Mathematical Models for Supporting Available to Promise (ATP)

© Michael O. Ball

Mathematical Models for Supporting Available to Promise (ATP)

Michael Ball R. H. Smith School of Business & Institute for Systems Research

University of Maryland

based on joint work with C.Y. Chen & Z.Y. Zhao

© Michael O. Ball

Outline

1. Introduction and Overview of Model

2. Research Topics

3. Experience from Toshiba Prototype

© Michael O. Ball

Outline


2. Research Topics


© Michael O. Ball

Available to Promise (ATP) &Assemble to Order (ATO)

The Available to Promise (ATP) Function provides a response to a customer order with a quantity and delivery date commitment.

In an assemble-to-order (ATO) production environment, final product assembly is not carried out until a customer order is received; also consider make-to-order (MTO), configure-to-order (CTO).

Why ATO, MTO, CTO??– Provide customers with greater product variety– Reduce inventory

© Michael O. Ball

Push and Pull Production Systems

Order raw materials

transport & storage

Produce product

Deliver product to customer/retailer

transport & storage

customer orderForecast demand

Order raw materials

transport & storage

Produce product

Deliver product to customer/retailer

transport & storage

customer order

PUSH VS PULL

© Michael O. Ball

Push-Pull Systems

Manufacturingincl final assembly

Manufacturing Assemblyto

order

product models

generic products and components inventory

suppliers

Push-pull boundary

forecast driven order driven

© Michael O. Ball

ProductionPlanning

(MPS,MRP)

ProductionExecution

Warehouse

Optimization-basedATP

Order Management

ProcurementOrder (PO)

Sales forecast

Production status

Confirmed ordersPseudo orders

Committed orders

Order placement

Order Delivery

Push-based planningPull-based promising

Manufacturing & LogisticsManufacturing & Logistics

Due date promise

Promised quantity& due dates

Sales & MarketSales & Market

Matl PlanningMatl Planning

MaterialDelivery

Product Delivery

Supplier

Customer

Dmd Prod. CtlDmd Prod. Ctl

The Role of Advanced ATP in Production Planning and Control

© Michael O. Ball

Conventional ATP (make-to-stock environment)

localinventory

inventoryin warehouse

this week’splanned

production

next week’splanned

production

immediatedelivery

deliveryin 2 days

deliveryin 1 week

deliveryin 2 weeks When can you

deliver orderfor 6 units??

© Michael O. Ball

ATP in ATO/CTO/MTO Environment

O rder P rom ising : Q uan tity quo ting D ue-date quo ting

••

AT P

P ush P u llO rder Fu lfillm en t: C onfiguration p lann ing P roduction scheduling

••

M ate ria lAvailab ility

(M ate rial Types)

C apacity Ava ilab ilityC ustom er

O rders(O ld and N ew )

C apacity P lanning

A ggregate P lann ing

M aste r P roductionSchedu ling (M PS)

M ate ria l R equ irem entsP lann ing (M R P )

Production

A ssem bly

Packaging

Shipp ing

Pick ing

x

ATP in assemble-to-order environment:match available resources to customer orders

Decisions: accept/reject/split order; order quantities and delivery dates

Considerations: order profitability; customer priority; customer satisfaction (reducing response/delivery time); production

efficiency

Resources:• raw material and component availability• production capacity

customerorders

© Michael O. Ball

Classes of Products

• Discrete parts electronics product production

• Specific cases considered (all in B2B setting):– Maxtor hard disk drive– Toshiba Notebook PC– Toshiba Point-of-Sale terminal

© Michael O. Ball

Real-Time vs Batch ATP

Real-time ATP: response and order commitment given for each order immediately after receipt of order

Batch ATP: orders collected over time interval, e.g. one hour, one 8-hour shift, one day, etc.; response and order commitments generated for batch of orders at end of each time period

Model described here solves batch ATP problem

It should be noted that there are very few true real-time ATP systems operating today; most systems that give an immediate response (including most web-based retail sites) produce an initial “soft” promise, run a batch ATP module later and then produce a “hard” promise.

