Supply chain optimization Jose Pinto - CEPAC

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Part 3

Process and Supply Chain Operations

Supply chain optimization

Jose Pinto

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I. Strategic Framework to the Analysis of Supply Chain Networks

II. Design of Supply Chain NetworksIII. Planning of Supply ChainsIV. Planning, Scheduling and Supply Chain

Management for Operations in Oil Refineries

AppendicesI. Demand ForecastII. Transportation IssuesIII. The Role of Inventory

Outline

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Supply Chain

Scope: a supply chain covers the flow of materials, information and cash across the entire enterpriseSupply chain management: process of integrating, planning, sourcing, making and delivering product, from raw material to end customer, and measuring the results globallyTo satisfy customers and make a profitWhy a ‘supply chain’?

4

Traditional View: Logistics in the Economy

1990 1996Freight transportation $352 $455 billionInventory expense $221 $311 billionAdministrative expense $ 27 $ 31 billion

Logistics related activity 11% 10.5% GNP

Source: Cass Logistics

5

Traditional View: Logistics in the Manufacturing Firm

Profit: 4%

Logistics cost : 21%

Marketing cost: 27%

Manufacturing cost : 48%

ProfitLogistics

Cost

Marketing Cost

Manufacturing Cost

6

Supply Chain Management: The Magnitude in the Traditional View

The grocery industry could save $30 billion (10% of operating cost by using effective logistics and supply chain strategies

A typical box of cereal spends 104 days from factory to sale

A typical car spends 15 days from factory to dealership

Compaq estimates it lost $0.5 billion to $1 billion in sales in 1995 because laptops were not available when and where needed

P&G estimates it saved retail customers $65 million by collaboration resulting in a better match of supply and demand

Laura Ashley turns its inventory 10 times a year, five times faster than 3 years ago

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Objectives of a Supply ChainMaximize overall value generated

Satisfying customer needs at a profitValue strongly correlated to profitabilitySource of revenue – customerCost generated within supply chain by flows of information, product and cashFlows occur across all stages – customer, retailer, wholesaler, distributor, manufacturer and supplierManagement of flows key to supply chain success

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Supply Chain Stages

Supplier Manufacturer Distributor Retailer Customer



9

Decision phases in a supply chainSupply chain strategy or design

Location and capacity of production and warehouse facilities?Products to be manufactured, purchased or stored by location?Modes of transportation?Information systems to be used?Configuration must support overall strategy

Supply chain planningOperating policies – markets served, inventory held, subcontracting, promotions, …?

Supply chain operationDecisions and execution of orders?

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Cycle View of Supply Chains

Customer Order Cycle

Replenishment Cycle

Manufacturing Cycle

Procurement Cycle

Customer

Retailer

Distributor

Manufacturer

Supplier

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Process view of a supply chain

Customer order cycleTrigger: maximize conversion of customer arrivals to customer ordersEntry: ensure order quickly and accurately communicated to all supply chain processesFulfillment: get correct and complete orders to customers by promised due dates at lowest costReceiving: customer gets order

12


Replenishment cycleReplenish inventories at retailer at minimum cost while providing necessary product availability to customerRetail order:

Trigger – replenishment point – balance service and inventoryEntry – accurate and quick to all supply chainFulfillment – by distributor or mfg. – On timeReceiving – by retailer, update records

13


Manufacturing cycleIncludes all processes involved in replenishing distributor (retailer) inventory, on time @ optimum costOrder arrival Production schedulingManufacturing and shippingReceiving

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Procurement cycleSeveral tiers of suppliersIncludes all processes involved in ensuring material available when required

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Supply chain macro processes

CRM (Customer Relationship Management) – all processes focusing on interface between firm and customers

ISCM (Internal Supply Chain Management) – processes internal to firm

SRM (Supplier Relationship Management) – all processes focusing on interface between firm and suppliers

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Push/Pull View of Supply Chains

Procurement,Manufacturing andReplenishment cycles

Customer OrderCycleCustomer

Order arrives

PUSH PROCESSES PULL PROCESSES

Pull – processes in response to a customer orderPush – processes in anticipation of a customer order

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Supply chain performance –Strategic fit and scope

NewProduct

Development

Marketingand

Sales

OperationsSupply and

ManufactureDistribution Service

Finance, Accounting, Information Technology, Human Resources

Business Strategy

New ProductStrategy

MarketingStrategy Supply Chain Strategy

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Achieving strategic fit

Quantity - lot sizeResponse timeProduct varietyService levelPriceInnovation

ImpliedDemand

UncertaintyRegular Demand

Uncertainty due to customers demand and

Implied Demand Uncertainty due to

uncertainty in Supply Chain

Understanding the Customer and Demand Uncertainty

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Levels of Implied Demand Uncertainty

Low High

Price ResponsivenessCustomer Need

DetergentLong lead time steel

High FashionEmergency steel

Implied Demand Uncertainty Low HighProduct Margin Low High Average Forecast Error 10% 40-100% Average Stockout rate 1-2% 10-40%Average markdown 0% 10-25%

Fischer (1997) Harvard Bus. Rev, March-April, 83

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Supply source uncertaintySupply uncertainty increases with...

Frequent breakdownsUnpredictable and/or low yieldsPoor qualityLimited supplier capacityInflexible supply capacityEvolving production processes

Life cycle position of productNew products high uncertaintysalt vs existing automobile model vs new communication device

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Understanding the Supply Chain

High Low

Low

High

Cost (efficient)

Responsiveness to Quantity, Time, Variety, Innovation, Service level

DELL

AUTOMOTIVES

INTEGRATED STEEL MILLS

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Achieving Strategic Fit

Implied uncertainty spectrum

Responsive supply chain

Efficient supply chain

Certain demand

Uncertain demand

Responsiveness spectrum Zone o

f

Strateg

ic Fit

Low Cost

High Cost

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Responsive and Efficient Supply ChainsEfficient Responsive

Primary goal demand at lowest cost respond quickly

Product designstrategy

maximize performanceat minimum cost

create modularity

Pricing strategy Lower margins higher margins

Manufacturingstrategy

lower costs (highutilization)

maintain flexibility

Inventory strategy minimize to lower cost maintain buffer inventory

Lead time strategy reduce but not atexpense of costs

aggressively reduce

Supplier strategy select based on costand strategy

select based on speed,flexibility, reliability andquality

24

Product life cycle

Implied uncertainty spectrum

Responsive supply chain

Efficient supply chain

Product Maturity

Product Introduction

Responsiveness spectrum Zone o

f

Strateg

ic Fit

25

Strategic Scope

Suppliers Manufacturer Distributor Retailer Customer

Competitive Strategy

Product Dev. Strategy

Supply Chain Strategy

Marketing Strategy

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Drivers of Supply Chain Performance

Efficiency Responsiveness

Supply chain structure

Competitive Strategy

Supply Chain Strategy

Inventory Transportation Facilities Information

DriversTRADE OFF FOR EACH DRIVER

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Inventory‘What’ of supply chainMismatch between supply and demandMajor source of costHuge impact on responsivenessMaterial flow time

i = d t (i – inventory, d – throughput, t – flow time)

Role in competitive strategyComponents

Cycle inventory – average inventory between replenishmentsSafety inventory - to cover demand and supply uncertaintySeasonal inventory – counters predictable variation

Overall trade off: responsiveness vs. efficiency

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Transportation

‘How’ of supply chainLarge impact on responsiveness and efficiencyRole in competitive strategyComponents

Mode – air, truck, rail, ship, pipeline, electronicRoute selectionIn house or outsource

Overall trade off: responsiveness vs efficiency

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Facilities‘Where’ of supply chainTransformed (factory) or stored (warehouse)Role in competitive strategyComponents

Location - central or decentralCapacity – flexibility vs. efficiencyManufacturing methodology – product or process focusWarehousing methodology – storage – sku, job lot, crossdocking

Overall trade off: responsiveness vs. efficiency

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Affects every part of supply chainConnects all stagesEssential to operation of all stages

Role in competitive strategySubstitute for inventory

ComponentsPush vs. pullCoordination and information sharingForecasting and aggregate planningEnabling technologies

EDI, Internet, ERP, SCMOverall trade off: responsiveness vs. efficiency

Information

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Considerations for Supply Chain Drivers

Driver Efficiency Responsiveness

Inventory Cost of holding Availability

Transportation Consolidation Speed

Facilities Consolidation /Dedicated

Proximity /Flexibility

Information What information is best suited foreach objective

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Obstacles to achieving strategic fit

Increasing variety of products

Decreasing product life cycles

Increasingly demanding customers

Fragmentation of supply chain ownership

Globalization

Difficulty executing new strategies

All increase uncertainty

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Major obstacles to achieving fitMultiple global owners / incentives in a supply chain

Information Coordination & Contractual Coordination

Increasing product variety / shrinking life cycles / demanding customers/customer fragmentation

Increasing demand and supply uncertainty

Local optimization and lack of global fit

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Dealing with Product Variety: Mass Customization

MassCustomization

Low

HighHigh

Low

Long

Short

Lea

d T

ime

Cost

Customization

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Fragmentation of Markets and Product Variety

Are the requirements of all market segments served identical?

Are the characteristics of all products identical?

Can a single supply chain structure be used for all products / customers?

No! A single supply chain will fail different customers on efficiency or responsiveness or both.

