design of pull systems - university of michigan -...

©Izak Duenyas, 2002-2007

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Design of Pull Systems

Izak Duenyas

John Psarouthakis Professor of Manufacturing Management and Professor of Operations Management

The University of Michigan Business School


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Course Agenda

• Opening Discussion – Inventory, Variability, Push, and Pull

• Understanding Different Types of Pull Systems • Learning to Levelize through EPEI • Kanban Calculations and Implementations • Extending Pull to Purchased Parts • Bullwhip Effect and How to Counter it


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Pull System Design Opening Discussion

• Goals – Understand the role of inventory and inventory

management in today’s factory – Compare and contrast the push and pull approaches to

production control – Understand how and why pull systems work – Realize the important advantages that can be obtained

through pull systems – Acquire the skills necessary to implement pull

production control in a wide variety of manufacturing situations to


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Smooth Flow


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Buffered Flow


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Dam Variability!


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Cycle Time Variability

• Natural variability – operators – machines – material – environment

• Variability due to poor quality – scrap – rework

• Unexpected outages (during jobs) – power loss – machine failure – lack of material

• Scheduled outages (between jobs) – set-up operations


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Factory Variability

• Why do factories need buffers? – To protect against variability

• Buffers can take three forms – Inventory – Capacity – Lead time


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Why do we need inventory?

To Protect Against Variability


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Reasons for Inventory

• Variability Management • Protection from Uncertainty • Economies of Scale • Transportation • Smoothing of Demand


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Disadvantages of Inventory

• Higher costs – Item cost – Ordering cost

• Costs of forms, clerks’ wages, receiving costs, etc. – Holding cost

• Building lease, insurance, taxes. • Excess staff • Likelihood of damage • Obsolescence or shelf-life issues

• Harder to control • Hides production problems


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Organizational Learning The Sea of Inventory


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Organizational Learning Learning from experience


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Types of Inventory

• Raw Material • Components • Subassemblies • Work-in-process (WIP)

Finished Goods


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Materials Management

• Inventory Control – How much should I order? – When should I place my order?

• Production Control – How much should I make? – When should I start making it?


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Information

Material Danger!

Push Production Control


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“Improvements” to Push Production Control

• Better Forecast? • Better Computer Algorithm? • Can we infer anything about MRP and Related

Approaches? – MRP-II – ERP


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Inside MRP: The Underlying Logic

• Intent and Original Purpose – Plan material requirements – Determine what is needed and when it is needed – Explosion calculus

• Other applications – Schedule deliveries – Schedule the shop floor – For these purposes MRP is fundamentally flawed


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Information

Material

Pull Production Control


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Pull Production Control

• Material is delivered only to replenish what has been used.

• Production is authorized only to replenish what has been used.


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Push and Pull Definitions

• Push Systems: schedule work releases.

– inherently due-date driven – control release rate,

observe WIP level

• Pull Systems: authorize work releases.

– inherently rate driven – control WIP level, observe

throughput


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Push vs. Pull Mechanics

(Exogenous) Schedule

Production Process

PUSH PULL

(Endogenous) Status

Production Process

Job Job

Push systems are inherently make-to-order.

Pull systems are inherently make-to-stock.


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Push and Pull Line Schematics

Stock Point

Stock Point . . .

Pure Push (MRP)

Stock Point

Stock Point . . .

Stock Point

Stock Point . . .

Pure Pull (Kanban)

CONWIP

…

Full Containers Authorization Signals


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Continuum of Flow

Push or

Scheduled

Supermarket Pull

(Kanban)

FIFO Sequenced

Flow

Continuous Flow

(1 pc Flow)

Physically linked process steps & c/t’s can be balanced

Upstream process replenishes what customer process took away

Queue or lane between unlinked processes. Keep product in FIFO seq.. Less space req’d than supermarket.

