OPSM 301 Operations Management

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OPSM 301 Operations Management
Koç University

• Class 23
• Inventory Management

Zeynep Aksin zaksin_at_ku.edu.tr
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Recall Drivers of Supply Chain Performance
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Inventory

• The stock of any item or resource used in an
  organization
• All the money that the system has invested in
  purchasing things it intends to sell

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The Material Flow Cycle
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Types of Inventories

• Inputs - Raw Materials
• Processes - Work-in-Progress
• Outputs - Finished Goods

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Why do we need Inventory?

• Variability (uncertainty)
• Demand
• Capacity availability
• Materials and lead times
• Processing times
• Time
• Delivery lead time, production lead time
• Economies of Scale
• Purchasing, production

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Functions Provided by Inventories

• Purpose /Reason Type Cost
• Transportation Pipeline Transportation
  Costs
• Economies in Setups Cycle Stocks Setup/Order
  Costs
• Seasonality in Demand Seasonal Stock
  Smoothing Costs
• Uncertainty in Demand Safety Stock
  Shortage/Stock-out
• Costs
• Economies in Purchase Cycle Stocks Price
  Discounts
• Inflation and/or
• Price Fluctuations Speculative Stock Costs
  due to Price

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Inventory Costs

• Purchase Cost
• Ordering Cost
• Receiving and inspection
• Transportation
• Holding (Carrying) Cost
• Cost of money
• Insurance
• Taxes
• Shrinkage, spoilage, obsolescence
• Stock-out (Shortage) Cost
• Lost sales, customers etc.
• Emergency shipment costs

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The Basic Trade-off
Efficiency
Responsiveness

• Inventory Costs
• Ordering cost
• Carrying cost
• Obsolescence
• Damage

• Shortage Costs
• Lost margin
• Customer goodwill
• Lost customer

Key question How much inventory?
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Economies of Scale Inventory Management for a
Retailer

• The South Face retail shop in the John Hancock
  Tower has observed a stable monthly demand for
  its line of Gore-Tex jackets on the order of 100
  jackets per month. The retail shop incurs a
  fixed cost of 2,000 every time it places an
  order to the Berkeley warehouse for stock
  replenishment. The marginal cost of a jacket is
  200, and South Faces cost of capital is
  approximately 25.
• What order size would you recommend for The
  South Face?

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Parameters EOQ Model

• D demand rate (units per year)
• C unit production cost, not counting
  setup or inventory costs (dollars per
  unit)
• S fixed or setup cost to place an order
  (dollars)
• H holding cost (dollars per year) if the
  holding cost is consists entirely of
  interest on money tied up in inventory,
  then H iC where i is an annual interest
  rate.
• Q the unknown size of the order or lot size

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Inventory Usage Over Time
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Cost Minimization Goal
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Total Annual Cost

• Using calculus, we can take the derivative of the
  total cost function and set the derivative
  (slope) equal to zero
• We can also use economic intuition

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Find most economical order quantity
Spreadsheet for The South Face
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Deriving the EOQ
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EOQ Model if there is a lead time L
Qopt
Units on hand
ROP
Time
L
L
ROP Reorder point L Lead time (constant) Q
Economic order quantity
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EOQ Example

• Annual Demand 1,000 units
• Days per year considered in average daily demand
  250
• Cost to place an order 10
• Holding cost per unit per year 0.50
• Lead time 7 days
• Cost per unit 15

Determine the economic order quantity and the
reorder point
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An EOQ Example
Determine optimal number of needles to order D
1,000 units S 10 per order H .50 per unit
per year
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An EOQ Example
Determine optimal number of needles to order D
1,000 units Q 200 units S 10 per order H
.50 per unit per year
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An EOQ Example
Determine optimal number of needles to order D
1,000 units Q 200 units S 10 per order N
5 orders per year H .50 per unit per year
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An EOQ Example
Determine optimal number of needles to order D
1,000 units Q 200 units S 10 per order N
5 orders per year H .50 per unit per year T
50 days
Total annual cost Setup cost Holding cost
TC (5)(10) (100)(.50) 50 50 100
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Reorder Point Curve
Figure 12.5
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Reorder Point Example
Demand 8,000 iPods per year 250 working day
year Lead time for orders is 3 working days
8,000/250 32 units
ROP d x L
32 units per day x 3 days 96 units
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Economic Order Quantity (EOQ) Model

• Economic Order Quantity (EOQ) Model
• Robust, widely used
• Insensitive to errors in estimating parameters
  (40-20-2 Rule)
• 40 error in one of the parameters
• 20 error in Q
• lt 2 of total cost penalty

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An EOQ Example
Management underestimated demand by 50 D 1,000
units Q 200 units S 10 per order N 5
orders per year H .50 per unit per year T 50
days
Total annual cost increases by only 25
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An EOQ Example
Actual EOQ for new demand is 244.9 units D
1,000 units Q 244.9 units S 10 per
order H .50 per unit per year
Only 2 less than the total cost of 125 when the
order quantity was 200
TC 61.24 61.24 122.48