Operations Management (MD021)

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Operations Management(MD021)

• Inventory Management

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Agenda

• Inventory Definitions
• Processes for Inventory Management
• Economic Order Quantity Inventory Models
• Reorder Point/Reorder Quantity Inventory Models
• Single Period Inventory Models

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Inventory Definitions
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Inventory is a stock or store of goods
Demands determine the type of inventory an
organization will carry.
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Each firm carries types of inventories relevant
to its production demands

• Raw materials purchased parts
• Partially completed goods called work in
  process (WIP)
• Finished-goods inventories
• manufacturing firms
• Merchandise
• retail stores

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Each firm carries types of inventories relevant
to its production demands

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

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Example My Wifes Business (Goodies For Girls,
Inc.)

• Business Line direct-to-consumer retailing
• In-home parties for selling ladies romance
  enhancement products
• Inventories
• Products for sale (about 200 SKUs)
• Ordering sheets, post-cards, envelopes, plastic
  bags, credit card swiping machines
• Startup 600 investment in inventories
• Maximum Inventory 25,000
• Great customer service, slow inventory turns,
  lots of cash tied up
• Present Inventory 14,000
• Reasonable customer service, much better
  inventory turns, less cash tied up

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Inventory is carried for many different reasons
across different industries

• To meet anticipated demand
• Meeting demand in a timely manner enhances
  customer satisfaction
• Smooth production requirements across seasons
• Produce one season, sell in next (or throughout
  year)
• To decouple successive operations and maintain
  continuity of production
• Protects against machine breakdowns
• To protect against stock-outs
• Vendors do not always deliver on time

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Inventory is carried for many different reasons
across different industries

• To take advantage of order cycles to minimize
  purchasing and inventory costs
• Minimum order size requirements, full truck loads
• To help hedge against price increases
• Buy now at low price, store goods for future use
• To permit operations to operate
• Operations require a certain amount of WIP
  inventory
• To take advantage of quantity discounts
• Vendors often give discounts when ordering large
  quantities

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Operations Strategy

• Having too much inventory is not good
• Tends to hide problems
• Makes it easier to live with (i.e. ignore)
  problems than to eliminate them
• Costly to maintain large stocks of inventories
• Opportunity costs of potentially doing something
  else with the money tied up in inventory
• Wise objectives
• Reduce lot sizes
• Reduce safety stock
• Reduce ordering costs and holding costs
• These are difficult to calculate, and often
  underestimated, leading to higher order sizes

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Objective of Inventory Control

• To achieve satisfactory levels of customer
  service while keeping inventory costs (costs of
  ordering and carrying inventory) within
  reasonable bounds

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Processes for Inventory Management
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An effective inventory management approach will
have certain information

• A system to keep track of inventory on hand and
  on order
• A reliable forecast of demand
• Knowledge of order lead times and lead time
  variability
• Reasonable estimates of
• Holding costs
• Ordering costs
• Shortage costs
• A classification system for inventory items

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Inventory Counting Systems

• Periodic System
• Physical count of items made at periodic
  intervals
• Walgreens (1987) manager walked around weekly,
  ordered everything needed across whole store
• Perpetual Inventory System
• System that keeps track of removals from
  inventory continuously, thus monitoringcurrent
  levels of each item
• 2005 grocery store scanners (bar codes)
• 2005 RFID-based systems

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Perpetual inventory counting systems range from
low-tech to high-tech

• Two-Bin System - Two containers of inventory
  reorder when the first bin is empty
• Universal Product Code (UPC) Bar code printed
  on a label that has information about the item
  to which it is attached
• Radio Frequency Identification (RFID) Computer
  chip embedded in a label on side of package,
  cases, or pallets

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Radio Frequency Identification (RFID) used in
tags, chips, implants, and wristbands
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RFID tags are activated by RFID reader devices
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Lead time must be matched against expected demand

• Lead time time interval between ordering and
  receiving the order
• If we expect that demand will occur on a certain
  day in the future, we will need to place an order
  several days earlier, and account for
• Lead time
• Lead time variability