Sequenced Pull

(Golfball)

Process FIFO

Traditional Batch & Queue

Ideal State of Lean

Main line signals a feeder process what to produce

Each process has own schedule, sequence, & batch size


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Traditional Production System for Batch (Mass Production)

• Push type production • Job shop type production

Characteristics:

• Production Instruction - all processes 1 wk/1 mo. Buckets - MRP (material requirements planning)

• Production instruction - processed by hand or computer • Build-up inventory between processes • Long production lead time

Process “A”

Process “B” Shipping Customer

Production Control

N-2 N-1 N

Order


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“A” Type Production System • Pull or Fill-up system

Characteristics:

• Keep store of all product variations • Kanban is used as production

instruction to replace what has been withdrawn (type & quantity)

• Formal production instruction to one location (shipping)

Conditions:

• High volume - High frequency

Merits:

• Short lead time from order to ship

• Minimal inventories • Easily adjusts to changes in

demands • Work site is self-managed • Standardize conveyance

operations

Process “1”

Process “2” Shipping Customer

MA MB

MD MC

A’ B’ C’ D’

A’ B’

D’ C’ C’ C’


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“B” Type Production System • Sequential Production System

Characteristics:

• Pull system - kanban • Produce in order of sequential plan • Store in straight line (keep order of

production) • Production instruction given at beginning

of process (when kanban arrives) • No finished goods inventory • Fixed number in-process stock

Conditions:

• High volume - Low frequency • Low volume - Low frequency • Lead time is required for production

Merits:

• No finished inventory required for low frequency production

• Fixed production lead time

Process 1 “H”

Process 2 “F” Shipping Customer

Production Control

Order

ME MF

MH MG

G’ E’

Frequent withdrawal (takt time)

E F G H

Sequential Production Plan


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“C” Type Production System

Characteristics:

• Products using type A-B system are produced on same line

• Inventory of all variations of product for A type - only one unit of product for B type

• Kanban used to produce what has been withdrawn

Conditions:

• High frequency products produced by fill-up system

• Low volume products produced by sequential plan

Merits:

• No need to keep inventories for low frequency products

• High frequency products can meet changing production demands because of short lead time

Process 1

Process 2 Shipping Customer

MA MB

MD MC A’

B’ C’ D’

A’ B’

D’ C’

Production Control

• Mixture of A type - B type

Order

ME MF

MH MG E

F G H F E


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Advantages of Pull Systems

• Low Unit Cost: – high throughput – low inventory – little rework

• High External Quality: – high internal quality – pressure for good quality – promotion of good quality

(e.g., defect detection)

• Good Customer Service: – short cycle times – steady, predictable

output stream

• Flexibility: – avoids committing jobs

too early – tolerates mix changes

(within limits) – encourages floating

capacity


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The Magic of Pull

• Pulling Everywhere?

You don’t never make nothin’ and send it no place. Somebody has to come get it.

• – Hall 1983

• WIP Cap: – Kanban – WIP cannot exceed number of cards – “WIP explosions” are impossible

WIP


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Pull System Design

Understanding Kanban Systems


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Information and Material Flow

• Pull System Design – Mechanisms for Conveying Information – Mechanisms for Conveying Material

• Types of systems – Floor markings – Bins – Cards – Electronics – Other


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Kanban ~ means Visual Signal

There are two basic ways to Signal:

1. In-Process Kanban ~ No Card a visual signal to pace the movement of products in a flow manufacturing process. Signal = Space or Container

2. Material Kanban ~ Card a visual signal to replenish materials consumed in a lean production process. Signal = Card


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Kanban - Two Types

Kanban

Production Instruction Signal Kanban (Lot Production)

Withdrawal (Move) External Supplier


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Supermarket Pull System Customer process goes to supermarket

and withdraws what it needs when it needs it Supplying process produces to replenish what was withdrawn

Purpose: - A way to control production between flows - Controls production at supplying process without trying to schedule

