Inventory

Parts and materialsAvailable capacityHuman resources

© 1995 Corel Corp.© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.

© 1995 Corel Corp.

What is Inventory?

The Functions of Inventory

To ”decouple” or separate various parts of the production processTo provide a stock of goods that will provide a “selection” for customersTo take advantage of quantity discountsTo hedge against inflation and upward price changes

Inventory

Process stage

Demand Type

Number & Value Other

Raw Material WIP & Finished

Goods

Independent Dependent

A Items B Items C Items

Maintenance Dependent Operating

Inventory Classifications

Sources of Waste JIT “fights” seven types of waste

Waste of motion --excessive or unnecessary human activity Waste of waiting --jobs waiting to be processed Waste of inventory --building up unnecessary inventory

stocks Waste of conveyance --jobs being unnecessary moved Waste of processing --excessive or unnecessary operations Waste of overproduction --producing more than demanded Waste of correction (defective products) --waste due to

scrap, rework, repair, etc.

Higher costs Ordering (or setup) cost

Costs of processing, clerks’ wages etc. Holding (or carrying) cost

Building lease, insurance, opportunity, taxes etc.

Difficult to controlHides production problems

Disadvantages of Inventory

Holding Costs Breakdown(Approximate Ranges)

Category

Housing costs

Material handling costs

Labor and administration cost

Investment costs

Pilferage, scrap, and obsolescence

Cost as a % of Inventory Value

6%(3 - 10%

3%(1 - 3.5%0

3%(3 - 5%)

11%(6 - 24%)

3%(2 - 5%)

Order QuantityOrder Quantity

CostCost

Holding Cost Curve

Holding Cost CurveTotal Cost Curve

Total Cost Curve

Ordering & Setup Costs CurveOrdering & Setup Costs Curve

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

EOQ Model:Minimize the overall Costs

Inventory Holding Costs

ObsolescenceInsuranceExtra staffingInterestPilferageDamageWarehousingEtc.

Ordering Costs & Setup Costs

Order processingClerical supportClean-up costsRe-tooling costsRelocation or adjustment costs

Underline Decisions Supported by EOQ Models

Objective: Minimizing the total inventory costsHow much to order (Economic Order Quantity)When to order? (Reorder Point)How often should we place orders (Ordering Period)Others How to Take advantage of quantity discount What if the lead time and demand are not constant? Heuristics: Fixed Period Systems

Basic EOQ Model (Constant Demand and Lead Time)

Reorder Reorder Point Point (ROP)(ROP)

TimeTime

Inventory LevelInventory Level

AverageAverageInventory Inventory

(Q*/2)(Q*/2)

Lead TimeLead Time

Optimal Optimal Order Order QuantityQuantity(Q*)(Q*)

Derive the EOQ: Finding Q* that Minimizes the Total Costs

HQ

SQ

DTC

2

Total inventory cost = Order (Setup) cost + Holding cost

To minimize TC, we set the derivative of TC with respect to Q* equal to 0

02

)()(

2

H

Q

DS

dQ

TCd

Thus,

H

DSQ

2*

Optimal Order Quantity

Expected Number of Orders

Expected Time Between Orders Working Days / Year

= =× ×

= =

= =

Q*D SH

ND

Q*

TN

2

DD = Demand per year = Demand per year

SS = Setup (order) cost per order = Setup (order) cost per order

HH = Holding (carrying) cost = Holding (carrying) cost

EOQ Model Equations: How much to Order

Reorder Point: When to Order?

When there is lead time between order and delivery, we need to identify the reorder point to avoid out of stock.This provides answer for the second inventory “When to order?”ROP = (Demand per day)(Lead time for a new order in days) = d L Working Days / Year

=dD

EOQ ExampleElectronic Assembler, Inc. has to order 2920 TX5 circuit boards per year. The

ordering cost is $80 per order; and the holding cost per unit per year is $50. The purchase price is $28. The items can be delivered in 5 days. The company would like to reduce its inventory costs by determining the optimal number of circuit boards to obtain per order. The conditions of ordering and inventory handling satisfy the assumptions of the EOQ model.

Annual demand D = 2,920 unitsDaily demand d = 2,920/365=8 unitsHolding cost H = $50 per unit per yearOrdering cost S = $80 per orderPurchase price P = $28 per unit Lead time LT = 5 days

Answer the following questions with detailed calculations and explanation:

1. Optimal quantity per order (EOQ):2. Annual total relevant costs (optimal):3. Annual total costs (optimal):4. Number of orders per year: 5. Inventory cycle time (Nd=365 working days per year): 6. Reorder Point (ROP):

Allows partial receipt of material Other EOQ assumptions apply

Suited for production environment Material produced, used immediately Provides production lot size

Lower holding cost than EOQ model

Production Order Quantity Model

POQ Model


TimeTime


AverageAverageInventoryInventory

Lead TimeLead Time

Optimal Optimal Order Order QuantityQuantity(Q*)(Q*)

