Inventory Control

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Inventory Control
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Lecture Topics

• Week 1 Introduction to Production Planning and
  Inventory Control
• Week 2 Inventory Control Deterministic Demand
• Week 3 Inventory Control Stochastic Demand
• Week 4 Inventory Control Stochastic Demand
• Week 5 Inventory Control Stochastic Demand
• Week 6 Inventory Control Time Varying Demand
• Week 7 Inventory Control Multiple Echelons

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Lecture Topics (Continued)

• Week 8 Production Planning and Scheduling
• Week 9 Production Planning and Scheduling
• Week 12 Managing Manufacturing Operations
• Week 13 Managing Manufacturing Operations
• Week 14 Managing Manufacturing Operations
• Week 10 Demand Forecasting
• Week 11 Demand Forecasting
• Week 15 Project Presentations

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Inventory in the US Economy
98.60
billion
122.10
Farm
billion
(7.9)
Other
(9.8
424.60 billion
Manufacturing
(33.9)
290.40 billion
Wholesale
(23.2)
316.00 billion
Retail (25.2)
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Inventory Types
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Inventory Types

• Raw Materials
• Work-in-process (WIP)
• Finished goods inventory (FGI)

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Inventory Location
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Inventory Location

• Manufacturing Facility
• In-Transit
• Warehouse
• Retailer
• Customer

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Benefits of Inventory
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Benefits of Inventory

• Reduces ordering, setup transportation costs
  (economies of scale)
• Buffer against demand fluctuations
• Buffer against supply fluctuations
• Supply shortages
• Variability in supply lead times

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Benefits of Inventory (continued)

• Buffer against price fluctuations
• Benefits from quantity discounts
• Protects production capacity
• Allows production smoothing
• Reduces managerial complexity (eliminates the
  need for coordination)
• Can increase demand

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The Cost of Inventory
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The Cost of Inventory

• Tied up capital
• Warehousing cost
• Deterioration
• Obsolescence
• Demand shortfall
• Quality defects
• Changes in raw material prices
• Changes in product design specifications

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• What if demand uncertainty and variability are
  eliminated?

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• What if demand uncertainty and variability are
  eliminated?
• What if replenishment lead times are made
  insignificant?

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• What if demand uncertainty and variability are
  eliminated?
• What if replenishment lead times are made
  insignificant?
• What if ordering setup costs are made
  negligible?

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• What if demand uncertainty and variability are
  eliminated?
• What if replenishment lead times are made
  insignificant?
• What if ordering setup costs are made
  negligible?
• What if production capacity is never a
  constraint?

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Characteristics of Inventory Systems

• Demand
• Constant
• Time varying
• Stochastic
• Supply lead time
• Deterministic
• Stochastic
• Load-dependent
• Review
• Continuous review
• Periodic review

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Characteristics of Inventory Systems (continued)

• Excess Demand
• Backordering
• Lost sales
• Impatient customers
• Item substitution
• Capacity
• Unlimited
• Limited
• Deterministic
• Stochastic

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Characteristics of Inventory Systems (continued)

• Number of items customer classes
• Single item
• Multiple items
• Single customer class
• Multiple customer classes
• Inventory quality
• Perishability
• Obsolescence
• Imperfect yield

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Cost Measures

• Holding cost (h)
• Capital cost
• Taxes and insurance
• Deterioration, spoilage, obsolescence
• Ordering (setup) cost (A)
• Purchasing (production) costs (c)
• Shortage cost (p)
• backordering cost
• lost sale cost

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Example

• h ic (cost per unit per time period)
• 28 cost of capital
• 2 taxes and insurance
• 6 storage cost
• 1 breakage cost
• 37 total interest charge (i) per year
• If c 100, then h ic 37

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The Economic Order Quantity (EOQ) Model
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Assumptions of the Basic Model

• Demand occurs continuously over time with a
  constant rate and constant time between
  consecutive orders
• Inventory can be replenished instantaneously
• There are no capacity limits or limits on the
  size of replenishment orders
• A replenishment order incurs a fixed ordering (or
  setup) cost
• Multiple products can be analyzed independently
  of each other
• No backorders are allowed

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Notation

• D demand rate (units per unit time)
• c unit purchase/production cost (dollars per
  unit)
• A fixed cost to place an order (dollars)
• h holding cost (dollars per unit per unit
  time) if the holding cost consists entirely of
  interest on money tied up in inventory, then hic
  where i is an interest rate.
• Q the size of the order (a decision variable)

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Inventory versus Time
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Inventory versus Time
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Costs

• Holding cost

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Costs

• Holding cost
• Ordering/setup cost

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Costs

• Holding cost
• Ordering/setup cost
• Production cost
• c per unit

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Total Cost

• Total cost per unit time
  

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Total Cost

• Total cost per unit time
  
• Total cost per unit

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Economic Order Quantity
hQ/2
Y(Q)
AD/Q
Q
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The Economic Order Quantity
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The Economic Order Quantity
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Optimal Cost

• Optimal average cost per unit
• Optimal average cost per unit time (e.g., per
  year)

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Sensitivity to Order Quantity

• Ordering and holding cost from using Q
• Ratio

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Sensitivity to Order Quantity

• Ordering and holding cost from using Q
• Ratio
• Example
• Q' 2Q, then the ratio of the actual to
  optimal cost is (1/2)2 (1/2) 1.25

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Sensitivity to Order Quantity

• Large deviations from the optimal order quantity
  lead to relatively small deviations from the
  optimal cost.

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Order Quantity versus Order Interval

• Order Interval
• Let T represent time between orders, then
• Total cost
• Optimal Order Interval

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Some Limitations of the EOQ Model

• Demand is deterministic and constant
• Instantaneous replenishments
• Ordering costs are constant and independent of
  order size
• No accounting for interactions among multiple
  items
• No backordering

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Extensions

• Non-zero order replenishment lead times
• Non-zero safety stocks
• Finite supply capacity
• Backordering

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Non-Zero Replenishment Lead Times
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Non-Zero Replenishment Lead Times

• If L is the lead time and r is the reorder
  point, then r DL
• A non-zero lead time has no effect on Q or Y(Q)

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Non-Zero Safety Stocks

• If ss is the safety stock, then
• A non-zero safety stock affects Y(Q) but has no
  effect on Q