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II.Designing the supply chain network

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FACILITY DECISIONS: Network Design Decisions

Facility roleWhat processes are performed

Facility locationWhere should facilities be located

Capacity allocationHow much capacity should be allocated to each facility

Market & supply allocationWhat markets should each facility serveWhat supply sources should feed each facility

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Factors Influencing Network Design DecisionsStrategic

Cost or Responsiveness focus

TechnologicalFixed costs and flexibility determine consolidation

MacroeconomicTariffs and Tax incentives. Stability of currency

Political stability - clear commerce & legal rulesInfrastructure

sites, labor, transportation, highways, congestion, utilities

CompetitionLogistics and facility costs

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The Cost-Response Time Frontier

Local FG

Mix

Regional FG

Local WIP

Central FG

Central WIP

Central Raw Material and Custom production

Custom production with raw material at suppliers

Cost

Response Time HighLow

Low

High

40

Logistics and facilities costs

Inventory costsTransportation costs

Inbound and outboundFacility (setup and operating) costsTotal logistics costs

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Service and Number of Facilities

Number of Facilities

ResponseTime

Facilities Costs

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Costs and Number of Facilities

Costs

Number of facilities

Inventory

Facility costs

TransportationFrequent inbound

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Cost Build-up as a function of facilities

Percent Service Percent Service Level Within Level Within

Promised TimePromised Time

TransportationTransportationCos

t of O

pera

tions

Cos

t of O

pera

tions

Number of FacilitiesNumber of Facilities

InventoryInventoryFacilitiesFacilities

Total CostsTotal Costs

LaborLabor

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Framework for network design decisions

Define a supply chain strategyCOMPETITIVE strategy

Define a regional facility strategyLocation, roles and capacity

Select desirable sitesHard infrastructure – transport, utilities, suppliers, warehousesSoft infrastructure – skilled workforce, community

Choose locationPrice location and capacity allocation

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A Framework for Global Site Location

PHASE ISupply Chain

Strategy

PHASE IIRegional Facility

Configuration

PHASE IIIDesirable Sites

PHASE IVLocation Choices

Competitive STRATEGY

INTERNAL CONSTRAINTSCapital, growth strategy,existing network

PRODUCTION TECHNOLOGIESCost, Scale/Scope impact, supportrequired, flexibility

COMPETITIVEENVIRONMENT

PRODUCTION METHODSSkill needs, response time

FACTOR COSTSLabor, materials, site specific

GLOBAL COMPETITION

TARIFFS AND TAXINCENTIVES

REGIONAL DEMANDSize, growth, homogeneity,local specifications

POLITICAL, EXCHANGERATE AND DEMAND RISK

AVAILABLEINFRASTRUCTURE

LOGISTICS COSTSTransport, inventory, coordination

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Manufacturer Storage with Direct Shipping

Manufacturer

Retailer

Customers

47

Factories

Retailer

Customers

In-transit merge by carrier

In-Transit Merge Network

48

Factories

Customers

Warehouse storage by distributor/retailer

Distributor Storage with Carrier Delivery

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Factories

Customers

Distributor/retailer warehouse

Distributor Storage with “Last Mile” Delivery

50

Factories

Customers

Cross Dock DC

Pickup sites

Retailer

Manufacturer or Distributor Warehouse with Consumer Pickup

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Tailored Network: Multi - Echelon Finished Goods Network

RegionalRegionalFinishedFinished

Goods DCGoods DC

RegionalRegionalFinishedFinished

Goods DCGoods DC

Customer 1Customer 1DCDC

Store 1Store 1

NationalNationalFinishedFinished

Goods DCGoods DC

Local DCLocal DCCrossCross--DockDock

Local DC Local DC CrossCross--DockDock

Local DCLocal DCCrossCross--DockDock

Customer 2Customer 2DCDC

Store 1Store 1

Store 2Store 2

Store 2Store 2

Store 3Store 3

Store 3Store 3

52

Network Optimization ModelsAllocating demand to production facilitiesLocating facilities and allocating capacity

Speculative StrategySingle sourcing

Hedging StrategyMatch revenue and cost exposure

Flexible StrategyExcess total capacity in multiple plantsFlexible technologies

Which plants to establish? How to configure the network?

Key Costs:Fixed facility costTransportation costProduction costInventory costCoordination cost

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Capacitated Plant Location Models

Max , ,1 1 1

n n m

i i i j i ji i j

Profit f y c x= = =

= ⋅ + ⋅∑ ∑∑

,1

1,...n

i j ji

x D j m=

= =∑

,1

1,...m

i j i ij

x K y i n=

≤ ⋅ =∑{ }0,1 1,...iy i n∈ =

n number of potential plant locationsm number of marketsfi annualized fixed cost of keeping plant i opencij cost of producing and shipping from i to j

Dj annual demand from market j

Ki potential capacity of plant i

yi 1 if plant i is open; 0 otherwise

xij quantity shipped from plant i to market jDecisions

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Gravity Location Models

x, y Warehouse Coordinatesxn, yn Coordinates of delivery location ndn Distance to delivery location nfn Cost per ton mile to delivery location nDn Quantity to be shipped

−− +=n yyxxd nn

22 )()(

Min Total Cost1

k

n n nn

TC D d f=

= ⋅ ⋅∑

ASSUMPTION: TRANSPORT COSTS GROW LINEARLY WITH SHIPMENTS

55

Demand Allocation ModelWhich market is served by which plant?Which supply sources are used by a plant?

s.t.

All mkt demand satisfied

No factory capacity exceed

xij quantity shipped from plant site i to customer j

Cij cost to produce & ship one unit from factory i to market j

n no. of factory locationsm no. of marketsDj annual demand from

market j Ki annual capacity of factory i

,1

1,...n

i j ji

x D j m=

= =∑

,1

1,...m

i j ij

x K i n=

≤ =∑, 0 1,... ; 1,...i jx i n j m≥ = =

, ,1 1

n m

i j i ji j

MinC c x= =

= ∑∑

56

Warehouse and Plant Location ModelPlant and warehouse locations?Quantities shipped between various points?

, , , , , ,1 1 1 1 1 1 1 1

n t l n n t t m

i i e e h i h i i e i e e j e ji e h i i e e j

MinC f y f y c x c x c x= = = = = = = =

= + + + +∑ ∑ ∑∑ ∑∑ ∑∑

Fixed costsplants

warehouse

Shipping costsSupply source to plant

Plant to warehouseWarehouse to market

57

Warehouse and Plant Location Model,

11,...

n

h i hi

x S h l=

≤ =∑

, ,1 1

0 1,...l t

h i i eh e

x x i n= =

− ≥ =∑ ∑

,1

1,...t

i e i ie

x K y i n=

≤ =∑

, ,1 1

0 1,...n m

i e e ji j

x x e t= =

− ≥ =∑ ∑

,1

1,...t

e j je

x D j m=

= =∑

,1

1,...m

e j e ej

x W y e t=

≤ =∑

Supplier capacity

Balance supply-plant

Supplier capacity

Balance plant-warehouse

Warehouse capacity

Demand satisfaction

58

Network design decisions in practiceDo not underestimate the life span of plants

Long life hence long term consequencesAnticipate effect future demands, costs and technology changeStorage facilities easier to chance than production facilities

Do not gloss over cultural implicationsLocation – urban, rural, proximity to others

Do not ignore quality of life issuesWorkforce availability and morale

Focus on tariffs & tax incentives when locating facilities

Particularly in international locations

III.Supply chain management of flexible process networks - Lagrangean-based

decomposition techniques

Peter ChenJose M. Pinto

Content

MotivationDecomposition techniques considered

Lagrangean and Lagrangean/surrogate relaxationSubgradient and Modified subgradient optimization

Problem StatementCPFN Model

StructureObjective and constraints

ObservationDecomposition Applied

Lagrangean relaxationLagrangean/surrogate relaxation

Strategies ProposedResultsConclusionFuture Work

Motivation

Difficulties faced by most chemical companiesIncreasing number of competitorsIncreasing product variety from customer demandLarger and more complicated process networkMore efficient management is needed to survive and stay competitive

Why decomposition techniques are neededThe optimization of process networks are very difficult to solve using standard (full-scale) method.

Large computational effortTechnological barriers

Comparison of techniques are necessaryVarious decomposition techniques existThe effectiveness of the techniques is not standardized

Problem StatementA process network interconnects in a finite number of ways.

Processes I1~I4I1 is dedicatedI2, I3, and I4 are flexible

Chemicals J1~J6J1 and J2 are purchasedJ3 is consumed or sold as productJ4 and J6 are purchased or producedJ5 is sold as product

Sites C1 & C2C1: consists of all the processes and production schemes, contains byproduct J6.C2: doesn’t have I1, I3 contains only 3 schemes, and J6 is not produced.

Markets L1~L4L1 and L2 sells raw materialsL3 and L4 buys products

Bok et al. (2000) Ind. Eng. Chem. Res. 39, 1279-1290.