© Michael O. Ball

Mixed Integer Programming Model

MODEL SUMMARYObjective FunctionMaximize: (net revenue) – (production

cost) – (material cost) – (inventory cost) – (order denial penalty) – (capacity under-utilization penalty) – (order lateness penalty)

Constraints– Order commitment constraints– Material requirement constraints– Production capacity constraints– Production smoothness constraints– Inventory constraints

iZ : indicates if order i is accepted, (1 if accepted; 0 otherwise),

: the commitment level for order i,

: the material requirement from the kth supplier for the jth type of material for the ith order during time period t (here i consists of both new and old orders).

iC

)(tX ijk

MAJOR DEC VARIABLESATP vs Production Planning & inventory mgmt: short time horizon; fixed resources; front end/back end integration

© Michael O. Ball

Product Structure in ATO/MTO/CTO Environments

S11

S12

S31

Smn

S21

M1

Mk

P1

P2

Pr

C1

C2

Cq

C3

M2

constraints

constraints

suppliers raw materialse.g. disk drive,LCD, etc

products, e.g. pc model w. options

customers

(material compatibility, customer preference, production capacity, etc.)

© Michael O. Ball

Customer Preference and Material Compatibility Constraints

S11

S12

S21

Snmn

Sn1

S1m1

M1

M2

Mn

C1

C2

customers

suppliers materials

customer-supplierpreferences

materialincompatibilities

© Michael O. Ball

Dynamic Use of ATP Model

ATP DecisionModel (period t)

neworders

order commitments

for periodst+2, t+3, …

order commitmentspromise dates, quantities

production schedulefor period t+1

© Michael O. Ball

Production Flexibility

production planand resource

allocation fixed

production planand resource

allocation flexible(subject to quantityand delivery date

commitment)

batchinginterval

batchinginterval

© Michael O. Ball

Outline


2. Research Topics


© Michael O. Ball

Research Topics

1. Model Simplification/Aggregation & Polyhedral Projection

2. Real Time vs Batch ATP: Applying Techniques from Analysis of Heuristics

3. Modeling Stochastic and Dynamic Problem Aspects

© Michael O. Ball

1. Model Simplification/ Aggregation and Polyhedral Projection

P = {(x,y) : A1x + A2y = b, x,y 0}The projection of P onto x is the polyhedron:

P’ = {x : there exists a y s.t. (x,y)P}Min cx s.t. (x,y) P Min cx s.t. xP’

Examples:x = material allocation variables & y = product

configuration variables.x = weekly resource allocation variables & y = daily

resource allocation variables.

© Michael O. Ball

Material Compatibility Constraints

The direct approach to modeling material compatibility would be to include explicit product configuration variables (in general there could be a very large number of such variables)

Consider the following special case (from Maxtor):

PCB

HDA

Bplate

extension to multiple levels

components can be arranged into levels;incompatibility constraints only exist between adjacent levels;

Product specification is path that avoids all incompatible edges

© Michael O. Ball

Material Compatibility Constraints

X11 X12 X13 X14 X15

X21 X22 X23 X24 X25

A product using component (1,1) or (1,4) must also use (2,2), (2,3) or (2,4) X22 + X23 + X24 X11 + X14

Must be satisfied by all compatible material assignments, i.e. necessary condition.All such constraints provide necessary and sufficient conditions for “level incompatibility systems”Based on results on projection of perfectly matchable sub-graph polytope (Balas and Pulleyblank)

5 instances (e.g. suppliers) of generic component 1

5 instances (e.g. suppliers) of generic component 2

incompatibilities

© Michael O. Ball

2. Real-Time vs Batch ATP and Size of Batching Interval

• Real-Time ATP: as each order comes in make decision based on customer response (accept or not, time/quantity) and production resource allocation equivalent to “greedy” algorithm

• Batch ATP: collect all orders that arrive in batching interval; optimize customer response and resource allocation over this set.

• Real-Time vs Batch ATP greedy heuristic vs optimization.

