1 Inventory Control: Part 2 - Lot-Size Inventories.

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Inventory Control:Part 2 - Lot-Size Inventories

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Types of Inventories By Function

- Lot-Size (Cycle or Replenishment)

- Instantaneous (Purchase)

- Non-Instantaneous (Produce)

- Safety (Fluctuation or Buffer)

- Anticipation (Seasonal)

- Transportation (Pipeline)

- Hedge (Beyond Scope of Class)

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Lot-Size Stocks: Instantaneous Receipts

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Lot-Size Stocks: Instantaneous

LetQ = Order QuantityA = Usage (Forecast Demand)S = Order (Setup) Cost per Orderc = Purchase Price per Item i = Cost as % of PurchaseH = Holding Cost per Unit = ic

TC = Order + Holding = S(A/Q) + ic(Q/2)

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Lot-Size Stocks: Instantaneous, Example

Joe the plumber has gone into the designer plunger business. He buys basic plungers from a well-known supplier in Washington D.C. and customizes them. He maintains a huge raw materials plunger inventory in Defiance, Ohio. Demand averages about 1,000 items per month; holding costs per month are 50% of purchase costs; and order costs are $30. Joe buys plungers for $12. How much and how often should Joe order? Determine total relevant costs.

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Lot-Size Stocks: Instantaneous, Example

A = 1000 Plungers per Month

S = $ 30 per Order

c = $ 12 per Item

i = 50% of Purchase Costs

H = (.50)($12) = $ 6 per Unit per Month

TC = Order + Holding = (30000/Q) + (6)(Q/2)

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Lot Size Stocks: Instantaneous, Example

Q Order Holding Total (TC) 50 $600 $150 $750100 300 300 600150 200 450 650200 150 600 750

Best Q or Q* is Apparently 100

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Lot Size Stocks: Instantaneous, Example

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Lot Size Stocks: Instantaneous

Let Holding = Order Cost at Best Answer

(ic)Q/2 = S(A/Q) Q2

ic = 2AS Q* = (2AS/ic)0.5 = EOQ (1)

TC* = (2ASic)0.5 (2)

N*= A/Q* = # of Orders (3)

T* = 1/N* = Reorder Time (4)

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Cycle Stocks: Instantaneous Example

A = 1000 Items per Month S = $30 per Order c = $12 per Item

i = 50% of Purchase Costs H = (.50)($12) = $6 per Unit per Month

Q*(EOQ) = (2AS/ic)0.5 = (2x1000x30/6)0.5 = 100 TC* = (2ASic)0.5 = (2x1000x30x6)0.5 = $600 N* = A/Q* = 1000/100 = 10

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Lot-Size Stocks: Instantaneous, Price Discounts

A distributor buys an average of 1,600 Snortoff Vodka bottles a year. Bottles cost $0.98 if orders are at least 800 bottles; otherwise bottles cost $1.00. Order costs are $5.00 and holding costs are 10% of purchase per year. Determine the economic order quantity.

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Lot-Size Stocks: Price (or Quantity) Discounts

Let x = Price Break Point

If Q < x, We Have Regular Price c1

Q x, We Have Discounted Price c2

Example Problem

If Q < 800, Regular Price c1 = $1.00 Q 800, Discounted Price c2 = $0.98

Also: A = 1600 per Year, S = $5, i = 10%

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Lot-Size Stocks: Price Discounts

TC = Order + Holding + Purchase

TC = S(A/Q) + ic(Q/2) + cA (1)

Q* = (2AS/ic)0.5 (2)

TC* = (2ASic)0.5 + cA (3)

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Lot-Size Stocks, Price Discount Rules

1. Compute Q* Using Equation (2) and c2. If Answer is x, Stop. You Have Answer.

2. Calculate TC* Using Equation (3) and c1. Calculate TCx Using Equation (1), c2, and Q = x.

3. If TCx TC*, Q* = x.

4. If TC* < TCx, Calculate Q* from Equation (2) Using c1.

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Lot-Size Stocks, Quantity Discount Example

(1) Q* = (2AS/ic)0.5 = [(2x1600x5)/(.10x.98)]0.5 = 404 404 < 800, So Go On!

(2) TC* = (2ASic)0.5 + cA =

[(2x1600x5x.1x1)]0.5+(1x1600)=$1640

TCx = S(A/Q) + ic(Q/2) + cA = (5)(1600)/800) + (.1x.98)x(800/2) + (.98)(1600) = $1617

(3) $1617 < $1640, So Q* = x = 800

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Lot-Size Stocks: Non-Instantaneous Receipts

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Lot-Size Stocks:Non-Instantaneous

LetQ = Run SizeA = Forecast Demand (or Usage Rate = d)S = Setup Cost per OrderH = Holding Cost per Item

p = Production/Delivery Rate

Tp= Time Machine On IMAX is Maximum Inventory

TC = Setup + Holding

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Lot-Size Stocks:Non-Instantaneous

Suppose p = 100 per Hour, d = 50 per Hour, Tp = 2 Hours

What is Q? What is IMAX?

Note that Q = pTp (100x2) or Tp (Time On) = Q/p

Also, IMAX = (p - d)Tp (50x2) = (p - d)(Q/p) = [1-(d/p)]Q

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Lot-Size Stocks:Non-Instantaneous

TC = Setup + Holding

TC = S(A/Q) + H(IMAX/2) TC = S(A/Q) + (1-(d/p)) (HQ/2) (1)

Q* = [(2AS/H) (p/(p-d))]0.5 (2)

TC* = [2ASH (1-(d/p))]0.5 (3)

N* = (A/Q*) (4)

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Incorporating Q* (Or EOQ) into MRP

We Can Use EOQ as Lot Size in MRP Creates Excessive Inventory Due to “Lumpy”

Demand Let Q* = EOQ = 250

Week 1 2 3 4 5 6 7 8 9 10 Total

Net Requirements 100 50 150   75 200 55 80 150 30 890

Planned Order Receipts 250   250     250     250    

Ending Inventory (Available) 150 100 200 200 125 175 120 40 140 110 1360

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Period Order Quantity (POQ)

POQ = Q* / A = T* A is Often in Weeks POQ Normally Reduces Inventory and

Number of Orders When Compared with EOQ Ordering

E.g. POQ = 250 / 89 = 2.81 3 Weeks

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POQ Example

Week 1 2 3 4 5 6 7 8 9 10 Total

Net Requirements 100 50 150   75 200 55 80 150 30 890

Planned Order Receipts 300       330     260      

Ending Inventory (Available) 200 150 0 0 255 55 0 180 30 0 870

POQ Reduces Inventory and Number of Orders.

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