L1

L2 L4

L3

CFPN StructureI1.K1

I2.K1

I2.K2

I3.K1

I3.K2

I3.K3

I3.K4

I2.K1

I2.K2

I3.K1

I3.K2

I3.K3

I4.K1

I4.K2

I4.K1

I4.K2

Site 1

Site 2

J1 J2 J3 J4 J5 J6

CFPN Model – Objective FunctionObjective – Maximize the operating profit of the network

∑∑∑

∑∑∑∑

∑∑∑

∑∑∑∑∑

∑∑∑

∑ ∑ ∑∑∑

∑∑∑∑

∑∑∑∑

∈ ∈ ∈

∈ ∈ ∈ ∈

∈ ∈ ∈

∈ ∈ ∈ ∈ ∈

∈ ∈ ∈

∈ ∈ ∈ ∈ ∈

∈ ∈ ∈ ∈

∈ ∈ ∈ ∈

−

−

−

−

−

−

−

=

Jj Ll Ttjctjct

Dd Ll Cc Ttdlctdlct

Jj Cc Ttjltjlt

Ii Kk Kk Cc Ttctikkcikk

Jj Cc Ttjctjc

Ii JMj Kk Cc Ttijkctikct

Jj Ll Cc Ttjlctjlt

Jj Ll Cc TtjlctjltCPFN

F

YP

SF

Z

V

W

P

SZMax

i i

ik i

φ

ω

θ

ζ

ξ

δ

ϕ

γ

'''

Amount chemical sold

Amount chemical bought

Process operation cost

Inventory cost

Changeover cost

Shortfall penalty cost

Transportation cost

Raw material delivery cost

List of Assumptions

AssumptionsMass balance of raw materials and byproducts are proportional to the main product of the process and respective production scheme.The operating cost of a process is proportional to the amount of main product produced.Changeover only implies in cost and the overall time spent is negligible.Only one delivery of chemicals from one market over τc time interval is allowed. Demand is given by a range of values, having an upper and a lower bounds

CFPN Model – Constraints

Ratio of input chemicals to the main product

Ratio of output chemicals to the main product

Limits production under available capacity

Indicates when changeover occurred ( Zikk’ct = 1)

Allows only one production scheme per time period

TtCcKkJMjJIjIiWW iikikcjkctijijkcijkct ∈∈∈∈∈∈= ,,,',,'µ

TtCcKkJMjJOjIiWW iikikcjkctijijkcijkct ∈∈∈∈∈∈= ,,,',,'µ

TtCcKkJMjIiQW iikjicijckijkct ∈∈∈∈∈≤ ,,,,ρ

TtCcKkKkIiZYY iijctikkctikikct ∈∈∈∈∈≤−+ + ,,',,1 '1'

TtCcKkIiY ijKk

ikcti

∈∈∈∈=∑∈

,,,1

CFPN Model – Constraints (Cont’d)

Mass balance of chemicals in the network

Delivery of raw materials

Limits one delivery of chemicals over a τc time interval.

Prevents the purchase of raw material from exceeding the available amount

TtCcLlJjPYPPDd

Ujlctdlctjlct ∈∈∈∈≤ ∑

∈

,,,

TtCcLlDdYPYPYP dlcttdlctdlc ∈∈∈∈≤++ −− ,,,11,2,

TtLlJjaP Ujlt

Ccjlct ∈∈∈≤∑

∈

,,

{ }TtCcJjFWSVFPWV

cCctjc

Ii Kkijkct

Lljlctjctjct

Lljlct

Oi Kkijkcttjc

j ij i

∈∈∈+++=+++ ∑∑∑∑∑∑∑−∈∈ ∈∈∈∈ ∈

− ,,'

'1,

CFPN Model – Constraints (Cont’d)

Limits the product sales below the maximum allowable demand

Shortfall penalty if the minimum demand is not met

Bounds

TtLlJjSdSFSFCc

jlctLjlttjljlt ∈∈∈−+≥ ∑

∈− ,,1,

{ }1,0,0,,,,,,

1

'

'

∈

≥≤

≤

dlctikct

ctikkijkctjctjltjlctjlctjct

ctikk

Ujctjct

YPYZWVSFSPF

ZVV

TtLlJjdS Ujlt

Ccjlct ∈∈∈≤∑

∈

,,

Decomposition techniques considered

RelaxationLagrangean relaxation

Easier to solveRelaxing the right constraintObtaining a good multiplier

Lagrangean/surrogate relaxationReduction in the oscillating behavior

Updating multipliersSubgradient optimization

Simple algorithm structure

Modified subgradient optimizationAccelerating convergence

A more suitable step sizeImproved search direction

Solving relaxed problems

Updating the multipliers

Terminating criteria

Returning Solutions

Yes

No

Lagrangean and Lagrangean/surrogate relaxation

Lagrangean relaxation

Lagrangean/surrogate relaxation

n

m

yx

eDyCxbByAxdycxZ

}1,0{0

max

∈

≥

≤+≤+

+=

( )( )

n

m

yx

eDyCxByAxbucxuZ

}1,0{0

max)(

∈

≥

≤++−+=

( )( )

{ } .1,00

max)(

n

m

u

y

xeDyCx

ByAxbutcxtZ

∈

≥

≤++−⋅+=

General MIP

Narciso and Lorena, EJOR 1999, 114, 165

Subgradient and modified subgradient optimization

Subgradient optimization

Modified subgradient optimization

kk

kk gtuu +=+1( )( )2k

kk

kg

uLwlt −= ( )0,2 2121 >−≤≤ εεεε kl

kk

kk dtuu +=+1

;1−+= kk

kk dgd ξ

;)1(0 crr LLL αα −+=

( ) ≥

= − otherwiseerrif

rrr 26.316933.0

20εα

≥−

=−

−

−

Otherwise

gdIfd

gd kk

k

kk

k

0

,0121

1

γξ

−

= 2

)(1k

k

kk

d

uLLtβ

Fumero, Comp. & Oper. Res. 2001, 28, 33-52.

Observation

Constraints that link variables at different time period

The model can be decomposed into |T| separate problems if the variables at different time periods in these constraints are treated as different variables.

TtCcKkKkIiZYY iijctikkctikikct ∈∈∈∈∈≤−+ + ,,',,1 '1'

{ }TtCcJjFWSVFPWV

cCctjc

Ii Kkijkct

Lljlctjctjct

Lljlct

Oi Kkijkcttjc

j ij i

∈∈∈+++=+++ ∑∑∑∑∑∑∑−∈∈ ∈∈∈∈ ∈

− ,,'

'1,

TtCcLlDdYPYPYP dlcttdlctdlc ∈∈∈∈≤++ −− ,,,11,2,

TtLlJjSdSFSFCc

jlctLjlttjljlt ∈∈∈−+≥ ∑

∈− ,,1,

Decomposition applied

Following equations are declared and converted to the equivalentinequality form

Following variable replacement are done

The model is decomposed into |T| sub-problems through relaxation

Ctdlctdlc

Btdlctdlc

Adlctdlct

Bikctikct

Atikctikc

Ctjltjl

Bjltjlt

Ctjctjc

Bjctjct

YPYPYPYPYPYP

YYYY

SFSFSFSF

VVVV

2,2,1,1,

1,1,

1,1,

1,1,

,,

,

,

,

−−−−

++

−−

−−

→→→

→→

→→

→→

Cdlct

Bdlct

Cdlct

Bdlct

Cdlct

Bdlct

Bdlct

Adlct

Bdlct

Adlct

Bdlct

Adlct

Bikct

Aikct

Bikct

Aikct

Bikct

Aikct

Cjlt

Bjlt

Cjlt

Bjlt

Cjlt

Bjlt

Cjct

Bjct

Cjct

Bjct

Cjct

Bjct

YPYPandYPYPYPYP

YPYPandYPYPYPYP

YYandYYYY

SFSFandSFSFSFSF

VVandVVVV

≤≥→=

≤≥→=

≤≥→=

≤≥→=

≤≥→=

Lagrangean relaxation

Relaxing the following inequalities into objective

Adding the remaining inequalities as constraints

Resulting objective function

Cdlct

Bdlct

Bdlct

Adlct

Bikct

Aikct

Cjlt

Bjlt

Cjct

Bjct YPYpYPYPYYSFSFVV ≥≤≥≤≤ ,,,,

Cdlct

Bdlct

Bdlct

Adlct

Bikct

Aikct

Cjlt

Bjlt

Cjct

Bjct YPYpYPYPYYSFSFVV ≤≥≤≥≥ ,,,,

∑ ∑∑∑∑ ∑∑∑∑ ∑∑

∑ ∑∑∑∑ ∑∑∑ ∑∑

∑ ∑∑∑∑ ∑∑∑ ∑∑∑∑∑ ∑∑

∑ ∑ ∑ ∑∑∑ ∑∑∑∑ ∑∑∑

∈ ∈ ∈ ∈∈ ∈ ∈ ∈∈ ∈ ∈

∈ ∈ ∈ ∈∈ ∈ ∈∈ ∈ ∈

∈ ∈ ∈ ∈∈ ∈ ∈∈ ∈ ∈ ∈ ∈∈ ∈ ∈

∈ ∈ ∈ ∈ ∈∈ ∈ ∈ ∈∈ ∈ ∈ ∈−

−+

−+

−+

−+

−+

−

−

−

−

−

−

−

=

Tt Dd Ll Cc

Cdlct

Bdlct

YPdlct

Tt Dd Ll Cc

Adlct

Bdlct

YPdlct

Tt Jj Ll

Bjlt

Cjlt

SFjlt

Tt Ii Kk Cc

Bikct

Aikct

Yikct

Tt Jj Cc

Bjct

Cjct

Vjct

Tt Jj Lljctjct

Tt Dd Ll Cc

Adlctdlct

Tt Jj Cc

Bjltjlt

Tt Ii Kk Kk Ccctikkcikk

Tt Jj Cc

Bjctjc

Tt Ii JMj Kk Ccijkctikct

Tt Jj Ll Ccjlctjlt

Tt Jj Ll CcjlctjltLRCFPN

YPYPuYPYPuSFSFu

YYuVVuF

YPSFZV

WPSZMax

i

i i

ik i

)()()(

)()(

21

'''

φ

ωθζξ

δϕγ

Lagrangean relaxation (Cont’d)

