Notes

1
Notes

• Quiz This Friday
• Covers 13 March through today

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MGTSC 352

• Lecture 21
• Inventory Management
• AE Noise exampleMethods for finding good
  inventory policies 1) simulation2) EOQ LTD
  models
• Using EOQ for the Distribution Game
  Multi-Echelon Systems

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Why Keep Inventory?

• Seasonality (anticipated variation)
• Provide flexibility (unanticipated variation)
  a.k.a.
• Economies of scale
• Price speculation (not an ops reason)
• Something to work on
• NDR,JP

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Inventory By Where it IS

• Raw Materials
• Finished Goods
• Work in Process
• Or, with apologies to PS, One mans ceiling is
  another mans floor.

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Inventory
Time
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Acquisition Costs (pg. 142)

• No matter what the inventory policy,
• acquisition costs Demand X Cost
• They dont change,
• So they dont go in the model
• (Unless you get quantity discounts, then it
  matters.)

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Order Costs

• Number of orders per year ?
• (3695 VCRs / year)/(80 VCRs / order)
• 46.2 orders / year
• Total order cost per year ?
• (46.2 orders / year)(30 / order)
• 1385.63 / year
• Total Order Costs S D/Q

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Holding Costs (pg. 143)

• Minimum inventory ? 0 for now
• Later Safety Stock
• Maximum inventory Q (SS)
• Average inventory ?
• Q/2 (80)/2 40 VCRs
• Total holding cost per year ?
• (40 VCR-years)(37.5 / VCR / year) 1500 / year
• Total Holding Costs HQ/2

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EOQ Economic Order Quantity Model
pg. 144

• Given demand is constant
• Find the Q that minimizes total cost
• Total cost acquisition cost order cost
  carrying cost shortage cost

• Total relevant cost order cost carrying cost

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EOQ Derivation
pg. 147

• S order cost (/order)
• H carrying cost (/item/year)
• D demand (units/year)

• Q order quantity
• N number of orders per year
• Iavg average inventory

Relevant cost order cost carrying
cost RC S ? N H ? Iavg RC(Q) S ? D /
Q H ? Q / 2
Note you can change year to day, week, or any
other time unit, as long as you are
consistent Common mistake inconsistent time units
To Excel
11
EOQ Formula
pg. 147
Relevant cost ordering cost carrying
cost RC S ? N H ? Iavg RC(Q) S ? D /
Q H ? Q / 2
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The magic part (optional)
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pg. 147

• Using EOQ for AE Noise YNOS XD
• D 10.12 VCRs/day,
• S 30/order,
• H 0.10/VCR/day
• ? Q SQRT(2?10.12?30/0.10) 77.9
• ? round to Q 78
• N 10.12/78 0.13 orders/day 47.4
  orders/year
• Order every 365/47.4 8 days
• Relevant cost
• RC(Q) S ? (D/Q) H ? (Q/2)
• 30 ? (10.12/78) 0.10 ? (78/2)
• 3.90 3.90
• 7.80 / day 2,847 / year

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• Common mistake using inconsistent time units
• D 10.12 VCRs/day, S 30/order, H
  37.5/VCR/year
• ? Q SQRT(2?10.12?30/37.5) 4
• Off by (77.9 4)/77.9 95
• Will not be worth a lot of part marks

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More on EOQ Economies of Scale
Pg. 149

• The Capital Health Region operates four
  hospitals. Presently each hospital orders its
  own supplies and manages its inventory. A common
  item used is a sterile intravenous (IV) kit, with
  a weekly demand of 600 per week at each hospital.
  Each IV kit costs 5 and incurs a holding cost
  of 30 per year. Each order incurs a fixed cost
  of 150 regardless of order size. The supplier
  takes one week to deliver an order. Currently,
  each hospital orders 6,000 kits at a time.
• Question 1 Could costs be decreased by ordering
  more often?
• Question 2 Would it make sense to centralize
  inventory management for the four hospitals?

Fictional data
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Analysis for one Hospital

• D 600 / week (600 / week) ? (52 weeks/year)
  31,200 / year
• S 150 / order
• H 0.3 ? 5 1.50 / kit / year
• Q SQRT(2 ? D ? S / H) 2,498 2,500
• Costs
• Q 6,000 S ? D / Q H ? Q / 2 780 4,500
  5,280
• Q 2,500 S ? D / Q H ? Q / 2 1,872
  1,875 3,747
• 29 savings

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Analysis for one Hospital

• D 600 / week (600 / week) ? (52 weeks/year)
  31,200 / year
• S 150 / order
• H 0.3 ? 5 1.50 / kit / year
• Q SQRT(2 ? D ? S / H) 2,498 2,500
• Close your course pack
• Active Learning How do we change the analysis if
  inventory management were centralized for the
  four hospitals?

