited useful life
• Focuses on two costs
• shortage cost - unrealized profit per unit
  revenue per unit minus cost per unit
• excess cost - purchase cost minus salvage
  value

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Optimal Stocking Level

• In the case where the distribution of demand is
  continuous, find the order quantity that provides
  the area under the distribution and to the left
  equal to the optimal service level
• In the case where the distribution of demand is
  discrete, choose the order quantity so that
  provides the optimal service level is equaled or
  exceeded