Resulting objective function at time period t

The total profit is equal to the summation over the time periods

∑∑∑∑∑∑

∑∑∑∑∑∑∑

∑∑∑∑∑∑∑∑∑∑∑

∑∑∑ ∑ ∑∑∑∑∑∑∑∑

∈ ∈ ∈∈ ∈ ∈

∈ ∈∈ ∈ ∈∈ ∈

∈ ∈∈ ∈ ∈∈ ∈∈ ∈ ∈ ∈

∈ ∈∈ ∈ ∈ ∈∈ ∈ ∈∈ ∈ ∈−

−+−+

−+−+−+

−−−−

−−−=

Dd Ll Cc

Cdlct

Bdlct

YPdlct

Dd Ll Cc

Adlct

Bdlct

YPdlct

Jj Ll

Bjlt

Cjlt

SFjlt

Ii Kk Cc

Bikct

Aikct

Yikct

Jj Cc

Bjct

Cjct

Vjct

Jj Lljctjct

Dd Ll Cc

Adlctdlct

Jj Cc

Bjltjlt

Ii Kk Kk Ccctikkcikk

Jj Cc

Bjctjc

Ii JMj Kk Ccijkctikct

Jj Ll Ccjlctjlt

Jj Ll Ccjlctjlt

tLRCFPN

YPYPuYPYPu

SFSFuYYuVVu

FYPSFZ

VWPSZMax

i

i i

ik i

)()(

)()()(

21

''' φωθζ

ξδϕγ

∑∈

−− =Tt

tLRCFPNLRCFPN ZZ

Lagrangean relaxation - Constraints

CcKkJMjJIjIiWW iikikcjkctijijkcijkct ∈∈∈∈∈= ,,',,'µ

CcKkJMjJOjIiWW iikikcjkctijijkcijkct ∈∈∈∈∈= ,,',,'µ

CcKkJMjIiQW iikjicijckijkct ∈∈∈∈≤ ,,,ρ

CcKkKkIiZYY iijctikkCtcik

Bikct ∈∈∈∈≤−+ + ,',,1 '1,'

CcKkIiY ijKk

Bikct

i

∈∈∈=∑∈

,,1

{ }CcJjFWSVFPWV

cCctjc

Ii Kkijkct

Lljlct

Bjctjct

Lljlct

Oi Kkijkct

Ctjc

j ij i

∈∈+++=+++ ∑∑∑∑∑∑∑−∈∈ ∈∈∈∈ ∈

− ,'

'1,

CcLlJjPYPPDd

Ujlct

Cdlctjlct ∈∈∈≤ ∑

∈

,,

CcLlDdYPYPYP Adlct

Btdlc

Ctdlc ∈∈∈≤++ −− ,,11,2,

List of constraints

Lagrangean relaxation – Constraints (Cont’d)

LlJjaP Ujlt

Ccjlct ∈∈≤∑

∈

,

LlJjdS Ujlt

Ccjlct ∈∈≤∑

∈

,

LlJjSdSFSFCc

jlctLjlt

Ctjl

Bjlt ∈∈−+≥ ∑

∈− ,1,

1,, ' ≤≤≤ ctikkUjct

Cjct

Ujct

Bjct ZVVVV

Cdlct

Bdlct

Bdlct

Adlct

Bikct

Aikct

Cjlt

Bjlt

Cjct

Bjct YPYpYPYPYYSFSFVV ≤≥≤≥≥ ,,,,

0,,,,,,,, ' ≥ctikkijkctCjct

Bjct

Cjlt

Bjltjlctjlctjct ZWVVSFSFSPF

{ }1,0,,,, ∈Cdlct

Bdlct

Adlct

Bikct

Aikct YPYPYPYY

Lagrangean/surrogate relaxation

Lagrangean/surrogate relaxation is done in a similar fashion like the Lagrangean relaxationResulting objective function at each time period t

Subject to the same constraints as the Lagrangean relaxation Total Profit:

−+−+

−+−+−×+

−−−−

−−−=

∑∑∑∑∑∑

∑∑∑∑∑∑∑

∑∑∑∑∑∑∑∑∑∑∑

∑∑∑ ∑ ∑∑∑∑∑∑∑∑

∈ ∈ ∈∈ ∈ ∈

∈ ∈∈ ∈ ∈∈ ∈

∈ ∈∈ ∈ ∈∈ ∈∈ ∈ ∈ ∈

∈ ∈∈ ∈ ∈ ∈∈ ∈ ∈∈ ∈ ∈−

Dd Ll Cc

Cdlct

Bdlct

YPdlct

Dd Ll Cc

Adlct

Bdlct

YPdlct

Jj Ll

Bjlt

Cjlt

SFjlt

Ii Kk Cc

Bikct

Aikct

Yikct

Jj Cc

Bjct

Cjct

Vjct

Jj Lljctjct

Dd Ll Cc

Adlctdlct

Jj Cc

Bjltjlt

Ii Kk Kk Ccctikkcikk

Jj Cc

Bjctjc

Ii JMj Kk Ccijkctikct

Jj Ll Ccjlctjlt

Jj Ll Ccjlctjlt

tLSCFPN

YPYPuYPYPu

SFSFuYYuVVut

FYPSFZ

VWPSZMax

i

i i

ik i

)()(

)()()(

21

''' φωθζ

ξδϕγ

∑∈

−− =Tt

tLSCFPNLSCFPN ZZ

General Algorithm Setting bounds and

determining parameters 1

Fix: Yikc,1Vjc,1SFjl,1YPdlc,1

2


3


T…Fix: Yikc,t-1Vjc,t-1SFjl,t-1YPdlc,t-1

|T| sub-problems

Fix Yikct and YPdlct

Terminating Criteria

Starting next iteration

Updating the multipliers:

Subgradient optimization

Modified subgradient optimization

No

Return lower bound and corresponding solution

Yes

t = 2t = 3

t = T

Linking Constraints

Full Scale

t = 1

Proposed strategy

Strategy ALagrangean relaxation with subgradient optimization

Strategy BLagrangean relaxation with modified subgradient optimization

Strategy CLagrangean/surrogate relaxation with subgradient optimization

Strategy DLagrangean/surrogate relaxation with modified subgradient optimization

Results – Calculation time

Calculation time vs time period

0

200400

600800

1000

0 20 40 60 80

time period

Cal

cula

tion

time

(sec

)

Full-scaleStrategy AStrategy C

Results – Solution value

Solution Value vs time period

05000

1000015000200002500030000

0 20 40 60 80

time period

Solu

tion

valu

e ($

)

Full-scaleStrategy AStrategy C

Results – Percent difference from the optimum

1.3131.31742

0.8240.83335

0.8260.82928

1.7231.19521

0.5360.55414

0.0000.0007

Strategy CStrategy Atime period

Conclusion

Calculation timeTime spent is much less than the full scale method

Solution valueThe percentage deviation from the optimum is below 2%

Lagrangean vs. Lagrangean/surrogate relaxationLagrangean/surrogate always used equal or more iterationsLagrangean/surrogate spent slightly more timeFor same number of iterations, Lagrangean relaxation gave equal or better solution value

Alternative approaches

Decentralized approachModel predictive control strategies

Multiproduct, multiechelon distribution networks with multiproduct batch plants (Perea, Ydstie and Grossmann, 2003)

Comparison with integrated approachPoorer coordination of the supply chain decisionsSmaller computational time

Future work

Implementing modified subgradient optimizationTesting strategies B and D and compare them with A and CSearch for new strategies

Other decomposition methodsApplying search_t* algorithm for each set of multiplier values

JOSÉ M. PINTO

IV.Planning, Scheduling and Supply

Chain Management for Operations in Oil Refineries

OUTLINE

• Introduction • Planning Models

– refinery diesel production

• Scheduling models– crude oil scheduling– fuel oil / asphalt area

• Logistics– oil supply model

• Petroleum Supply Chain• Conclusions

MOTIVATION

Refinery TargetsProfitability Maximization (Pelham and Pharris, 1996; Ramage, 1998)

Minimization of Operational Costs(Bodington and Shobrys, 1996)

Beginning of Computational Applications for Planning/Scheduling:

Petrochemical Industry: 1950s (Linear Programming) (Symonds, 1955; Bodington, 1992) (Dantzig, 1963)

CPI in general: 1970s (Reklaitis, 1991; Kudva and Pekny; 1993)

ADVANCESAvailability of more powerful and less expensive computers;Mathematical Developments:

Time representation; (Moro and Pinto, 1998)

Combinatorics in MIP;(Raman and Grossmann, 1994)

Non-convexities in MINLP;(Viswanathan and Grossmann, 1990)

Consequences for the Petroleum Industry: (Ramage, 1998)

Unit Level Optimization (FCC, Crude Unit, etc..)

Large Portions of the Plant or Plant-wide Optimization

1980’s 1990’s

OPTIMIZATION IN REFINERY OPERATIONS

LPs in crude blending and product pooling (50´s) (Symonds, 1955)

Advanced control : MPC (Cutler, DMCC,1983)

Planning models (Coxhead, Moro et al, 1998.)

crude selection, crude allocation for multi refinery

partnership models for raw material supply

OVM Refinery, Austria (LP) (Steinschorn and Hofferl, 1997)

In-house simulation models for scheduling (Magalhaes et al., 1998)

Scheduling optimization models

gasoline blending (Bodington, 1993)

gasoline production, TEXACO(NLP) (Rigby et al., 1995)

crude oil unloading (Lee et al., Shah, 1996)

OUTLINE


– refinery diesel production• Scheduling models

– crude oil scheduling– fuel oil / asphalt area


• Conclusions

Objectives

• To develop a general representation for refinery units

– streams with multiple inputs and destinations

– nonlinear mixing and process equations

– bounds on unit variables

• To apply to the production planning of a real world refinery

– diesel production

– to satisfy multiple specifications

PLANNING MODEL FOR REFINERIES

TYPICAL PROCESS UNIT

UNIT EQUATIONS

- Feed flowrate:

- Feed Properties:

Pu,F,j = fj ( Qu’,s,u , Pu’,s,j ) u’ Uu, s Su’,u, j Js

- Total flowrate of each product stream:

Qu,s = f ( Qu,F , Pu,F,j , Vu ) j JF, s SU

- Unit product stream properties:

Pu,s,j = fj ( Pu,F,j , Vu ) j Js, s SU

- Product streams flowrates (splitter):

s SU

Qu F Qu s us Su uu Uu

, ' , ,,

=∈ ′′∈∑∑

Q Qu s u s uu Us,u

, , ,= ′′∈∑

∈∈

∈

∈∈

∈∈∈

HYDROTREATING UNIT (HT)

HT MODEL

Feed flowrate:

QHT,F=QCD1,HD,HT+QCD2,HD,HT+QFCC,LCO,HT+QCK,CGO,HD

Feed properties:

PHT,F,j = fj (Qu’,s,HT , Pu’,s,j ) u’ UHT , s Su’,HT, j JHT

Example - Flash Point (FP)

Iu,HD,FP = exp[10006.1/(1.8 Pu,HD,FP+415) - 14.0922] u UHT

( )PHT F FP, , ..

ln .=

+−

0 5510006 1

14 0922415

αα =

∈

∈

∑

∑

Q I

Q

u HD HTu HT

u HD FP

u HD HTu HT

U

U

, , , ,

, ,

∈

∈∈∈

REAL-WORLD APPLICATION

Planning of diesel productionPetrobras RPBC refinery in Cubatão (SP, Brazil).