Supermarket Part

“PRODUCTION” Kanban

“WITHDRAWAL” Kanban

Withdrawn Part


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Tammy

350 per hour

1.0 hour set-up

Stamping

800 pieces per hour

0.75 hour set-up

Clara

De-burr Operation

Eva

Assembly 1500

pieces per day

Empty

Full

Suppliers

Signal to produce more Parts

Finished Product

Marketplace

Raw Material

Marketplace

Stamped Parts

Marketplace

Information Flow

Material Flow

Produce, Inspect, Sort

Purchased Items

Marketplace

Pull

Pull

Pull Pull

Pull

Material Flow Information Flow

A Pull System Using Bins


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Example - “No Cards”

Supermarket

Paint Weld

Production KB Signal = Empty Slot

Withdrawal KB Signal = Paint Schedule


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Levels of Withdrawal/ Production Instruction

1. Piece by Piece (the ultimate goal)

2. Kanban by Kanban

3. Lot by Lot (general purpose equipment, ie. Stamping, Molding, etc.)

4. Batch (Mass Production)


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Containers to Convey Material and Information

• Containers Can Be Used to Convey Material – Specified quantity in each container – Number of containers determines amount of WIP – Depends on product type and specific situation

• Containers Can Be Used to Convey Information – The container is the signal: empty means send more – Not lost or misplaced as readily as cards are – Information can be written on the container itself – Empty containers can be placed in a designated location

for refill


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Number of Containers

• Where – K = number of containers – D=Demand rate – CT = Container lead time—time to refill the container – Q = Bin quantity – SF=Safety Factor – For safety factor, a common sense thing to do is to use

%swing—percentage difference between common maximum and average.


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• Assume – Demand = 20 pieces per hour – Cycle time=1 hour and 15 minutes – Bin Quantity = 4 pieces – Safety factor=1 ( I.e, %swing is around 100%, which

means maximum demand can be as much as twice the average)


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• We would use 15 bins for this system


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The Science Behind the Safety Factor

• The term D(CT)/Q corresponds to the average number of bins you will use up in the time that an empty bin comes back filled up.

• The demand and the cycle time may not be deterministic, i.e., there may be some randomness associated with them.

• Therefore we need to consider the standard deviation of bins used up while one bin comes back full from the supplying process.


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The Science Behind Safety Factor

• The bin number equation can be rewritten as K= m+zs Where m=the average number of bins used up while

an empty bin comes back filled up; m=D(CT)/Q. s=the standard deviation of the number of

bins used up while an empty bin comes back filled up.

z=3 for a shortage probability of 1/1000. z=2.3 for a shortage probability of 1/100. The zs term is SAFETY INVENTORY.


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The Kanban card

• Conveyance Kanban – Controls movement of material

• Production Kanban – Controls production of material

• Purchasing Kanban – Controls the procurement of production material

• Signal Kanban – Controls movement or production of a batch of material


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Withdrawal Card Rules

• The withdrawal card specifies the kind and amount of material to convey

• When a container is first accessed, the card is placed in the card mailbox

• The card is taken to the upstream marketplace and attached to a full container

• The full container with the card attached is taken to the point of use.


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Pull System Design Inbound and Outbound

Fabrication Assembly Outbound Inbound


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Pull System Design The Withdrawal Card



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Withdrawal and Production Card Relationship

• Consider process A (upstream) and B (downstream).

• When process B uses a part from its inbound marketplace for production, a withdrawal kanban is issued. This kanban is taken to the outbound marketplace for process A. A unit is taken and a production kanban is issued to produce another unit in process A.


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Withdrawal Card Calculations

• Where – Kw = number of cards or containers – D = Demand – CT = Withdrawal lead-time – Q = Bin quantity – SF=Safety Factor

• Notice how formula is exactly the same as before!


