Re Order Level

8/12/2019 Re Order Level

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Reorder Level Additional assumption: Lead time is known and constant

No need to carrying stock from one cycle to the next

So each order should be scheduled to arrive as existing stock runsout

Reorder level = demand during lead time = lead time x demand per unit timeROL = LT x D

Reorder level = demand during lead time = lead time x demand per unit timeROL = LT x D

Revisit Ex 1 : Carpet Sell. Given that product lead time is 5 days. Calculate reorderlevel (ROL)1


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Reorder Level with Longer Lead TimeWhen lead time is longer than the stock cycleThere is always one order outstanding.

Example:when it is time to place order B, there is one order, Aoutstanding and due to arrive before B.

The stock on hand plus the outstanding order must be enough

to last until B arrive or equal the lead time demand

Stock on hand Stock on order + = LT x DROL

ROL Stock on order -= LT x D

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Reorder Level with Longer Lead TimeWhen lead time is very longSeveral orders are outstanding at anytimeWhen lead time is between n and n +1 cycle length

n x T < LT < (n+1) x TThere are n orders

outstanding

ROL Stock on order -Lead time demand=n x Q o-LT x D=

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Discussion Questions

What are the benefit of short lead times? How canthese be achieved in practice?

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IM 322Inventory Management

Chapter 4Chapter 4 Models for Known Demand

Textbook:

Donald Waters, Inventory Control and Management, 2nd

ed-6-


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Chapter OutlineExtension of EOQ by relaxing

some assumptions1. Discount in the unit cost /

price from suppliers2. Increasing cost with higher

quantity3. Finish replenishment rate4. Back orders

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Price Discount from SuppliersCosts vary with the quantity ordered (Q)

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Price Discount from Suppliers

Price discount for higherquantity orders

P = Unit price of itemExample:

Quantity (Q) Unit Price

0 - 100 $10

101 - 200 $8

201 or more $6

Q op t

holding cost

Reordering cost

I n v e n

t o r y

c o s

t ( $ )

Q (P 2 ) = 100 Q (P 3 ) = 200

TC (P 3 = $6 )

TC (P 2 = $8 )

TC (P 1 = $10 )

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Procedure for FindingBest Order Size

Start

1. Take the next lowestunit cost

2. Find the lowest pointusing EOQ equation

3. Is this pointvalid?

4. Calculate the cost atthe break point

5. Calculate the cost atthis valid minimum

6. Compare the costs ofall the points considered

7. Find the lowest costand corresponding Q

End

YES

NO

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Ex 1a: Sweatshirt in Bookstore

Order Size Discount

1-299

300-499500-799800 and up

0%

2%4%5%

The university bookstore purchases sweatshirts with schoollogo from a vendor. The vendor sells the sweatshirts to thestore for $38 a piece. The cost to bookstore for placing an

order is $120, and the annual carrying cost is estimated as$9.5 per unit. 1700 sweatshirts are estimated to be soldduring the year. The vendor has offered the bookstore thefollowing volume discount:

What is an optimal order quantity?12


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Price Discount from Suppliers:

Finding the lowest valid cost

HC

D RC Q

o

=

2

iio UC I

D RC Q

=

2

Holding cost can be expressed aproportion of the unit cost (I)

For each unit cost (UC i), the minimumpoint of the cost curve comes with Q oiQoi for each curve could be either

Valid minimum: within the range of validorder quantities for this particular unit cost

Invalid minimum: falls outside the valid order

range for this particular unit cost

Case 2: All costs are constant except the unit cost (orunit price from supplier) and holding cost

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Ex 1b: Sweatshirt in BookstoreEx 1b: Sweatshirt in BookstoreThe university bookstore purchases sweatshirts with schoollogo from a vendor. The vendor sells the sweatshirts to the

store for $38 a piece. The cost to bookstore for placing anorder is $120, and the annual carrying cost is 25% of thecost of sweatshirt. 1700 sweatshirts are estimated to be soldduring the year. The vendor has offered the bookstore the

following volume discount:

What is an optimal order quantity?

Order Size Discount

1-299

300-499500-799800 and up

0%

2%4%5%

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Rising cost with larger quantity

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Ex 2 Rising delivery costKwok Cheng Ho makes a range of high

quality garden ornaments. On average

day he uses 4 tons of fine grain sand.This sand costs $20 a ton to buy, and$1.90 a ton to store for a day.

Deliveries are made by modified lorries thatcarry up to 15 tons, and each delivery ofa load or part load costs $200.

Find the cheapest way to ensurecontinuous supplies of sand

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Finishreplenishmentrate

ProductionProductionand demandand demand

(PT)(PT)

DemandDemandonlyonly(DT)(DT)TT

Production quantityProduction quantity

Demand duringDemand duringproduction intervalproduction interval

Maximum inventoryMaximum inventory

I n v e n

t o r y

L e v e

l

I n v e n

t o r y

L e v e

l QQ

TimeTime

IImaxmax

P D

D

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CASE 1


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CASE 3


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CASE 3


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CASE 3


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CASE 1, CASE 2, CASE 3


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EX 2

Documents

Re Order Level