Three types of diesel oil:

Metropolitan Diesel. Low sulfur levelsmetropolitan areas

Regular Diesel. Higher sulfur levelsother regions of the country

Maritime Diesel. High flashing point.

DIESEL SPECIFICATIONS

PropertyREGULAR

DIESELMETROPOLITAN MARITIME

DENSITYmin / max

0.82/0.88

0.82/0.88

0.82/0.88

FLASH POINTmin (°C)

- - 60.0

ASTM 50%min / max (°C)

245.0/310.0

245.0/310.0

245.0/310.0

ASTM 85%max (°C)

370.0 360.0 370.0

CETANE NUMBER min 40.0 42.0 40.0SULFUR CONTENT max

(% WEIGHT)0.5 0.2 1.0

MAIN RESULTS

Potential Improvement US$ 23,000 / day or US$ 8,000,000 / yrImplemented with on-line data acquisition

OUTLINE





• Conclusions

PROPOSED APPROACH FOR PLANNING AND SCHEDULING

CrudeScheduling

FRACTIONATION

LPG Scheduling

Fuel Oil / AsphaltScheduling

REFINERY PLANNING

SHORT TERM CRUDE OIL SCHEDULING Crude Oil System

OBJECTIVES

maximize total operating profitrevenue provided by oil processing cost of operating the tanks

generate a schedule for crude oil operations receiving oil from pipelinewaiting for brine settlingfeeding the distillation units

TIME SLOT REPRESENTATION

MILP OPTIMIZATION MODEL

Max total operating profitsubject to:

Timing constraintsPipeline material balance equationsPipeline operating rules

Pipeline always connected to a tank

Material balance equations for the tanksVolumetric equationsComponent volumetric balance

Tank operating rulesMinimum settling time

Rules for feeding the distillation unit

DECISION VARIABLES

slot k

Ypj,kYdf,j,k

fraction f

REAL-WORLD EXAMPLE

Oil parcel Volume

(m3)

Start time

(h)

End Time

(h)

Composition

1 60,000 8 20 100% Bonito

2 50,000 48 58 100% Marlin

3 1,000 58 58.2 100% Marlin

4 60,000 100 112 100% RGN

Tank initial conditions

Distillation target flowrate = 1500 m3/h

RESULTS

MODEL SOLUTION

• GAMS / OSL

• CPU time2.80 hrs (Pentium II 266 MHz 128 MB RAM)

• Variable size time slot model912 discrete variables

3237 continuous variables

5599 equations

• Fixed size time slot model

21504 discrete variables !

OUTLINE





• Conclusions

FUEL OIL/ASPHALT PRODUCTION SCHEDULING PROBLEM

•The plant produces ≅ 80% of all Brazilian fuel oil;

•The plant has relevant storage limitations;

•Complexity of distribution operations;

•End of the monopoly in the Brazilian oil sector.

Product Base Diluent usedFO1FO2FO3FO4UVO1UVO2CAP07CAP20

OCC+LCO or OCC or LCOOCC+LCO or OCC or LCOOCC+LCO or OCC or LCOOCC+LCO or OCC or LCOpure LCOpure LCOpure HGpure HG

RASF RASF RASF RASF RASF RASF RASF RASF

major specification:viscosity

MATHEMATICAL MODELS

non-convex MINLP (5 bilinear products in the viscosity constraints);

Uniform Discretization of Scheduling Horizon;

Objective Function: Minimize the Operational Cost.

First Approach:

MILP;

Second Approach:

Linear Transformation

COST = Raw-Material Costs + Inventory Costs + + Pumping Costs + Transition Costs

MINLP MODEL

) CHANGETRAN()]FIDCB(

)VQCINVD()VQCINVQ()VICINVI(

FRASFMCRFRLCOCDFOCCRCD)FDCCD([COST

p,n

O

1o

P

1p

N

1nn,p,ot,o,i

I

1i

O

1oi

t,d

D

1ddt,q

Q

1qqt,i

I

1ii

t3t2t,s

T

1t

S

1ss

⋅+⋅+

+⋅+⋅+⋅+

+⋅+⋅+⋅+⋅=

∑∑∑∑∑

∑∑∑

∑ ∑

= = == =

===

= =

Minimize:

Material Balance Constraints:

Subject to:

volume in i at t’ = initial volume in i + [ inputs in i up to t’ - ( outputs from i up to t’ ) ]

the volume capacities of all tanks are also subject to bounds

Operating Rules for the Plant:

at each t, the plant production must be stored in one single tank

,...,T1 t1)(XQC)(XICQ

1qq,t

I

1ii,t ==+∑∑

==

FO area UVO/asphalt area

Demand Supply of Plant Products

∑=

==≤+O

1oi,o,ti,t ,...,T1,...,I; t1 i1)(XIDXIC

simultaneous tank loading and unloading is not allowed (exception: HG storage tank)

FO area

Operating Rules for the Plant (continuation):

UVO / Asphalt may be sent to truck terminals only between 6:00 a.m. and 6:00 p.m.

,...,Q1 q;b)DT/12(t1)1b()DT/12()];DT/12/(T[,...,1b

HTXQD bq,t

=⋅≤≤+−⋅=

≤

while a asphalt is produced, the RASF diluent must be HG

,...,T 1 t0XDRASF)(XQC8

5q,t1q,t ==−∑

=

while asphalt is produced, the OCC stream from UFCC must be directed to storage in TK-42208

Material Flow Constraints:

,...,T1 t1)XZ1(XDRASF t,t1 =≤−+

flowrates to oil-pipelines must obey pump limitations

,...,T1,...,O; t1,...,I; o1 iFIDXIDFID0 maxi,o,ti,o,t ===⋅≤≤

flowrates to truck terminals must obey pump limitations

,...,T1,...,Q; t1 qFQDXQDFQD0 maxq,tq,t ==⋅≤≤

Viscosity Constraints:

at each t, the viscosity adjustment must be done regarding the kind of product

,...,T1) tXIC(MIFO)XQC(MIUVVISC i,t

I

1i Pppq,t

Q

1q Vvvt

iq

=⋅+⋅= ∑ ∑∑ ∑= ∈= ∈

also, the availability of diluents should be considered

,...,T1t]}FRLCOFOCCRFRASFU)(FDRASF([VISC

]MIDFRLCOMIDFOCCRMIRASFFRASFU)MID(FDRASF{[

,...,T 1t

VISC]}FRLCOFOCCRFRASFU)(FDRASF([

]MIDFRLCOMIDFOCCRMIRASFFRASFU)MID(FDRASF{[

ttt

D

1dd,tt

3t2tt

D

1d

2s

Sssd,t

t

ttt

D

1dd,t

3t2tt

D

1d

2s

Sssd,t

d

d

=+++⋅=

=⋅+⋅+⋅+⋅

=

=+++

⋅+⋅+⋅+⋅

∑

∑ ∑

∑

∑ ∑

=

=

≤

∈

=

=

≤

∈

or

5 bilinear products non-convex MINLP

EXACT MILP MODEL

Similar MINLP model structure; More continuous variables than MINLP model;More constraints than MINLP model;Combinatorial feature of the MINLP model preserved.

Characteristics:

Structure: non-convex

MILP Model = MINLP Model +

Nonlinear Viscosity Constraints

+ Linearized Constraints

CONSTRAINTS FOR LINEAR TRANSFORMATION

,...,T1',...,I; t1)] i(FIDK[FIRASFKMIVIZVIKO

1oi,o,t

't

1ti,tii'i,t ==−+⋅= ∑∑

==

,...,T1',...,Q; t1) qFQDK(FQRASFKMQVQZVQK q,t

't

1tq,tqq'q,t ==−+⋅= ∑

=

,...,T1 t)FQRASFK()FIRASFK(MIDFRLCO

MIDFOCCR)MIDFDRASF( MIRASFFRASFU

I

1i

Q

1qt,qt,i3t

2t

D

1ds

2s

Sst,dt

d

=+=⋅+

+⋅+⋅+⋅

∑ ∑

∑ ∑

= =

=

≤

∈

,...,T1,...,I; t1t itan consU U XICFIRASFK i,ti,t ===⋅≤

,...,T1,...,Q; t1t qtanconsU UXQCFQRASFK q,tq,t ===⋅≤

,...,T1,...,I; t1 i VIKMIVI t,iit,i ===⋅

,...,T,...,Q; t qVQKMQVQ q,tqq,t 11 ===⋅

,...,T1t ;O,...,1,...,I; o1 i FIDKMIFID t,o,iit,o,i ====⋅

,...,T1,...,Q; t1 qFQDKMQFQD q,tqq,t ===⋅

Mat

eria

l Bal

ance

Flow

Vis

cosi

ty

(48)