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Managers must estimate several types of
inventory-related costs

• Holding (carrying) costs cost to carry an item
  in inventory for a length of time, usually a year
• Annual cost of 20-40 of value (unit price) of
  an item
• Ordering costs costs of ordering and receiving
  inventory
• fixed dollar amount per order, regardless of
  order size
• Shortage costs costs when demand exceeds supply
• difficult to calculate often assumed

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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

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Cycle Counting

• A physical count of items in inventory. Counts
  are conducted periodically.
• A items counted frequently
• B items counted less frequently
• C items counted least frequently
• Cycle counting management trades off inventory
  accuracy against costs of counting
• How much accuracy is needed?
• When should cycle counting be performed?
• Who should do it?

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Example My Wifes Business (Goodies For Girls,
Inc.)

• Inventory Tracking System
• Spreadsheets
• Peachtree Accounting System
• Demand Forecast
• None highly random, very difficult to do
• Wife communicates frequently with party hostesses
  to determine potential demand
• Lead Times and Lead Time Variability
• 7 Days ( variability due to UPS)
• UPS has shipment tracking decreases uncertainty
• Costs of holding, ordering, shortage
• Holding approx 20-30 of price Ordering cost
  of wifes time Shortage shipping cost for
  mailing out product to customer
• Classification system
• In my wifes head she knows what the good
  sellers are
• Spreadsheet A/B/C classification of historical
  sales (high sellers)

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Economic Order Quantity Inventory Models
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Economic Order Quantity (EOQ) Models

• Economic order quantity (EOQ) model
• Economic production quantity (EPQ) model
• Quantity discount model

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Assumptions of EOQ Model

• Only one product is involved
• Annual demand requirements are known
• Demand is even 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
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Total Cost Under the Economic Order Quantity
Assumptions
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Cost Minimization Goal
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q)
QO
(optimal order quantity)
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Deriving the EOQ

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

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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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Example My Wifes Business (Goodies For Girls,
Inc.)

• Bottles of Soapy Water
• Yearly Demand (D) 400
• Unit Price 11
• Holding cost (H) 3
• Ordering cost (S) 50 (cost of one hour of time
  UPS shipping cost)

Thus, she orders 12 cases of 10 at a time
covering about 3 months of demand.
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Economic Production Quantity (EPQ)

• Relevant when production is 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 (EPQ) 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)
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Economic Run Size
Solving a similar equation as for EOQ, we get the
following equation for the optimal run size for
EPQ
p production or delivery rate u usage rate
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Quantity Discounts

• Volume (Per Unit) Discounts
• 1 to 49 10/unit
• 50 to 100 9/unit
• 100 and up 8/unit
• Case Discounts
• Single units 10/unit
• Case of 10 90 9/unit

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Quantity DiscountingTotal Costs with Purchasing
Cost
Quantity discounts are price reductions offered
to customers to induce them to buy in large
quantities.
The buyers goal is to select the order quantity
that will minimize total cost.
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Taking the derivative with respect to Q doesnt
change the EOQ formula
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Total Cost with Constant Carrying Costs
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Example My Wifes Business (Goodies For Girls,
Inc.)

• Shimmer Time Body Glitter
• Yearly Demand (D) 200
• Unit Price 10
• Holding cost (H) 3
• Ordering cost (S) 10
• Price is 8 for orders over 25 7 for orders
  over 50

TC(Q) (Q/2)H (D/Q)S PD
Decision Order in lots of 50
TC(37) (37/2)3 (200/37)10 8(200) 1709.50
TC(50) (50/2)3 (200/50)10 7(200) 1515.00
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Reorder Point, Reorder Quantity Inventory Models
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Reorder point models

• Goal is to place an order when the amount of
  inventory on hand is still sufficient to satisfy
  demand during the time it takes to receive that
  order (i.e., the lead time)

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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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The reorder point leaves you with lead time
inventory plus safety stock
Safety stock reduces risk of stockout during lead
time
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How do we determine the reorder point quantity?

