ie305 ch 4 inventory and economic order quantity

1

IE 305 - BUS 307IE 305 - BUS 307IE 305 - BUS 307IE 305 - BUS 307

CHAPTER 4CHAPTER 4

Inventory and Economic Order Quantity Inventory and Economic Order Quantity (EOQ)(EOQ)

2

INVENTORYINVENTORYINVENTORYINVENTORY

Adequate system to keep track of materials Adequate system to keep track of materials receivedreceived

Adequate, secure storage facilities and effective Adequate, secure storage facilities and effective requisition proceduresrequisition procedures

Inventory records must be kept up-to-date.Inventory records must be kept up-to-date. Physical inventory is essential to counter human Physical inventory is essential to counter human

mistakes or mislaid parts.mistakes or mislaid parts. The more the inventory is worth, the more The more the inventory is worth, the more

frequently physical checks should be made.frequently physical checks should be made.

3

INVENTORYINVENTORYINVENTORYINVENTORY

4

Why Keep Inventory?

Example 1. Ajay’s Orange Juice consumption

Costs:

Risks:

1.8L carton / 1 each week 300ml carton/ 1 each day

Refrigeration

Capital tied up (interest cost)

Low volume surcharge

Travel to shop each day

May go bad May want 2 on some days

OPTION 1 OPTION 2

5

Example 2. Hospital blood bank

Setup time involved in procuring blood

- find a donor- check for infection- test for blood type

Patient cannot wait !

Why Keep Inventory?

6

Example 3. Computer manufacture

Alternatives:(a) fewer workers on speaker line

=> lose mass production efficiency(b) run speaker line for short periods

=> inventory

computer assembly line

speaker assembly line

100 computers/hr

800 speakers/hr

Why Keep Inventory?

7

Example 4. Retail

4.1. Empty shop less attractive to customers

4.2. Out of stock loss of sale, loss of goodwill

Problem: cost of holding inventorycapital is held up (interest)space is occupied (rental)

insuranceproduct obsolescence/decay

Why Keep Inventory?

8

Components of Inventory Control Models

1. Ordering costshow much does it cost to order a batch of materials

2. Holding costshow much does it cost to store materials

3. Shortage penalty (out-of-stock penalty)what is the estimated loss on an out-of-stock event

4. Revenuewhat is the cash made by selling an item

5. Salvage costvalue of item at the end of its shelf life

6. Discount rateto account for the time value of capital

9

Inventory Control and EOQInventory Control and EOQInventory Control and EOQInventory Control and EOQ

The primary questions of inventory control are The primary questions of inventory control are how much to order at any one time and when to how much to order at any one time and when to order.order.

Economic order quantity is the amount of goods Economic order quantity is the amount of goods whose total procurement and carrying costs are whose total procurement and carrying costs are at a minimum.at a minimum.

10

Relationship between time and quantity of inventoryRelationship between time and quantity of inventory

Inventory Control and EOQInventory Control and EOQInventory Control and EOQInventory Control and EOQ

11

Time Relationship to Inventory QuantityTime Relationship to Inventory QuantityTime Relationship to Inventory QuantityTime Relationship to Inventory Quantity

The ideal inventory (EOQ) quantity will The ideal inventory (EOQ) quantity will minimize total costminimize total cost Carrying costCarrying cost Procurement costProcurement cost

12

Time Relationship to Inventory QuantityTime Relationship to Inventory QuantityTime Relationship to Inventory QuantityTime Relationship to Inventory Quantity

The ideal inventory (EOQ) quantity will The ideal inventory (EOQ) quantity will minimize total costminimize total cost Carrying (Holding) costCarrying (Holding) cost Procurement (Order) costProcurement (Order) cost

13

Carrying CostsCarrying CostsCarrying CostsCarrying Costs

Those costs that are associated with ordering materials Those costs that are associated with ordering materials from the ordering cost through receiving, inspection and from the ordering cost through receiving, inspection and storagestorage

The cost component consists of:The cost component consists of: Storage costsStorage costs MaintenanceMaintenance Clerical tasksClerical tasks InsuranceInsurance ObsolescenceObsolescence TaxesTaxes

14

Carrying Costs (contd.)Carrying Costs (contd.)Carrying Costs (contd.)Carrying Costs (contd.)