• Variants of Batch ATP based on size of batching interval

© Michael O. Ball

Profitability -- Customer Service Tradeoff

order commit production delivery

– As response times decrease, customer service improves

– Longer response times provide more production flexibility leading to higher revenues and/or lower costs

time

depends on length of

batching interval

Two key customer service criteria:Time to commit:Time to delivery:

© Michael O. Ball

Missed Orders vs Batching Interval Size: Maxtor Scenario

Missed Orders vs. Batching Interval Size

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12

Batching Interval Size (time periods)

Nu

mb

er

of

Mis

sed

Ord

ers

80% Resource Level 70% Resource Level

© Michael O. Ball

Tangible Profit vs Batching Interval Size: Maxtor Scenario

Tangible Profit vs. Batching Interval Size(at 70% resource level)

7,300

7,350

7,400

7,450

7,500

7,550

1 2 3 4 5 6 7 8 9 10 11 12

Batching Interval Size (time periods)

Tan

gib

le P

ro

fits

(th

ou

san

ds $

)

Tangible Profit with Both Flexibilites Tangible Profit with Preference Flexibility

Tangible Profit with Quantity Flexibility Tangible Profit with No Flexibility

© Michael O. Ball

Tangible Profit vs Batching Interval Size: Toshiba Notebook Scenario

Batching Interval Effects

350

370

390

410

430

450

470

490

510

530

1 2 3 4 5 6 7

Batching Interval Size (days)

Tan

gib

le P

rofi

t ($

m)

Base Scenario(100% Resource)

80% Resource

ReducedAcceptable Due-Date Range

80% Resourcewith ReducedAcceptable Due-Date Range

© Michael O. Ball

3. Stochastic and Dynamic Problem Aspects: Material Reservation Policy:

It is sometimes useful to reserve material from one time period in anticipation (forecast) of more profitable or higher priority orders that might arise in a later time period.

Material reservation policy:• For each raw material:

– Material reserve level

– Per unit shortfall penalty (material “price”)

• Orders that violate material shortfall penalty are not accepted unless they remain profitable when charged the shortfall penalty

Basis for Formal Analysis: Stochastic Dynamic Programming

© Michael O. Ball

Effect of Material Reservation Policy: Toshiba Notebook Scenario

Reserve Policy Effects

135140145150

155160165170

1 2 3 4 5 6 7

Inventory Reserve Level (days)

Ta

ng

ible

Pro

fit (

$m

)

No ShortfallPenalty

10% ShortfallPenalty





© Michael O. Ball

Other Research Issues

• What is nature of customer service/production efficiency tradeoff?– key issue: what is value of reducing time to order

commitment and/or time to ship date• Model support for real-time ATP• Multiple sales channel strategies• Coupling ATP models to supply chain infrastructures (ERP

and SCM systems)• Scalability issues• B2B vs B2C strategies• ATP as a strategic weapon

© Michael O. Ball

Outline


2. Research Topics


© Michael O. Ball

Variation in Fixed Resources over Time

tInventory W W+1 W+2 W+3 W+4 W+5 W+6 W+7 ->

Customer orders

Order CommitmentResources

Fixed production capacity

Fixed Production Schedule

Fixed material availability and production capacity

© Michael O. Ball

Flexibility in Adjusting Material Availability

W+4, 100{A, B, C}

Extra Cost

W+2 W+3 W+4 W+5W+1

2 weeks expedite 1 week de-expedite

W+6

Expedite cost

Inventory holding cost

De-expedite cost

A BC

Inventory cost savings

© Michael O. Ball

Scenario comparing current approach and optimization-based approach

Inv MO PC1 PC2 PC3

#1#1

t

#2#2

#1 #1

#1 #1#2

#2

#1#1#2

#2

PC Expedite

Re-commitC-ATP A-ATP

Due date

violation

© Michael O. Ball

Daily ATPDaily ATPWeekly ATP

• Customer orders

• Weekly resource availability

Daily ATPs

Committed week, qty

Weekly resource allocation

Daily resource availability

• Committed date, qty

• Daily resource allocation

Aggregation

Weekly production& inventory plan

Two level (approximate) model used to allow for solution of real (large) problem instances

© Michael O. Ball

-20

-15

-10

-5

0

5

10

15

20

25

-6 -4 -2 0 2 4 6 8 10 12 14

Inventory holding decrease (%)

Du

e d

ate

vio

latio

n d

ecr

ea

se (

%)

Trade-off Analysis of Multiple Objectives

Inventory only

Due date only

Due date weightincrease

Inventory weightincrease

© Michael O. Ball

Factory

Warehouse

Sales

MO, PC

MO, PC

MO, PC

Finished goods

TransportationProduction Orders

Commitment

Supply Chain ATP Model (preliminary implementation completed):

Documents

Mathematical Models for Supporting Available to Promise (ATP)