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Analysis for four hospitals managed together

• D 4 ? 31,200 / year 124,800 / year
• S 150 / order
• H 1.50 / kit / year
• Q SQRT(2 ? 124,800 ? 150 / 1.5) 4,996 5,000
• Costs
• Each hospital operated independently 4 ? 3,747
  14,988 / year
• All four together S ? D / Q H ? Q / 2
  3,744 3,750 7,494 / year
• 50 savings
• Quadrupling demand doubles the optimal order
  quantity and doubles the total relevant cost

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Four hospitals managed together

• Costs
• Each hospital operated independently 4 ? 3,747
  14,988 / year
• All four together S ? D / Q H ? Q / 2
  3,744 3,750 7,494 / year
• 50 savings
• Quadrupling demand doubles the optimal order
  quantity and doubles the total relevant cost

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• Determining ROP with EOQ model
• Lead time 5 days
• Demand during lead time (5 days) ? (10.12 VCRs
  / day) ? 51 VCRs
• ? Set ROP 51 VCRs

Problem this calculation assumes constant
demand. May lead to shortages too frequently
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What happens to Holding Cost when we Increase ROP?
Pg. 149

• EOQ constant demand, zero safety stock
• ROP avg. demand during lead time
• Iavg (min max)/2 (0Q)/2 Q/2
• Holding cost H ? Q / 2
• If we add safety stock SS, then
• ROP avg. demand during lead time SS
• Iavg Q/2 min SS Q/2
• Holding cost H ? (SS Q / 2)

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Pg. 152
How Shortages Happen
Inventory
Active learningHow could we have avoided the
shortage?
Time
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Inventory
The demand during the lead time is uncertain.
Here are 4 possibilities.
Well see how to pick ROP so as to provide a
specified fill rate to Excel
Time
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LTD Recap

• LTD worksheet in AE Noise workbook
• Purpose vary ROP (and Q, if desired) and see
  what happens to the fill rate
• LTD-exotic version can vary the lead time
• Useful for comparing suppliers that provide
  different lead times

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Simulation versus EOQ
pg. 151
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Back to the Distribution Game Can we use EOQ
here?
Pg. 158
Retailer
A multi-echelon system
Retailer
Supplier
Warehouse
Retailer
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Using EOQ for a two-echelon system

• Upper echelon
• Use warehouse holding cost rate
• Ignore higher cost of holding inventory at
  retailers
• Lead time 15 (supplier ? warehouse) 5
  (warehouse ? retailer) 20 days
• Lower echelon
• Use incremental retailer holding cost rate
• Lead time 5 days
• Coordination warehouse order size should be a
  multiple of the sum of the retailer order sizes

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Data
Assume open 250 days / year

• Supplier to warehouse transit time 15 days
• Warehouse to retailer transit time 5 days
• Demand per retailer 500 per year
• Selling price 100/unit
• Purchase price 70/unit
• Supplier to warehouse order cost 200
• Warehouse to retailer order cost 2.75
• Warehouse holding cost 10/unit/year
• Retailer holding cost 12/unit/year

To Excel
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Upper echelon Use warehouse holding cost rate
(Ignore higher cost of holding inventory at
retailers) Lead time 15 (supplier ? warehouse)
5 (warehouse ? retailer) 20 days
Upper echelon
Retailer
Retailer
Supplier
Warehouse
Retailer
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Lower echelon Use incremental retailer holding
cost rate retailer holding cost rate
warehouse holding cost rate Lead time 5 days
Lower echelon
Retailer
Retailer
Supplier
Warehouse
Retailer
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Coordination

• Suppose each retailer uses QLower 20. If all
  retailers order at once, the total is 60.
• Active learning you are the warehouse manager.
  Knowing the retailer order sizes, how would you
  pick the warehouse order size?

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Using EOQ for a 2-echelon system the details

• Upper echelon
• DUpper 3 ? DRetailer
• SUpper SWarehouse
• HUpper HWarehouse
• LTUpper LTSupplier ? Warehouse LTWarehouse ?
  Retailer
• ROPUpper DUpper ? LTUpper
• Lower echelon
• DLower DRetailer
• SLower SRetailer
• HLower HRetailer - HWarehouse
• LTLower LTWarehouse ? Retailer
• ROPLower DLower ? LTLower
• Coordination QUpper n ? SUM(QLower)
• Choose n (an integer) and QLower to minimize
  total cost for the whole system

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Data
Assume open 250 days / year

• Supplier to warehouse transit time 15 days
• Warehouse to retailer transit time 5 days
• Demand per retailer 500 per year
• Selling price 100/unit
• Purchase price 70/unit
• Supplier to warehouse order cost 200
• Warehouse to retailer order cost 2.75
• Warehouse holding cost 10/unit/year
• Retailer holding cost 12/unit/year

To Excel