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Withdrawal Lead-time

• Total time required for – Waiting in card mailbox – Moving to the upstream marketplace – Moving back to point of use (attached to a full

container)


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Pull System Design The Production Card



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Production Card Rules

• The production card authorizes production • When a full container is taken from the outbound

marketplace, the production card is removed and placed in a production card mailbox

• The production card is placed on an empty bin • Production is authorized to produce enough material

to fill the bin


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Production Card Calculations

• Where – KP = number of cards or containers – D = Demand – CT = Production lead-time – Q = Bin quantity – SF=Safety Factor


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Levels of Withdrawal/ Production Instruction

1. Piece by Piece (the ultimate goal)

2. Kanban by Kanban

3. Lot by Lot (general purpose equipment, ie. Stamping, Molding, etc.)

4. Batch (Mass Production)


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When is a Card Needed?

Piece by Piece Kanban by Kanban Lot by Lot


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1) Piece by Piece Application Single Product

1 Product is withdrawn from single product market. Withdraw card may or may not be used. Usually, empty space at process B lineside is the Kanban.

2 Single product market. Usually no more than one to three products in market.

3 Withdrawal by Process B releases a “Signal” which serves as Production Instruction Kanban. Signal can be anything, disk, light, etc. Shows permission to produce.

4 Process A receives “signal” and produces one more product.

(Produces only one product without variation) Flow of Production

Use of card not necessary. All three elements of Kanban are known. What - Process “A” produces only one product. How Many - only one piece. Permission - given by signal.

Process A

Process B

1

3

2 4


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2) Standard Application (Kanban by Kanban)

1 Process B uses withdraw Kanban to remove product

from Process A 2 Operator exchanges

withdraw Kanban for P/I kanban already on product in Process A market.

3 P/I returns to process A to be produced to replace what Process B has removed.

Flow of Production

Process A

Process B

1

2

3


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3) Lot by Lot Application (general purpose equipment)

Signal Kanban

• Stamping press produces 3 products (A,B, & C) • All stamping production is in fixed lots Lot size for “A” is 8 boxes • Next process, Weld, withdraws

from marketplace box by box using Kanban

• Order point for “A” is two boxes remaining • When stamping production begins, they

will produce 8 new boxes of “A”

Weld

Withdrawal box by box

Stamping (Lot by Lot Production)

8 Box Lots

A

B C

Flow of Production

8 7 6 3

4 5

1 2


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C

Press

IN Press Weld

OUT

B

In

Lot by Lot Scenario 1: FIFO Flow Lane on Floor

A C

B B

B B

B B

A A

Yellow line is trigger

Red line is Max


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Weld

Place lot reorder card on 2nd to last container.

A

Out

In

A

Lot by Lot Scenario 2 Flow-through Roller Racking

Stamping

1

3

2

AD4

Weld withdraws from Press Supermarket box by box using Withdraw Kanban

Boxes pulled until order point (box with Kanban on it, is reached).

Product “A” Kanban is moved to Production Instruction Queue (Priority Board). Notice stamping is currently producing “D”. Once “D” is complete, Kanban will be put on “D” Order point in market.

“A” moves into “currently producing” slot. Die change is made and “A” production starts - 8 boxes.


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BA C

Press

Weld

Lot Making board

In Out

B

B

A

A A

A

A

A B

B

B

B

C

C

C

D

D

D

D

C

D

D

D

D

A

B C

D

D

D

D

Lot by Lot Scenario 3&4: Non-FIFO Storage

B

1 4 5

2

Box by Box withdrawal from Non FIFO storage.

Cards are placed on each box in

storage. When pulling product, exchange withdraw card for production instruction card. P/I card hung on Lot marking board.

Cards accumulate until they reach the fixed and marked “order point” line in yellow on the board.

Cards are gathered and returned to the press.

Die change is made and production of product A begins. Produce only the number of boxes that the process has cards.

