Part I: Continuous Review System

a$.$ EOQ $($Economic Order Quantity$)$:

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$=$

$2$

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EOQ$=$

H

$2$DS

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$$

$=$

$0\mathrm{.}27$

$\backslash$times

$11\mathrm{.}70$

H$=0\mathrm{.}27\backslash$times $11\mathrm{.}70$

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$$

$$

$=$

$2$

$\backslash$times

$90$

$\backslash$times

$54$

$0\mathrm{.}27$

$\backslash$times

$11\mathrm{.}70$

EOQ$=$

$0\mathrm{.}27\backslash$times $11\mathrm{.}70$

$2\backslash$times $90\backslash$times $54$

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Calculate EOQ.

b$.$ Average Time Between Orders:

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$=$

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Average Time Between Orders$=$

D

EOQ

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c$.$ Safety Stock and Reorder Point:

Z$\backslash$text$\{-$score $($for $80\%$ service level$)\}=0\mathrm{.}84$

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$$

$=$

$0\mathrm{.}84$

$\backslash$times

$3$

$\backslash$times

$15$

Safety Stock$=0\mathrm{.}84\backslash$times

$3$

$$

$\backslash$times $15$

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$$

$$

$=$

$3$

$\backslash$times

$90$

$+$

Safety Stock

Reorder Point$=3\backslash$times $90+$Safety Stock

d$.$ Annual Holding Cost and Annual Ordering Cost for Lot Size of $500$:

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$$

$=$

$500$

$2$

$\backslash$times

$0\mathrm{.}27$

$\backslash$times

$11\mathrm{.}70$

Annual Holding Cost$=$

$2$

$500$

$$

$\backslash$times $0\mathrm{.}27\backslash$times $11\mathrm{.}70$

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$$

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$$

$=$

$90$

$500$

$\backslash$times

$54$

Annual Ordering Cost$=$

$500$

$90$

$$

$\backslash$times $54$

e$.$ Annual Cost Saved by Shifting to EOQ:

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$=$

$($Annual Cost with Lot Size $500)$

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$($Annual Cost with EOQ$)$

Annual Cost Saved$=($Annual Cost with Lot Size $500)($Annual Cost with EOQ$)$

f$.$ Impact of Demand Forecast Error on Total Costs:

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$=$

$($Cost with Actual Demand $60)$

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$($Cost with Forecasted Demand $90)$

Total Costs$=($Cost with Actual Demand $60)($Cost with Forecasted Demand $90)$

g$.$ Impact of Ordering Cost Reduction on Total Costs:

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$=$

$($Cost with Actual Demand $60)$

$$

$($Cost with Reduced Ordering Cost $6)$

Total Costs$=($Cost with Actual Demand $60)($Cost with Reduced Ordering Cost $6)$

Part II: Periodic Review System

a$.$ Additional Safety Stock Needed:

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$=$

$0\mathrm{.}84$

$\backslash$times

$($

$5$

$+$

$3$

$)$

$\backslash$times

$15$

Additional Safety Stock$=0\mathrm{.}84\backslash$times

$(5+3)$

$$

$\backslash$times $15$

b$.$ Target Inventory at Each Review Period:

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$$

$$

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$$

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$$

$$

$=$

$90$

$\backslash$times

$5$

$+$

Additional Safety Stock

Target Inventory$=90\backslash$times $5+$Additional Safety Stock

c$.$ Order Quantity at the Periodic Review:

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$=$

Target Inventory

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Current Inventory

Order Quantity$=$Target Inventory$$Current Inventory