• Calculation accounts for
• The rate of demand
• The lead time
• Demand and/or lead time variability
• Stock-out risk (safety stock)

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Assuming demand and lead time are constant (as in
EOQ)

• Reorder Point Quantity
• ROP d X LT
• d demand rate (units per time)
• LT lead time (in same units of time)
• Example
• Usage 12 order forms/day
• Lead time 7 days
• ROP (12 forms/day)(7 days) 84 order forms
• Reorder when 84 order forms are left

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When lead times are random, reorder point (ROP)
must be adjusted
The ROP based on a normal Distribution of lead
time demand
ROP expected demand during lead time safety
stock
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When we have an estimate of standard deviation of
demand during lead time

• Example
• Demand during lead time 84 forms
• sdLT 2
• ROP 84 forms zsdLT 84 1.96(2) 88 forms
• Reorder when 88 order forms are left

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When only demand is variable

• Example
• Usage 12 order forms/day sd 3
• Lead time 7 days
• ROP (12 forms/day)(7 days) 1.96(7)0.5(3) 84
  15.5 90
• Reorder when 90 order forms are left

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When only lead time is variable

• Example
• Usage 12 order forms/day
• Average Lead time 7 days sLT 1
• ROP (12)(7) 1.96(12)(1) 84 24 108
• Reorder when 108 order forms are left

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When both demand and lead time are variable

• Example
• Average Usage 12 order forms/day sd 3
• Average Lead time 7 days sLT 1
• ROP (12)(7) 1.96(7)(9) (144)(1) 84
  1.96(14.4) 84 27.7 112
• Reorder when 112 order forms are left

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Single Period Inventory Model(The Newsboy
Problem)
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Single Period Inventory Model

• Single period model model for ordering of
  perishables and other items with limited useful
  lives
• how many newspapers should a newsboy on a street
  corner stock for a specific day?
• magazines
• fresh fruits
• fresh vegetables
• seafood
• cut flowers
• commemorative t-shirts and souvenirs
• spare parts

54
Single period model balances costs of a shortage
against excess costs

• Shortage cost generally the unrealized profits
  per unit (plus loss of customer goodwill)
• Cshortage Cs revenue per unit cost per unit
• Excess cost difference between purchase cost and
  salvage value of items left over at the end of a
  period
• Cexcess Ce original cost/unit salvage
  value/unit

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Single Period Model

• Continuous stocking levels
• Demand can be approximated using a continuous
  distribution
• Identifies optimal stocking levels
• Optimal stocking level balances unit shortage and
  excess cost
• Discrete stocking levels
• Demand can be approximated using a discrete
  distribution
• Service levels are discrete rather than
  continuous
• Desired service level is equaled or exceeded

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Continuous stocking level assuming a uniform
demand distribution

• Service level represents the probability that
  demand will not exceed the stocking level

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Continuous stocking level assuming a uniform
demand distribution

• Example The movie Gigli 2 will be released
  soon. A (somewhat crazy) retailer wants to
  determine the number of commemorative t-shirts to
  stock. Based on the rousingly successful Gigli,
  we have
• Demand uniform(1, 10)
• Cost/unit 5 per t-shirt
• Revenue 10 per t-shirt
• Salvage value 1 per t-shirt
• Cs revenue/unit cost/unit 10 - 5 5
• Ce cost/unit salvage value/unit 5 - 1
  4
• Service Level Cs/(CsCe) (5)/(5 4)
  0.555
• The optimal stocking level must satisfy demand
  55 of the time
• Soptimal 1 0.55(10-1) 1 5 6 t-shirts

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Discrete stocking levels involve inverse
transform from service level to order units
Here, we have a discrete uniform distribution,
probability of each demand equals 0.10
Cumulative Probability Service Level
1.0
Cs/(CsCe) 0.55
0.5
Gigli 2 t-shirts
0
1 2 3 4 5 6 7
8 9 10
Again, the optimal decision is to stock 6 Gigli
2 t-shirts.