(49)

(50)

(52)

(51)

(54)

(53)

(47)

(46)

REAL-WORLD EXAMPLE

instanceevaluated

Scheduling horizon: 3 days

Time span: 2 hours

Nominal production: 200,000 m3/month

PRODUCTION SCHEDULE AND STORAGE INFORMATION

0

1

TK-4

4113

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3307

TK-4

3301

TK-4

3302

TK-4

4108

TK-4

3302

TK-4

4108

TK-4

3301

TK-4

4108

TK-4

3301

TK-4

4108

TK-4

3302

TK-4

3307

TK-4

3301

TK-4

4113

TK-4

3301

TK-4

3301

TK-4

3307

TK-4

3307

TK-4

3301

TK-4

4108

TK-4

4108

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3301

TK-4

3303

TK-4

3302

TK-4

3307

TK-4

3301

TK-4

3301

TK-4

3301

TK-4

3301

START END

UVO1 UVO2 CAP07 CAP20 FO1 FO2 FO3 FO4

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Each

inte

rval

= 20

m3 /h

diluent from TK-42221 (HG) diluent from TK-42208 (OCC+LCO)pure OCC from UFCC pure LCO from UFCC

FO1 (p=1)

02468

10

1 4 7 10 13 16 19 22 25 28 31 34 37

TK-43301 (i=1)

TK-43302 (i=2)

FO2 (p=2)

02468

1012

1 36

TK-43303 (i=3)TK-43304 (i=4)

FO3 (p=3)

02468

10

1 36

TK-43305 (i=5)TK-43306 (i=6)

FO4 (p=4)TK-43307(i=7)

02468

10

1 36

CAP-20 (v=4)

0

2

4

1 36

TK-44110 (q=6)TK-44115 (q=7)TK-44116 (q=8)

CAP-07 (v=3)TK-44108 (q=5)

0

2

4

1 36

UVO2 (v=2)

0

2

4

1 36

TK-44111 (q=3)TK-44112 (q=4)

UVO1 (v=1)

0

2

4

1 36

TK-44113 (q=1)TK-44114 (q=2)

Schedule of diluents in the mixer

Volume (x 10-3 m3) in product storage tanks

OIL-PIPELINE TO SÃO PAULO - CASE A(RESTRICTED PERIOD: 6:00 a.m./12:00 p.m. - 1st day)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

OIL-PIPELINE TO SÃO PAULO - CASE B(RESTRICTED PERIOD: 0:00 a.m./6:00 p.m. - 2nd day)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

OIL-PIPELINE TO SÃO PAULO - CASE C(RESTRICTED PERIOD: 6:00 p.m./12:00 a.m. - 2nd/3rd days)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

OIL-PIPELINE TO SÃO PAULO - CASE D(RESTRICTED PERIOD: 12:00 a.m./6:00 a.m. - 3rd/4th days)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

UVO1 TRUCK TERMINAL

020406080

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h)

from TK-44113 (q=1)

from TK-44114 (q=2)

UVO2 TRUCK TERMINAL

020406080

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h)

from TK-44111 (q=3)

from TK-44112 (q=4)

CAP-07 TRUCK TERMINAL

from TK-44108 (q=5)

020406080

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h)

CAP-20 TRUCK TERMINAL

020406080

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h)

from TK-44110 (q=6)from TK-44115 (q=7)from TK-44116 (q=8)

Dispatch schedule for ultra-viscous oilTransfer schedule for fuel oils

TRANSITION PROCESS IN OIL-PIPELINES

to

t1 > to

t2 > t1

t3 > t2

TRANSITION COST

Final Product A

Final Product B

Final Product C

FLOW

UNDESIRABLE MIX

Refinery Market

4514

6890

15121512

4465

2629

MINLP model MILP model

number of 0-1 variablesnumber of constraintsnumber of continuous variables

68907985

1512 19684465

6733

WITHOUT TRANS.CONSTRAINTS

WITH TRANS.CONSTRAINTS

number of 0-1 variablesnumber of constraintsnumber of continuous variables

case MIP model nodes iterations CPU time (s) objectiveMILP 937 15674 570.46 969.61A MINLP - 13815 335.36 966.99MILP 1296 16626 711.01 965.72B MINLP - 15508 391.45 961.14MILP 764 13086 490.86 954.99C MINLP - 23792 531.98 956.99MILP 1197 23080 851.78 950.65D MINLP - 12845 299.30 959.49

OIL-PIPELINE TO SÃO PAULO(WITH TRANSITION MODELING)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

LOCAL OIL-PIPELINE(WITH TRANSITION MODELING)

0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

(m3/h) FO1FO2FO3FO4

MILP models

OUTLINE





• Conclusions

CRUDE OIL SUPPLY PROBLEM

• Solution of oil supply problems among crude oil terminals and refineries

MOTIVATION

• Increasing utilization of the system– Larger crude oil demand for crude oil in refineries– Outsource of transportation

• Potential economic impact– No systematic scheduling– Operations involve high costs and aggregated values

• Petrobras distribution complex– 4 refineries in the State of Sao Paulo

PETROBRAS DISTRIBUTION COMPLEX

Types of crude oil

PROBLEM SPECIFICATION

iDetermined by the petroleum origin

iApproximately 42 types of crude oil may be processed

Types ofcrude oil

Classes of crude oil

iSets of crude oil types with similar properties

iNecessary due to limited amount of tanks

i7 classes


Types of crude oil


Tankers

iTransport types of crude oil

iOverstay incurs in additional costs- US$ 10 k to US$ 20 k per day


Types of crude oil


Tankers

Piers

iDifferent capacities


TanksPiersiStore classes of crude

oil

iMinimum storage levels

iSettling time between loading and unloading operations

Types of crude oil


Tankers


Tanks

Pipe-lines


Tankers

Piers

iFlow rate at each pipeline limited by the density of the heaviest crude oil class

iPossible to connect to at most one tank at everytimeTypes of

crude oil


Tanks

Pipe-lines

Sub-stations

Types of crude oil


Tankers

Piers

iBuffer operations between terminal and refineries

iStore difference in flow rate between inlet and outlet pipelines


Mathem

atical formulation

Tanks

Tankers

Substations

Refineries

Pipelines

Crude types

Piers

• Input parameters– Operating

constraints– Initial

inventory– Costs– Possible

allocations

System operation

iSchedules- Allocation of

crude oil types to classes

- Assignment of tankers to piers

- Loading- Unloading- Settling

OBJECTIVES

Terminal

Pipelines

Substations

RefineriesImpossible to solve complete problem

PROPOSED STRATEGY

iDecomposition of the problem in three formulations

- Port Model

- Substation Model

- Algorithm to adjust timing of pipelines

PROPOSED STRATEGY

• Port Model

• Results– Allocation of tankers to

piers– Loading and unloading

profiles of tanks– Loading of pipelines– Timing of interfaces in

pipelines

PROPOSED STRATEGY

Port


Port Results for this refinery

PROPOSED STRATEGY

Pipelines

• Substation Model

Port

Pipelines

PROPOSED STRATEGY

Substations

Terminal

Pipelines

Substations


Refineries

… results for other refineries are determined

PROPOSED STRATEGY

MATHEMATICAL FORMULATION

• MILP model formulation• Time representation

– Continuous– Based on events

time

Vi Vi+1 Vi+2 Vi+3

Qi Qi+1 Qi+2 Qi+3

Xi Xi+1 Xi+2 Xi+3

Inventory level (cont. variable)

Amount generated (cont. variable)

Decision to produce (disc. variable)

Ti Ti+1 Ti+2 Ti+3Time events (cont. variable)

PROPOSED MODEL - VARIABLES

• Binary variables – Decisions– Assignment of ship n to pier p:– Unloading of ship n to tank t:– Unloading of tank t to oil pipeline o:

• Continuous variables– Timing– Inventory– Flowrates– Operating profit

pnA ,

etnLT ,,

eotUT ,,

MODEL ASSUMPTIONS AND OPERATING RULES

– Ships with earlier arrival date unload first in the same pier

– Each ship unloads to only one tank at any time

– Each pipeline receives crude oil from at most one tank at any time

– Each refinery is connected to the docking stations from one and

only one oil pipeline

– The same crude oil class has constant flowrates

PROPOSED MODEL - TIMING

• Ships, tanks and pipelines– Timing variables in each time event

• Initial• Final

• Matching of the timing variables– Unloading from ship n to tank t

– Unloading from tank t to pipeline o

fet

fen TTTN ,, =

seo

set TDTT ,, = f

eofet TDTT ,, =

set

sen TTTN ,, =

PORT MODEL - CONSTRAINTS

• Decisions

– Assignment of tanker n:

– Operation of tank t:

– Operation of tanker n:

– Operation of oil pipeline o:

1, =∑∈ nPp

pnA

1,,,, ≤+ ∑∑∈∈ tt Oo

eotNn

etn UTLT

1,, ≤∑∈ oTt

eotUT

1,, ≤∑∈ nTt

etnLT

PROPOSED MODEL – CONSTRAINTS

• Material balances– Tanks, Refineries

• Operational constraints– Ships and tanks: flowrate bounds

• Timing– Ships

– Tanks

( )∑∈

+≥nPp

entpnpn

startpn

sen ATN ,,,, .θτ

∑∈

≤nPp

endpn

fenTN ,, τ

fen

sen TNTN 1,, −≥

HTT fet ≤,

fet

set TTTT 1,, −≥

)1.( ,,,,,, −+∆+≥ ∑∑∈

′∈

′tt Nn

etnOo

eotdect

fet

set LTUTTTTT

PROPOSED MODEL – CONSTRAINTS

• Matching of timing variables– Ships ↔ Tanks

– Tanks ↔ Pipelines

)1.()1.( ,,,,,,, etns

ensetetn

sen LTHTNTTLTHTN −+≤≤−−

)1.()1.( ,,,,,,, etnfen

fetetn

fen LTHTNTTLTHTN −+≤≤−−

)1.()1.( ,,,,,,, eotset

seoeot

set UTHTTTDUTHTT −+≤≤−−

)1.()1.( ,,,,,,, eotfet

feoeot

fet UTHTTTDUTHTT −+≤≤−−

PROPOSED MODEL – OBJECTIVE FUNCTION

( )

( )

( )

cost) (interface .

tankers)oil theofcost (overstay .

cost)n utilizatio(pier .

tanks)in thecost (oil .

port) in the revenue oil initial - (final .

