© michael o. ball mathematical models for supporting available to promise (atp) michael ball r. h....
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© 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
1. Introduction and Overview of Model
2. Research Topics
3. Experience from Toshiba Prototype
© 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
1. Introduction and Overview of Model
2. Research Topics
3. Experience from Toshiba Prototype
© 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
20% ShortfallPenalty
30% ShortfallPenalty
40% ShortfallPenalty
50% 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
1. Introduction and Overview of Model
2. Research Topics
3. Experience from Toshiba Prototype
© 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
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