A

A B C D

1

A 4 A 3 A 2

B 1

3 B 2

C 1

C 2

1

3

2

3

Yellow line is trigger


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The Signal Card

• Three Types of Signal - Withdrawal – Production – Procurement

• Used when lot production (or withdrawal or procurement) is going to be required (sometimes with triangular kanbans)

• Requires specification of lot size and reorder point.


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A

B C

Welder

Stamping Press

“WITHDRAWAL” Kanban

“PRODUCTION” Kanban

Kanban Post “WITHDRAWAL” Kanban Post

Kanban Posts are used to collect kanban cards when there are large distances between processes and/or supermarket.


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Example Kanban Post


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Lot by Lot Production-2

Stamping

A

B C

5

Flow of Production

6 3

7

8 5

4 1

2

Box by Box Withdrawal

1

1 Box by box withdraw from Stamping market by process “B” 2 Cards are placed on each box in market. As process “B” pulls product, exchange withdraw card for production instruction card. P/I card hung on “lot making board”. 3 Cards accumulate until they reach the fixed and marked “order point” line on the board. 4 Cards are gathered and returned to the stamping press. 5 Die change is made and production of product “A” begins. Produce only the number of boxes that the process has cards.

A B C Order Point

Line

6 5 4 3 2 1

4 3 2 1 1

7 4

3

2

Products

Lot Making Board


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Lot Marking Board Example


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Parameters of a Signal Kanban

• You need to specify a reorder point and a batch size.

• In computing the batch size, you compute all other work that the supplying process has to do and control the supplying process according to the EPEI principal.

• EPEI principal: Try to have every product every interval where the interval is as short as possible.


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Kanban Calculations - Lot by Lot 1. Dedicate part numbers to machines (e.g. presses)

– based on current run times and run quantities 2. Select one machine to work on first 3. Collect volume data for all part numbers run on machine 4. Determine Run Quantities

A. Decide on an INITIAL GUESS run frequency • Decide time period to use for available machine time • Weekly, Daily, Every 3 days, etc. • Based on current run frequency for high runners and your goals;

– e.g. today high runners are set up once a week, so select Weekly

B. Document current state machine balance (utilization) based on initial guess run frequency, including both run time and changeover time. Use balance chart. See example.


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Kanban Calculations - Lot by Lot 4. Determine Run Quantities

C. Evaluate loading of machine against available time: • Goal: Roughly 85% run time, 10% setup, 5% PM • If overloaded, move some part numbers to another machine • If underloaded, move more part numbers on to this machine

D. Evaluate run quantities and resulting machine balance and Reevaluate loading of machine.

• Repeat until you find run quantities for all the part numbers that achieve a machine balance close to the machine loading goal.


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Machine Balance Chart

Machines (Presses)

Hours per week to load press

Set up Time

Run Time

PM Time


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Kanban Calculations - Lot by Lot

Supermarket Lane for Part A

Pull Side (Out)

Fill side (In)

Run Qty Wait Time SF

Yellow line is trigger Red line is Max Reorder Qty


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Kanban Calculations - Lot by Lot 7. Determine Maximum Inventory Qty (Red line)

= Run Qty + Reorder Qty

8. Determine practical quantities for Max. Inven. & Reorder Quantities – Look at how containers stack and align in supermarket rows.

9. Ongoing Adjustments to quantities – Track usage, evaluate shortages and stagnant inventory, adjust qty’s.


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Example Calculation • Consider a press that processes parts A,B,C,D. Available

Time is one shift-8 hours

• Sum of the run times=436 minutes. Leaves little time for PM and setup. Possible solution—move part D to another machine.

Part Cycle Time

Setup Time

Daily Demand

Total Run Time

A 2min 12min 50 100min

B 1 min 9min 100 100min

C 3min 12min 62 186min

D 1min 9min 50 50min


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Example Calculation • Consider a press that processes parts A,B,C,D. Available

Time is one shift-8 hours

• Sum of the run times=386 minutes. Leave 5%, roughly 24 minutes for PM. This leaves 70 minutes for setups per day. Since the sum of the set-up times is 33 minutes, you can cycle through the products twice in one day.