Relation between storage cost and quantityRelation between storage cost and quantity

15

Procurement CostsProcurement CostsProcurement CostsProcurement Costs

Comprises requisition cost, follow-up tasks, and Comprises requisition cost, follow-up tasks, and payment of invoicespayment of invoices

Varies inversely with the inventoryVaries inversely with the inventory Total procurement costs vary depending on the Total procurement costs vary depending on the

frequency of ordering.frequency of ordering. The two costs vary in opposite directionsThe two costs vary in opposite directions

Large lots minimize procurement costs but Large lots minimize procurement costs but increases storage costs.increases storage costs.

16

Procurement (Order) Costs (contd.)Procurement (Order) Costs (contd.)Procurement (Order) Costs (contd.)Procurement (Order) Costs (contd.)

Relation between procurement costs and quantityRelation between procurement costs and quantity

17

EOQ DeterminationEOQ DeterminationEOQ DeterminationEOQ Determination

Relation between total variable costs and quantityRelation between total variable costs and quantity

18

Order QuantityOrder Quantity

Annual CostAnnual Cost

Holding CostHolding Cost

Order (Setup) CostOrder (Setup) Cost

EOQ Model EOQ Model EOQ Model EOQ Model

19




Total Cost CurveTotal Cost Curve



20






Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)


21

Background and Definition of EOQBackground and Definition of EOQBackground and Definition of EOQBackground and Definition of EOQ

The approach is to build a model of an idealized The approach is to build a model of an idealized inventory system and calculate the fixed order inventory system and calculate the fixed order quantity that minimizes total costs. This optimal order quantity that minimizes total costs. This optimal order size is called the economic order quantity (EOQ).size is called the economic order quantity (EOQ).

EOQ, or EOQ, or Economic Order QuantityEconomic Order Quantity, is defined as , is defined as the optimal quantity of orders that minimizes total the optimal quantity of orders that minimizes total variable costs required to order and hold variable costs required to order and hold inventory. inventory.

22

How to use EOQ in a Company?How to use EOQ in a Company?How to use EOQ in a Company?How to use EOQ in a Company?

How much inventory should we order each month?

The EOQ tool can be used to model the amount of inventory that we should order each month.

23

How EOQ Works

The Principles Behind EOQ: The Holding Costs

Keeping inventory on hand

Interest

Insurance

Taxes

Theft

Obsolescence

Storage Costs

24

How EOQ Works

The Principles Behind EOQ: The Procurement Costs

Primarily the labor costs associated with processing the order:

Ordering and requisition

A portion of the freight if the amounts vary according to the size of the order

Receiving, inspecting, stocking

Invoice processing

25

How EOQ Works

The Total Cost Formula

Total Cost = Purchase Cost + Order Cost + Holding Cost

26

How EOQ Works


This represents the unchanging fixed costs

P = Purchase cost per unitR = Forecasted monthly usage

27

How EOQ Works


This represents the variable order costs

P = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)Q = The number of units ordered

28

How EOQ Works


This represents the variable holding costs

P = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)Q = The number of units orderedF = Holding cost factor

29

How EOQ Works

The EOQ Formula

Total Cost Formula

Taking the derivative of both sides of the equation and setting equal to zero to find the minimum value of the function, one obtains:

30






Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)


31

The result of differentiation

How EOQ Works

The EOQ Formula

The Economic Order Quantity

32

How EOQ Works

The EOQ Formula

Review and Summary of the EOQ Formula

P = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)F = Holding cost factor

33

Real Life Example:

Coca Cola Sales at Gas Station

34

Real Life Example:

Coca Cola Sales at Gas Station

35

Real Life Example:

First, Recall the EOQ Equation:

P = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)F = Holding cost factor

36

Real Life Example:

Next let’s identify the correct variables…

37

Real Life Example:


Forecasted Amount

38

Real Life Example:


Ordering Costs

39

Real Life Example:


Cost per Unit

40

Real Life Example:


Holding Cost Factor

41

Real Life Example:

R = Annual demand

C = Fixed ordering cost

P = Cost per case

F = Holding Cost Factor

42

Real Life Example:

R = 5200

C = $10 per order

P = $2

F = 20% of value of inventory per year

EOQ =2 (10) (5200)

(2 )(.20)510 Cases

43

When to Order: The Reorder PointWhen to Order: The Reorder PointWhen to Order: The Reorder PointWhen to Order: The Reorder Point

Without safety stock:Without safety stock:

With safety stock:With safety stock:

days/weeksintimelead

unitsindemandlydaily/week

unitsinpointreorderwhere

L

d

R

dLR

unitsin stock safety where

SSSSdLR

44

EOQ Example 2EOQ Example 2EOQ Example 2EOQ Example 2

Weekly demand = 240 unitsWeekly demand = 240 units No. of weeks per year = 52No. of weeks per year = 52 Ordering cost = $50Ordering cost = $50 Unit cost = $15Unit cost = $15 Annual carrying charge = 20%Annual carrying charge = 20% Lead time = 2 weeksLead time = 2 weeks

a)a) Q=?Q=?

b)b) TC=?TC=?

c)c) R=?R=?

45

EOQ Example 2 SolutionEOQ Example 2 SolutionEOQ Example 2 SolutionEOQ Example 2 Solution

yearunitsD /480,1224052

yearperunitperH 3$152.0

unitsH

DSQ 64598.644

3

50480,1222

unitsdLR

HQ

SQ

DTC

4802240

$1,934.945.96744.967

32

64550

645

480,12

2

46

Assumption for a basic modelAssumption for a basic modelAssumption for a basic modelAssumption for a basic model

The demand is known exactly, is continuous and is The demand is known exactly, is continuous and is constant over time.constant over time.

All costs are known exactly and do not vary.All costs are known exactly and do not vary. No shortages are allowed.No shortages are allowed. Lead time is zero – so a delivery is made as soon as Lead time is zero – so a delivery is made as soon as

the order is placed.the order is placed.

49

Other assumptions implicitly in the modelOther assumptions implicitly in the modelOther assumptions implicitly in the modelOther assumptions implicitly in the model

We can consider a single item in isolation, so we We can consider a single item in isolation, so we cannot save money by substituting other items or cannot save money by substituting other items or grouping several items into a single order.grouping several items into a single order.

Purchase price and reorder costs do not vary with the Purchase price and reorder costs do not vary with the quantity ordered.quantity ordered.

A single delivery is made for each order.A single delivery is made for each order. Replenishment is instantaneous, so that all of an order Replenishment is instantaneous, so that all of an order

arrives in stock at the same time and can be used arrives in stock at the same time and can be used immediately.immediately.

50

Some stock levels are not recorded continuously but Some stock levels are not recorded continuously but are checked periodically, perhaps at the end of the are checked periodically, perhaps at the end of the week.week.

Then an unexpectedly large demand might reduce Then an unexpectedly large demand might reduce stocks well below the reorder level before they are stocks well below the reorder level before they are checked.checked.

51

Another problem appears with large stocks, such as Another problem appears with large stocks, such as chemical tanks, coal tips or raw materials, where the chemical tanks, coal tips or raw materials, where the stock level is only known approximately. Then the stock level is only known approximately. Then the reorder level might be passed without anyone reorder level might be passed without anyone noticing.noticing.

52

QUESTIONS???QUESTIONS???

ie305 ch 4 inventory and economic order quantity

Documents