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1. Inventory Management - 60 Min1. Inventory Management - 60 Min

2. JIT - 30 Min2. JIT - 30 Min

3. Case Discussion - 30 Min3. Case Discussion - 30 Min

4. “Final” Problems - 60 Min4. “Final” Problems - 60 Min

Agenda: Agenda:

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Types of Inventory Raw material Work-in-progress Maintenance/repair/operating supply Finished goods

What is Inventory?What is Inventory?

Functions of inventory?

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The Functions of InventoryThe Functions of Inventory

To protect against lost sales - stock-outs To ”decouple” or separate various parts of the

production process To provide a stock of goods that will provide a

“selection” for customers To take advantage of quantity discounts To hedge against inflation and upward price changes

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Divides on-hand inventory into 3 classes A class, B class, C class

Basis is usually annual $ volume $ volume = Annual demand x Unit cost

Policies based on ABC analysis Develop class A suppliers more Give tighter physical control of A items Forecast A items more carefully

ABC AnalysisABC Analysis

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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

Classifying Items as ABCClassifying Items as ABC

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Inventory CostsInventory Costs Holding costsHolding costs - associated with holding or

“carrying” inventory over time Ordering costsOrdering costs - associated with costs of

placing order and receiving goods Setup costsSetup costs - cost to prepare a machine or

process for manufacturing an order Excess at EOLExcess at EOL - mark down, scrap Stock-out costsStock-out costs - a negative cost of inventory.

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Fixed order-quantity models Economic order quantity Production order quantity Quantity discount

Probabilistic models

Fixed order-period models

Inventory ModelsInventory Models

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Order QuantityOrder Quantity

Annual CostAnnual Cost

Holding Cost Curve

Holding Cost CurveTotal Cost Curve

Total Cost Curve

Order (Setup) Cost CurveOrder (Setup) Cost Curve

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

EOQ ModelEOQ ModelHow Much to Order?How Much to Order?

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Optimal Order Quantity

Expected Number of Orders

Expected Time Between Orders Working Days / Year

Working Days / Year

= =× ×

= =

= =

=

= ×

Q*D SH

ND

Q*

TN

dD

ROP d L

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

dd = Demand per day = Demand per day

LL = Lead time in days = Lead time in days

EOQ Model EquationsEOQ Model Equations

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EOQ ModelEOQ ModelWhen To OrderWhen To Order

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*)

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Answers how much to order and when to order

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 ModelProduction Order Quantity Model

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POQ Model Inventory LevelsPOQ Model Inventory Levels

Inventory LeveInventory Levell

TimeTimeSupply Supply BeginsBegins

Supply Supply EndsEnds

Production portion of cycleProduction portion of cycle

Demand portion of cycle with no Demand portion of cycle with no supplysupply

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D = Demand per year

S = Setup cost

H = Holding cost

d = Demand per day

p = Production per day

POQ Model EquationsPOQ Model Equations

Optimal 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

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Answers how much to order & when to order

Allows 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 ModelQuantity Discount Model

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Quantity Discount ModelQuantity Discount Model

Total cost = Setup cost + Holding cost + product cost

TC = (D/Q)(S) + (QH)/2 + PD

D = Annual Demand Q = Order QuantityS = Set or order costH = Holding cost P = Price

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Quantity Discount ModelQuantity Discount Model

TC = (D/Q)(S) + (QH)/2 + PD

Unit Cost Quantity Set Up Cost Holding Cost Product Cost Total Cost4.80$ 1,000 245.0$ 480.0$ 24,000.0$ 24,725.0$ 4.75$ 2,000 122.50$ 950.0$ 23,750.0$ 24,822.5$

Demand = 5,000 Set Up cost = 49$ Inventory cost + 20%

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Answer how much & when to order Considers Stock-out Costs Allow demand 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 ModelsProbabilistic Models

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ROP Demand Safety Stock Holding Cost Stockout Cost Total Cost50 50 0 -$ 960$ 960$ 50 60 10 50$ 240$ 290$ 50 70 20 100$ 100$

Units Probability50 0.360 0.270 0.1

Holding cost = 5$ Stock-out cost = 40$ Orders per year 6

Probabilistic Model ExampleProbabilistic Model Example

1. Stock out = 10(.2)($40)6 + 20(.1)($40)(6) = $9602. Stock out = 10(.1)($40)6 = $240

1.2.

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Answers how much to order 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 calls every 2 weeks

Fixed Period ModelFixed Period Model

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TimeTime

Inventory LevelInventory Level Target maximumTarget maximum

PeriodPeriod PeriodPeriodPeriodPeriod

Fixed Period ModelFixed Period ModelWhen to Order?When to Order?