Part Cycle Time

Setup Time

Daily Demand

Total Run Time

A 2min 12min 50 100min

B 1 min 9min 100 100min

C 3min 12min 62 186min


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Example Calculation 3

• Lot sizes (run quantities) are: 25 (A), 50(B)and 31 for C.

• Wait Time (kanban cycle time) for a product is ½ a day since we cycle through the products in half a day.


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Kanban Calculations for Signal Kanbans

RP=Reorder quantity D= Demand rate (e.g. daily demand) SF=Safety factor WT=Wait time (e.g., days)


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Signal Kanban Quantities • Therefore if we are setting signal kanban

quantities for part A (assume SF=0.5) • We have • RP=50per day*0.5days*1.5=37.5=38 pieces • Max=38+25=63

Supermarket Lane for Part A

Pull Side (Out)

Fill side (In)

Run Qty Reorder quantity

Yellow line is trigger at 38 pieces.

Red line is Max 63 pieces

25 pieces 38 pieces


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Runners

Repeaters

Rogues

Demand Patterns: Press Example


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Implementation Steps • Design Pull System

– Draw current state Value Stream Map (of affected processes, not door to door)

• Physically locate current inventory and cycle count pieces – Decide type of kanban - e.g. lot by lot or kanban by kanban. – Identify parts – Calculate Kanban size (initial cut)

• Analyze part volume in aggregate and fluctuation • Determine available floor space for inventory - supermarket, flow

lanes. • Determine replenishment time (kanban cycle time) - calculate process

capacity – Decide signaling -e.g. space, container and/or card – Draw future state Production Instruction pull loop and Withdrawal pull

loop. Use VSM

– Determine rules for inventory levels, replenishment points, card and container handling

– Meet with operators and supervisor to verify accuracy of data


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Implementation Steps - Continued • Implement Pull System

– Create Supermarket - mark floors, post signs, etc – Create cards, sequencing boards, and other visuals – If scope is large, implement the following steps for the

Production Instruction Pull Loop 1st, then repeat for the Withdrawal Loop

– Acquire containers – Ergonomic and safety review – Document routes, inventory levels, replenishment points, card &

container handling – Define roles & responsibilities – Train employees on new process

• Audit – Close follow up on execution of quantity, signaling, floor space

use, etc… – Analysis of performance, adjustments, refinements,

improvements


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When your pills get down to four,

Order more. Anonymous, from Hadley & Whitin

Inventory Management


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Objective

• Show the links between inventory management techniques and kanban/pull systems.

• Develop techniques for effective inventory management when buying from suppliers (who have not necessarily implemented kanban systems).

• Understand effective inventory management for complex, multiproduct systems.


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EOQ History

• Introduced in 1913 by Ford W. Harris, “How Many Parts to Make at Once” – Interest on capital tied up in wages – Material and overhead sets a maximum limit to the

quantity of parts which can be profitably manufactured at one time

– Set-up” costs on the job fix the minimum. – Experience has shown one manager a way to determine

the economical size of lots. – Early application of mathematical modeling to Scientific

Management


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EOQ Example

• You use significant amounts of a certain chemical in your manufacturing,and are trying to decide how often you should order this chemical.

• Your daily usage is 60 liters. • Manufacturer of chemical charges $60 per

liter, and there is also a fixed shipping cost of $500 whenever you order.

• (Assume a 20% annual interest rate).


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EOQ Modeling Assumptions

1. Demand is deterministic – there is no uncertainty about the quantity or timing of demand.

2. Demand is constant over time. 3. Products can be analyzed singly – either there is only a

single product or conditions exist that ensure separability of products.


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Notation

AVG= demand rate (units per day)

c = unit variable purchase cost (dollars/unit) K = fixed cost to place an order (dollars) h = holding cost (dollars per day)—annual holding

cost equals interest rate multiplied by unit cost.