)refineries the torevenue (oil .max

1

1,,,,

,,

,

0,

1

1'',,,

∑ ∑ ∑ ∑

∑

∑ ∑

∑ ∑

∑ ∑

∑ ∑ ∑ ∑ ∑

∈≠′

∈′

−

=′′

∈

∈

∈

∈ ∈ ∩∈

−

=

−

−

−−

−

−+

=

o CLOclcllc

CLOlc

E

eeolccl

facelccl

sen

n

sen

p Nn

startpn

endpn

pierp

c Nncn

crudec

cl Ttt

TEt

classcl

r CLRcl Oo TTt

E

eeot

classrcl

o o

p

c

cl

r r ocl

INTCOST

TCOST

COST

CCOST

VVREVP

QutREVR profit

ττ

SUBSTATION MODEL - MAIN ASSUMPTIONS

iTanks cannot be loaded and unloaded simultaneously

iOutlet pipelines cannot be loaded by inlet pipelines and tanks simultaneously

iSubstation must receive crude oil at the flow ratesgenerated by the Pot Model- Lots of crude oil

SUBSTATION MODEL – SUMMARY

iMinimize- Cost = cost of tank loading/unloading +

cost of pipeline alignment +cost of interface

- Subject to:- Assumptions of the substation model- Operating constraints 8 Tank loading/unloading 8 Pipeline operation

- Timing constraints8 Inlet pipelines8 Tanks8 Outlet pipelines

REAL-WORLD PROBLEMREPLAN

RECAP

SEBATRPBC

GEBAST

SEGUA

REVAP

OSBAT III

OSBAT II

OSVAT I

OSVAT II

OSvAT III

OSVAT IV

OSBAT IV

P4

P2

P3

P1

São Sebastião

São José dosCampos

Paulínia

Guararema

Capuava

Cubatão

• Problem 1– Port Model

• Problem 2– Substation

Model

Problem 3– Substation

Model

• Problem 4– Substation

Model

COMPUTATIONAL RESULTS

• Smaller optimality gaps for the Port Model

• Large variation on computational times

Problem 1 Problem 2 Problem 3 Problem 4

Number of continuous variables 1996 4954 712 703Number of binary variables 1039 759 66 123Number of constraints 7203 10337 1158 1682Relaxed LP solution 21,768.32 23.00 11.00 11.39Best Integer Objective 20,073.96 42.00 21.00 15.00Optimality gap 7.78% 82.61% 90.91% 31.74%Nodes 1118 3784 3921 422Iterations 62313 74410 19321 5244CPU time (Pentium III 450MHz) 1,457.51 s 3,602.07 s 134.69 s 28.28 s

Port Model Substation Models

PROBLEM 1 – TANKERS AND TANKSPEDREIRAS

08

27

01020304050

30 35 40 45TBN01

B

0

20

40

60

60 62 64 66 68 70

FRONT BREA

05

0

30

60

90

120

10 15 20 25 30

REBOUÇAS

38

0

10

20

30

40

40 45 50

MURIAÉ

01a

01b

0

20

40

60

80

45 55 65 75 85

120

TBN02

C

0

5

10

15

20

85 86 87 88 89 90

RAVEN

D

0

20

40

60

90 95 100 105

TBN03

B

0

10

20

30

139 141 143 145

VERGINA II

38

0

30

60

90

85 90 95 100

NORTH STAR

26

0

50

100

150

95 100 105 110 115TBN04

E

0

20

40

60

154 161 168

PRESIDENTE

29a29b

0

20

40

60

80

90 100 110 120

CANTAGALO

A

0

5

10

15

20

0 1 2 3 4 5

TQ3210

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3208

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3214

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3219

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3237

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3241

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3215

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3233

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3238

Vmin

Vmax

07

14212835

0 24 48 72 96 120 144 168

TQ3242

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3217

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3234

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3239

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3243

Vmin

Vmax

02040

6080

0 24 48 72 96 120 144 168

TQ3218

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3235

Vmin

Vmax

020406080

0 24 48 72 96 120 144 168

TQ3240

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

TQ3244

Vmin

Vmax

020

4060

80

0 24 48 72 96 120 144 168

17.4

58.2

58.2

17.4

35

16.9

38.0 (P4)

27.8

3.7 (P4)

11.9 (P4)

0.6 (P4)

25.4 4.7 (P4)

15 (P4)

5.3 (P3)

24.7 (P3)

37.8 (P2)

19.6

CANTAGALO

PRESIDENTE

FRONT_BREA NORTH_STAR

48.8

2.2

28.06.1 (P4)

28.0

25.4

53.3

24 Hrs

12.2 (P2)

42.4 (P2)

63.6 (P2)

26.0 (P2)

2.2

19.6

29.4 (P4)

1.4 (P2)

51.1 (P3)

30L (P-4)

2.8

19.6

55.5 (P4)

60.4

PEDREIRAS

MURIAE

6.2 (P2)

24.3 Hrs

26.0 Hrs 66.0 (P2)

50.3Hrs

27.8

34.4

24 Hrs

60.0 (P4)

11.5 (P4)

42.4

63.6

61.8

2.8

28.9 (P3)

24 Hrs

43.2 Hrs

REBOUCAS

VERGINA II

67.7

55.7 (P1)

62.4 (P2)

48.8

34.8

11.0

58.7

11.5

24 Hrs 60.0 (P4)

42.4

19.6

TBN01

16.9 (P1)

62.4

24 Hrs

63.6

11.5

28.0

2.8

4.5 (P4)

24 Hrs

62.4 (P1)

60.0

58.7

2.2

TBN02

16.9

46.4 Hrs

67.7

60.4

27.8

33.9

14.1

62.4

RAVEN

48.8

16.9

41

TBN03

60

19.6

61.8

65

TBN04

62.4

70.2

65.1 2.6

26.5

62.4 16.9 60 59.1

0 24 48 72 96 120 144 168

P-1

P-2

P-3

P-4

TQ3208

TQ3210

TQ3214

TQ3215

TQ3217

TQ3218

TQ3219

TQ3233

TQ3234

TQ3235

TQ3237

TQ3238

TQ3239

TQ3240

TQ3241

TQ3242

TQ3243

TQ3244

OSVAT

OSBAT

SEGUA/E

OSBATII/S

Tempo (horas)

PROBLEM 1 – GANTT CHART

PROBLEM 1 – REFINERIES AND PIPELINESREPLAN+REVAP

Min

Max

0

400

800

1200

1600

0 24 48 72 96 120 144 168

REPLAN+REVAP (detailed)

850

900

950

1000

0 24 48 72 96 120 144 168

RECAP+RPBC

Min

Max

0

200

400

600

0 24 48 72 96 120 144 168

RECAP+RPBC (detailed)

310

320

330

340

350

0 24 48 72 96 120 144 168

Profile Pipeline OSBAT_I e OSBAT_II

0 24 48 72 96 120 144 168Tempo (hours)

Flux

de

Oil

Stationde

Guaratuba

RPBC

CL-7

CL-6

CL-7

CL-6

CL-7 CL-6

GEBASTProfile Pipeline OSVAT_I e OSVAT_II

0 24 48 72 96 120 144 168Tempo (hours)

Flux

de

Oil Station

deRio

Pardo

SEGUA CL-3

CL-5

CL-6

CL-5

CL-3

CL-4

CL-5 CL-4

CL-5

CL-5

CL-6

CL-5

GEBAST

CL-4

Flow rate OSVAT_I e OSVAT_II (1000 m^3/h)

012345

0 24 48 72 96 120 144 168

Flow rate OSBAT_I e OSBAT_II (1000 m^3/h)

0

1

2

0 24 48 72 96 120 144 168

PROBLEM 4 – GANTT CHART

1

1

1

2.6

2.6

8.5

10.8

7.5

12.6

10.3

1.4

8.5

1

12.6

7.5

11.2

2.3

8.3

15.2

4.3

1.4

8.4

11.2

11.2

4.6

8.4

8.4

8.3

2.3

4.6

4.3

4.6

15.2 4.60 24 48 72 96 120 144 168

OSBATIII/S

TQ40

TQ41

TQ42

OSBATIV/E

RECAP/E

Time (hours)

PROBLEM 4 – TANKERS, REFINERIES AND PIPELINES

TQ40

Vmin

Vmax

05

10152025

0 24 48 72 96 120 144 168

TQ41

Vmin

Vmax

05

10152025

0 24 48 72 96 120 144 168

TQ42

Vmin

Vmax

05

10152025

0 24 48 72 96 120 144 168

RECAP

Min

Max

0

40

80

120

0 24 48 72 96 120 144 168

RECAP (detailed)

60

70

80

0 24 48 72 96 120 144 168Flow rate OSBAT_IV (1000m^3/h)

0

0,34

0 24 48 72 96 120 144 168

Profile Pipeline OSBAT_IV

0 24 48 72 96 120 144 168

Flux

de

Oil

CL-7 CL-6

CL-7

SEBAT

CL-7 CL-6

RECAP

OUTLINE





• Conclusions

CONCLUSIONS

The LP based Branch and Bound Method (solver OSL): is satisfactory to generate “good” feasible solutions;no guarantee of global optimum solutions for all instances;

Issues:time representationblending/pooling transitions

Problems can be modeled as large scale MILPs / non-convex MINLP;

The OA/ER/AP Method (solver DICOPT++): is efficient to circumvent the non-convexity problem;is satisfactory to generate feasible solutions;has computational performance similar to MILP model.