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Waste is ‘anything other than the minimum amount of equipment, materials, parts, space, and worker’s time, which are absolutely essential to add value to the product.’

— Shoichiro Toyoda President, Toyota

Introductory QuotationIntroductory Quotation

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Management philosophy of continuous and forced problem solving

Supplies and components are ‘pulled’ through system to arrive where they are needed when they are needed.

JIT: Attacks waste

Anything not adding value to the product (From the customer’s perspective)

Exposes problems and bottlenecks caused by variability Achieves streamlined production

What is Just-in-Time?What is Just-in-Time?

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Overproduction Waiting Transportation Inefficient processing Inventory Unnecessary motion Product defects

Types of WasteTypes of Waste

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Push versus PullPush versus Pull

Push system: material is pushed into downstream workstations regardless of whether resources are available

Pull system: material is pulled to a workstation just as it is needed

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ResultsResults Queue and delay reduction, speeds throughput, frees

assets, and wins orders Quality improvement, reduces waste and wins orders Cost reductions, increases margin or reduces selling

price Variability reductions in the workplace, reduces

waste and wins orders Rework reduction, reduces waste and wins orders

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Incoming material and finished goods involve waste

Buyer and supplier form JIT partnerships JIT partnerships eliminate

Unnecessary activities In-plant inventory In-transit inventory Poor suppliers

SuppliersSuppliers

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Few Nearby Repeat business Analysis to enable desirable suppliers to become or stay

price competitive Competitive bidding mostly limited to new purchases Suppliers encouraged to extend JIT to their suppliers

Characteristics of JIT Partnerships Characteristics of JIT Partnerships SuppliersSuppliers

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Characteristics of JIT Partnerships Characteristics of JIT Partnerships QuantitiesQuantities

Steady output rate Frequent deliveries in small-lot quantities Long term contract agreements Minimal paperwork Delivery quantities fixed for whole contract term Little or no permissible overage or underage Suppliers package in exact quantities Suppliers reduce their production lot sizes or store

unreleased material

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Help suppliers to meet quality requirements Close relationship between buyers’ and suppliers

quality assurance people

Characteristics of JIT Partnerships Characteristics of JIT Partnerships QualityQuality

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Characteristics of JIT Partnerships Characteristics of JIT Partnerships ShippingShipping

Scheduling of inbound freight Gain control by use of company-owned or contract

shipping and warehousing

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Goals of JIT partnershipsGoals of JIT partnerships

Elimination of unnecessary activitiesElimination (reduction) of in-plant inventoryElimination (reduction) of in-transit inventoryElimination of poor suppliers

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JIT objective: Reduce movement of people and material Movement is waste!

JIT requires Work cells for product families Moveable or changeable machines Short distances Little space for inventory Delivery directly to work areas

LayoutLayout

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Process Layout Work Cell

SawSaw

LatheLathe

GrinderGrinder

HeatHeatTreatTreat

LatheLathe

Lathe

Lathe SawSaw

HeatHeatTreatTreat

GrinderGrinder

GrinderGrinder

PressPress

PressPress 1

1

2

3

45

2

6

SawSaw

PressPress

Work Cell versusWork Cell versus Process Layout Process Layout

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Traditional: inventory exists in case problems arise

JIT objective: Eliminate inventory JIT requires

Small lot sizes Low setup time Containers for fixed number of parts

JIT inventory: Minimum inventory to keep system running

InventoryInventory

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JIT Scheduling TacticsJIT Scheduling Tactics Communicate the schedule to suppliers Make level schedules Freeze part of the schedule Perform to schedule Seek one-piece-make and one-piece-move Eliminate waste Produce in small lots Use kanbans Make each operation produce a perfect part

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Japanese word for card Pronounced ‘kahn-bahn’ (not ‘can-ban’)

Authorizes production from downstream operations ‘Pulls’ material through plant

May be a card, flag, verbal signal etc. Used often with fixed-size containers

Add or remove containers to change production rate

KanbanKanban

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All activities involved in keeping equipment in working order

Done to prevent failure JIT requires

Scheduled & daily PM Operator performs PM

Knows machines Responsible for product quality

Preventive Maintenance (PM)Preventive Maintenance (PM)

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Milling

Painting

RivetBattens

Insert Studs

MountHinges

GlueApp.

Final Assem.

Tent

Plywood Stock

F/R Stock

Rear & Front Assembly FlowRear & Front Assembly Flow

B - 2,500

B - 1,500

B - 500

B - 1,500

B - 1,000