Q the unknown size of the order or lot size

Decision Variable


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Inventory vs Time in EOQ Model

Q/AVG 3Q/AVG

Q

Inve

ntor

y

Time


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Costs • Holding Cost:

• Setup Costs: A per lot, so

• Production Cost: c per unit

• Cost Function:


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Chemical Example Costs

c = $60 per liter

A = $500 (estimated from supplier’s pricing)

h = (0.2)($60) = $12 per liter per year=$12/365 per

liter per day


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Economic Order Quantity

Solution

EOQ Square Root Formula


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Philosophies toward Randomness

1. Use deterministic model – adjust solution.

2. Use probabilistic model


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The (Q,r) Approach

• Motivation 1. Demand is rarely deterministic and continous. 2. We therefore can not use the EOQ alone. 3. However, we can use it along with a reorder point and

safety stock if we protect ourselves against demand uncertainty.

• Decision Variables: – Reorder Point: r

• affects likelihood of stock-out (safety stock). – Order Quantity: Q

• affects order frequency (cycle inventory).


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Inventory vs Time in (Q,r) Policy

Q

Inve

ntor

y

Time

r

l


98

Notation

• AVG = average demand per unit time (days) • STD = standard deviation of daily demand • LT = replenishment lead time in days • h = holding cost of one unit for one day • SL = service level (for example, 95%). This implies that the

probability of stocking out is 100% - SL (for example, 5%) • Also, the Inventory Position at any time is the actual inventory plus

items already ordered, but not yet delivered.

• Note: Time units can be anything as long as they’re consistent.


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Analysis

• The reorder point has two components: – To account for average demand during lead time:

LT x AVG – To account for deviations from average (we call this safety stock)

where z is chosen from statistical tables to ensure that he probability of stockouts during leadtime is 100% - SL.

Note: z=2.3 for SL=0.99. z=3.1 for SL=0.999


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Example:

• Best Airlines is trying to decide how much inventory to keep of a part used in maintenance of their aircrafts. They estimate they use an average of 14 per day with a standard deviation of 3. The part costs $150 per unit, and Best uses a 10% annual interest rate for its holding cost calculations. There is also a fixed cost of $500 every time an order is placed. The supplier delivers in 10 days. If Best would like to ensure that 99% of order cycles, it does not face a shortage, what inventory policy should it use?


101

Best Air Solution

In this case, safety inventory is about 22 units.


102

Single Product (Q,r) Insights

• Basic Insights: – Safety stock provides a buffer against stock-outs.

• Other Insights: – 1. Increasing demand tends to increase optimal order

quantity Q. – 2. Increasing leadtime tends to increase the optimal

reorder point. – 3. Increasing the variability of the demand process tends

to increase the optimal reorder point. – 4. Increasing the holding cost tends to decrease the

optimal order quantity and reorder point.


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Deciding on Service Level

• The tradeoff: – Too much inventory causes higher holding costs. – Too little inventory causes shortages resulting in lost

sales or backorders. • The reorder point should be set in such a way as

to balance the costs of having too much and too little inventory.


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Backorder Case

• Assume shortages are backordered. However, backorders cost money. What is backorder cost?

• Cycle Service Level=b/(b+h) – b=cost to backorder a unit per unit time – h=cost to hold a unit in inventory.


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Example- Best Air.

• Assume that a shortage of the part causes Best Air to delay or cancel its flights, causing a “backorder” cost of $5000 per day.

• What cycle service level should Best Air use? • b=$5000 per unit per day • h=$15/365 • b/(b+h)=0.999991


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Conclusion

• Signal kanban systems can also be used for purchased parts.

• Key factors in their implementation: – Supplier lead times – Average and standard deviation of daily demand – Fixed order costs – Holding costs – Backorder costs or service levels.

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