POQ Model Inventory Levels

TimeTime


Production Production Portion of CyclePortion of Cycle

Max. Inventory Max. Inventory Q·(1- d/p)Q·(1- d/p)

Q*Q*

Supply Supply BeginsBegins

Supply Supply EndsEnds

Inventory level with no demandInventory level with no demand

Demand portion of cycle Demand portion of cycle with no supplywith no supply

D = Demand per year

S = Setup cost

H = Holding cost

d = Demand per day

p = Production per day

POQ Model EquationsOptimal Order Quantity

Setup Cost

Holding Cost

= =

-

= *

= *

=

Q

H* dp

Q

D

QS

p*

1

(

0.5 * H * Q -d

p1

)-d

p1

( )

2*D*S

( )Maximum inventory level

Answers how much to order & when to orderAllows quantity discounts Reduced price when item is

purchased in larger quantities Other EOQ assumptions apply

Trade-off is between lower price & increased holding cost

Quantity Discount Model

Quantity Discount ModelHow Much to Order?

Lowest cost not in Lowest cost not in discount rangediscount range

Order Order QuantityQuantity

Total Total CostCost

Quantity which would Quantity which would be orderedbe ordered

TC for Discount 2

TC for Discount 2

Quantity to Quantity to earn earn

Discount 2Discount 2

Discount 2 Discount 2 PricePrice

Quantity to Quantity to earn earn

Discount 1Discount 1

TC for Discount 1

TC for Discount 1

Discount 1 Discount 1 PricePrice

TC forTC for

No Discount

No Discount

Initial PriceInitial Price

Allow demand and lead time to vary Follows normal distribution Other EOQ assumptions apply

Consider service level & safety stock Service level = 1 - Probability of stockout Higher service level means more safety

stock More safety stock means higher ROP

Probabilistic Models

Probabilistic ModelsWhen to Order?


OptimalOptimal Order Order

QuantityQuantity XX

Safety Stock (SS)Safety Stock (SS)

TimeTime


Lead TimeLead Time

SSSSROPROP

Service Service LevelLevel P(Stockout)P(Stockout)

Place Place orderorder

Receive Receive orderorder

FrequencyFrequency

0

20

40

60

80

100

0 50 100% of Inventory Items% of Inventory Items

% Annual $ Usage% Annual $ Usage

AABB CC

Class % $ Vol % ItemsA 80 15B 15 30C 5 55

ABC Classification: Pareto Principle (Critical few and trivial many)

Orders placed at fixed intervals Inventory brought up to target amount Amount ordered varies

No continuous inventory count Possibility of stockout between intervals

Useful when vendors visit routinely Example: P&G representative visits every

2 weeks

Heuristics: Fixed Period Model

TimeTime

Inventory LevelInventory Level Target maximumTarget maximum

PeriodPeriod PeriodPeriodPeriodPeriod

Heuristics: Fixed Period Model

Traditional: inventory exists in case problems ariseJIT objective: Eliminate redundant inventoryJIT requires Small lot sizes Low setup time Containers for fixed number of parts

JIT inventory: Minimum inventory to keep system running (lean but agile)

Implementing JIT via Agile Inventory Management

Scrap

Work in process inventory level(hides problems)

Unreliable Vendors

Capacity Imbalances

Lowering Inventory Reduces Waste

Scrap

Reducing inventory revealsproblems so they can be solved.

Unreliable Vendors

Capacity Imbalances

WIP

Lowering Inventory Reduces Waste

To Lower Inventory, Reduce Lot Sizes

Time

Inventory Level

Lot Size 200

Lot Size 80

Average inventory = 100

Average inventory = 40

Average inventory = (Lot size)/2

…Which Increases Inventory Costs

Lot Size

Cost

Holding CostTotal Cost

Setup Cost

Optimal Lot Size

SmallerLot Size

Unless Setup Costs are Reduced

Lot Size

Cost

Holding CostTotal Cost

Setup Cost

Original optimal lot size

New optimal lot size

Steps to Reduce Setup Time (Honda Assembly Line)

Initial Setup Time

Separate setup into preparation, and actual setup, doing as much as possible while the

machine/process is running (save 30 minutes)

Move material closer and improve material handling (save 20

minutes)Standardize and improve tooling

(save 15 minutes)

90 min

60 min

45 min

25 min

15 min

Use one-touch system to eliminate adjustments (save 10

minutes)Training operators and

standardizing work procedures (save 2 minutes)

Step 1

Step 2

Step 3

Step 5 13 minStep 4

Reducing Lot Sizes Increases the Number of Lots

Small lots increase flexibility to meet customer demands

Strategies for eliminating wasteand for eliminating waiting

A A B B B C

JIT Small Lots

Time

A A B B B C

Freeze Part of the Schedule

Flexibility between Nissan plant and Dealers

Five day before delivery: 100% flexibility

Four day before: Freeze number of each model

Three day before: Freeze change color

Two day: Freeze major options

One day before: Freeze minor options

Economy & Finance

Inventory