im lecture 7

Inventory ManagementDr. Najam Akber

Inventory Control

Economic Order QuantityDetermining how much to order

EOQ Assumptions

1. The demand and consumption is constant

2. All costs do not vary

3. Shortages do not take place

4. Lead time is zero

5. Items cannot be ordered in groups

6. No quantity discounts are available

7. A single delivery is made for each order

8. Replenishment is instantaneous

Inventory Control

EOQ Assumptions

Demand is constant

Consumption is constant(also called cycle time)

Part 03: Inventory Control and Forecasting

Inventory ControlEOQ Graphical Representation

Order Quantity

Co

sts

Total Cost

Ordering Cost

Holding Cost

Unit Cost

Optimal order quantity (EOQ)

Lowest cost


Inventory ControlEOQ Formulae

How much to order

When to order

Qo = EOQ RC = Reordering Cost

D = Demand per unit time To = Optimal cycle length

HC = Holding cost per item per unit time






Total Costs (TC) = Unit Costs x Demand per unit time + Variable Costs

= UC x D + VC

Variable Costs (VC) =

Total Optimal Costs (TCo) = UC x D + VCo

Optimal variable costs (VCo) = HC x Qo


Inventory ControlEOQ Working Example

JD Tradings buys 6,000 units of an item every year with a unit cost of $30. It costs $125 to process an order and arrange delivery, while holding and storage costs amount to $6 a year for each unit held. What is the best ordering policy for the item?

Calculate: Qo, To, VCo, TCo

Answers

EOQ = 500 units Optimal ordering time = 1 month

VCo = $3000 a year TCo = $183,000 a year


Inventory ControlWorking Example Graphical Representation

500 units

1 month 1 month 1 month


Inventory ControlWorking Example Graphical Representation

Order Quantity

Co

sts

Total Cost

Ordering Cost

Holding Cost

Unit Cost

EOQ = 500 units

?


Inventory ControlSensitivity analysis of EOQ formula

Assume the following modified values:

Demand = 6000 units a yearUnit cost = $30 a unitReorder cost = $125 an orderHolding cost = $7 a unit a year

The EOQ comes out to be 462.91 units in this case

Will a supplier give you 462.91 or even 463 units?

Most probably NO.

It could either be 450 units or 500 units

How sensitive the EOQ formula is to certain variations


Inventory ControlSensitivity analysis of EOQ formula

Now we calculate the variable costs for 450 units in one order:

How sensitive the EOQ formula is to certain variations

RC x D

Q

HC x Q

2VC = +

125 x 6000

450

7 x 450

2+= = $3241.67

RC x D

Q

HC x Q

2VC = +

125 x 6000

500

7 x 500

2+= = $3250.00

Orders of 450 units:

Orders of 500 units:

So an ordering quantity of 2.8% below optimal increases the variable costs by only 0.04%


Inventory ControlCorrespondence in variation of values in the EOQ formula


Inventory ControlEconomic Order Quantity

Uncertainty in Demand

VC increases more sharply in case of underestimates


Inventory Control

Economic Order QuantityDetermining how much to order

EOQ Assumptions

1. The demand and consumption is constant

2. All costs do not vary

3. Shortages do not take place

4. Lead time is zero

5. Items cannot be ordered in groups

6. No quantity discounts are available

7. A single delivery is made for each order

8. Replenishment is instantaneous



Uncertainty in Costs

Ordering costs are usually not easy to calculate.

What values of RC should be used in the EOQ formula in cases where RC is not known?



Uncertainty in Costs

Demand per week = 10 unitsWhat are the holding and ordering costs?

1010

RC = 5 HC

HC = RC/5


Inventory ControlFinite Lead Time

1 2 3 4 5 6 7 8 9

100

200

300

400

500

Weeks

Units

Lead Time = 1 week

LT

ROL = 220 units

Cycle Time

EOQ



ROL = LT x D

Rickety Radiators consumes piping joints at the rate of 100 units a week. They have calculated an EOQ of 250 units. If the lead time is one week, the best ordering policy is to order _______ units whenever the stock level comes down to _______ units.

250

100


Inventory Control

??

?

?

1

23

4

Finite Lead Time

1

2

3

4

250 units

2.5 weeks

1 week

100 units

Inventory ControlEOQ Graphical Representation

Order Quantity

Co

sts

Total Cost

Ordering Cost

Holding Cost

Unit Cost

Optimal order quantity (EOQ)

Lowest cost


How much to order

When to order








Total Costs (TC) = Unit Costs x Demand per unit time + Variable Costs

= UC x D + VC

Variable Costs (VC) =

Total Optimal Costs (TCo) = UC x D + VCo

Optimal variable costs (VCo) = HC x Qo

Inventory Control

Reflection Development of a basic inventory management

system

Two bin system

Three bin system

Biggest issue is the compatibility between known figures and actual condition of stocks

If one is not sure about the item demand or any of the costs then it is better to take a higher value because effect of error on EOQ values are lower on the higher side

Inventory Control

1 2 3 4 5 6 7 8 9

100

200

300

400

500

Weeks

Units

Lead Time = 1 week

LT

ROL = 220 units

Cycle Time

EOQ


ROL = LT x D

Rickety Radiators consumes piping joints at the rate of 100 units a week. They have calculated an EOQ of 250 units. If the lead time is one week, the best ordering policy is to order _______ units whenever the stock level comes down to _______ units.

250

100

What happens when the lead time is 3 weeks?

Inventory ControlLead time is greater than the cycle time

Cycle Time (T)

1st 2nd 3rd 4th 5th 6th 7th ..

Cycle Time (T) = 4 weeks Lead Time (LT) = 6 weeks

Lead Time(LT)


Cycle Time (T)

1st 2nd 3rd 4th 5th 6th 7th ..

Lead Time(LT)

nth

cycle(n+1)th

cycle

n T < LT < (n + 1) T


When LT < T Lead Time Demand = Reorder Level

LT x D n x QoROL =

When LT > T

ROLLT x D =

LT x D ROL= n x Qo+

Lead Time Demand = Reorder Level + Stock on order

im lecture 7

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