CONCLUSIONS - CHALLENGES

The understanding of the problem itself can constitute the major difficulty;

Large Scale Systems - Main theoretical difficulties:

The cooperation between the modeler level and the plant floor level is essential and remains as the main challenge for the Operational Research

Continuous work necessary due to the dynamic nature of scheduling problems.

Complex problems with high combinatorial features;

NP-Complete Problems

Large Scale Systems - Main practical difficulties

Infeasible computational times

ACKNOWLEDGEMENTS

Researchers

M. Joly R. MásL. MoroR. RejowskiP. Smania

Financial Support

Petrobras

CAPESCNPqFAPESP

Engineers

C.A. GrattiM. F. LehnerM.V. MagalhãesA.C. Zanin

General Petroleum Supply Chain

• Iyer et al. (1998).• Van den Heever and

Grossmann (2000).• Van den Heever et al.(2000).

Ierapetritou et al. (1999). • Kosmidis (2002).• Barnes et al. (2002).

Oil field Infrastructure

InternationalPetroleumCommerce

• Operations

Research.

• Lee et al. (1996).

• Pinto et al. (2000).

• Más and Pinto (2002).

Crude Oil

Supply

• Ponnambalam (1992).

• Bok et al. (1998).

• Pinto and Moro (2000).

Refinery -Planning/Scheduling

• Ross (2000).

• Iakovou (2001).

• Magatão et al. (2002).

• Stebel et al. (2002).

• Rejowski and Pinto (2003).

Distribution

Development of an optimization model

that is able to represent

a petroleum supply chain to support the

decision making planning process of

supply, production and distribution

Objective

Refinery - Processing Unit Model

( ) u

u ,t u ',s ,u ,tu ',s

QF Q∈

= ∑US

( )u

u ,s ,t u ,t u ,s u ,p ,t u ,s ,v u ,v ,tu

QS QF . f PF QGain .V∈

= + ∑VO

u ,s

u ,s ,t u ,s ,u ',tu '

QS Q∈

= ∑UO

( )

( )

u

u

u',s ,u ,t u ',s , p ,tu ',s

u ,p ,tu ',s ,u ,t

u ',s

Q .PSPF

Q∈

∈

=∑

∑US

US

u ,s ,p ,t u ,s ,p u ,p ,t u u ,t u ,v ,t uPS f ( PF | p ,QF ,V | v )= ∈ ∈PI VO

L Uu u ,t uQF QF QF≤ ≤ L U

u ,v u ,v ,t u ,vV V V≤ ≤

Feed mixing

Unit

model

Bounds

Product splitting stream

Supply, Distribution – Storage Model

Supply, Distribution - Pipeline Model

( ) u

u ,t u ',s ,u ,tu ',s

QF Q∈

= ∑US u ,s ,t u ',s ,u ,tQS Q=

u ,s ,t u ,s ,u ',tQS Q=

Uu ,t uQF QF≤

( )

( )

u dem SB

u f

p pipe

u ,t u,t u ,t u ,t u,tt u t

u u,v u ,v ,t u,t u u ,tu t v u t

u u ,t u u ,tu t u t

Max Z Cp . QF Vol .Cpet .Lot

[ Cr Cv .V ] .QF Cinv .Vol

Cinv .Vol Ct .QF

∈ ∈ ∈ ∈

∈ ∈ ∈ ∈ ∈

∈ ∈ ∈ ∈

= − −

− + −

− −

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

U T U T

U T VO U T

U T U T

PSC

Supply Chain Model

Large Scale MINLP

Supply Chain Model – cont. from previous slide

subject to the models of:

• processing units

• tank

• pipeline

{ }QF ,QS ,Q,Vol ,Lot PF ,PS ,V y 0,1+∈ℜ ∈ℜ ∈

units that compose refinery topologyrefineries that compose the supply chain

••

petroleum and product tanks that compose refineries petroleum and product tanks that compose terminals refineries and terminals that compose the supply chain

•••

pipeline network for petroleum supply pipeline network for product distribution••

Supply Chain Components

Petroleum Distribution Overview

Product Distribution Overview

RPBC flowsheet

Intermediate connections

Modeling Example

Tanks and CD1 Model

tan k1, petroleum,t tan k1, petroleum,CD1,tQS Q , t= ∀

tan k1, petroleum,CD1,t500 Q 20000, t≤ ≤ ∀

{ }

{ }

{ }

u ', petro leum ,C D 1 , p ,t u ', petro leum , pu ' tan k 1 ,2 ,3

C D 1 , p ,tu ', petro leum ,C D 1 ,t

u ' tan k 1 ,2 ,3

Q . P r opP F , t

Q

p YC 3C 4 ,YL N ,YH N ,YK ,YL D ,YH D ,YA T R

∈

∈

= ∀

∈

∑

∑

{ }C D 1 ,t u ', petro leum ,C D 1 ,t

u ' tan k 1 ,2 ,3Q F Q , t

∈= ∀∑

1 1CD1,s ,t CD1,t CD1, p ,t CD1,s ,V CD1,V ,tQS QF .PF QGain .V , t

s pC3C4 YC3C4

LN YLNHN YHNK YK

LD YLDHD YHDATR YATR

= + ∀

→ →

→ → →

→ →

CD1,s ,p ,t CD1,s ,p CD1,s,p CD1,V1,t CD1 CD1,sPS Prop +PGain .V ,s , p ,t= ∀ ∈ ∈SO PO

CD1,s

CD1,s ,t CD1,s ,u ',tu '

QS Q∈

= ∑UO

Refinery Multiperiod Planning – REVAP resultsDICOPT(NLP CONOPT++)(MIP OSL, CPLEX)

Demand profile - GLN

Steep

Smooth

Steep

Smooth

Refinery Planning – Model with Uncertainty

( )u p f u

c ,t u ,t ,c u,t,c u ,t ,c c ,t u ,t ,c u,s,t,cc t c t u s

Max Z prob Cp QF Vol prob Cf QS∈ ∈ ∈ ∈ ∈ ∈ ∈

= − −

∑ ∑ ∑ ∑ ∑ ∑ ∑

C T U C T U SO

{ }f uf p

u u ,t ,c u u,v u ,v ,t u,tc t u c t vu ,

Cb y [ Cr ( Cv .V )] QF∈ ∈ ∈ ∈ ∈ ∈∈

− − + ∑ ∑ ∑ ∑ ∑ ∑ ∑

C T U C T VOU \ U U

p

u ,t ,c u ,t ,ct u

Cinv Vol∈ ∈

−

∑ ∑

T U s.t. refinery constraints

c1 c2 cN

Discrete Scenarios

1

P1% P2% PN%

c,tprob =∑Cc∈

Planning under Uncertainty - REVAP results

Proposed Strategies and Results

Primal subproblem Dual subproblems Multipliers update

Strategy 1 Fixed assigment Lagrangean Subgradient

Strategy 2 Fixed inventory Lagrangean Subgradient

Strategy 3 Fixed inventory Surrogate Subgradient

Strategy 4 Fixed inventory Lagrangean Modified Subgradient

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60

Number of time periods.

CPU

seco

nds

Problem RMP Strategy 1 Strategy 2

Strategy3 Strategy4

Cases:1: Complete model

2: Pre-selection of some suppliers

3: Interruption of pipeline segment SG-RV

General constraints:Planning horizon: one / two time periods

Supply of 20 oil types

Generation of 32 products (6 transported with pipelines)

Supply Chain Example

Supply Chain Example – Petroleum Selection

LarabMarlinRgnCabiunAlbacoBicudoCondosoBonitCabiunaLarabeCoso

Case 1 Case 2

Case 3

Supply Chain Example – REVAP10905114047551

169451648911400

176419331001

00

871

600600660

0060

00

6551

Supply Chain Example – RPBC

138914081389

9824100759924544951775449

363636

151515

Supply Chain Example – Oil Supply

542005420054200

360003600025992

902009020080192

850085008500 35500

3550035500

Supply Chain Example – Product Supply

1764218311362

33452889

10800

2454025208

0

4400440011660

177001770017700

640364036403

65456089

11000200182001920018

Supply Chain Example – Intermediate Streams

60224666

48058

PFO1APFO1

A PFO4A

0530

Case Case 1 Case 2 Case 3

Number of time periods 1 2 1 2 1 2

Constraints 2304 4607 2306 4611 2304 4607

Variables 2544 5087 2544 5087 2544 5087

Discrete variables 195 390 195 390 195 390

Solution time (CPU s) 116.8 656.2 152 915.6 157.8 2301

Objective Value ($ x106) 20.4 41.3 20.3 41.1 18.0 36.3

Supply Chain Example – Computational Results

Mathematical programming

-General refinery topology

-General petroleum supply chain representation

-Representation of nonlinear properties and multiple periods

-Non-convex Large-Scale MINLP

Real-world applications

-General planning trends along multiple periods

-Analysis of scenarios (discrete probabilities)

-Intensive computational effort

Conclusions

Modeling

Upstream-Downstream Integration

Multi country supply chains (royalties, tariffs)

Modeling of uncertainties

Efficient solution methods

Decomposition (spatial, temporal, functional)

Approaches (Lagrangean Relaxation, Cross Decomposition)

Research needs

Supply chain optimization Jose Pinto - CEPAC

Documents

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