operations management in the fruit industrycepac.cheme.cmu.edu/pasilectures/bandoni/pasi 2005 -...
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Planta Piloto de Ingeniería QuímicaPlanta Piloto de Ingeniería QuímicaCamino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Camino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
J. Alberto BandoniJ. Alberto Bandoni
OPERATIONS MANAGEMENT IN THE FRUIT INDUSTRY
OPERATIONS MANAGEMENT IN THE FRUIT INDUSTRY
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
2
Introduction
Argentinean Fruit Industry Supply Chain Optimization
Frutas & Jugos ARG Co.: Case Study
Optimal Operation of a Packaging Plant
A Novel Method to Reduce Event Variables in Continuous-time Formulation for Short-term Scheduling
PRESENTATION OUTLINEPRESENTATION OUTLINE
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
3
ARGENTINE IN THE WORLDARGENTINE IN THE WORLD
NeuquénNeuquén
Iguazú FallsIguazú Falls
Buenos Aires
Buenos Aires
Bahía BlancaBahía Blanca
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
Planta Piloto de Ingeniería QuímicaPlanta Piloto de Ingeniería QuímicaCamino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Camino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Noemí Petracci, Guillermo Massini, J. Alberto BandoniNoemí Petracci, Guillermo Massini, J. Alberto Bandoni
Supply Chain Optimization in the Fruit Industry
Supply Chain Optimization in the Fruit Industry
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
FOCAPO 2003, Florida, USA, January 12-15, 2003FOCAPO 2003, Florida, USA, January 12-15, 2003
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BLACK AND NEUQUEN RIVERS HIGH VALLEY FRUIT INDUSTRY BLACK AND NEUQUEN RIVERS HIGH VALLEY FRUIT INDUSTRY
Neuquén and Black Rivers High Valley
Neuquén and Black Rivers High Valley
NW Region
NW Region
CuyoRegionCuyo
RegionMesopotamian
RegionMesopotamian
Region
The High Valley of RThe High Valley of Ríío Negro o Negro and Rand Ríío Neuquo Neuquéén,n,placed across two states placed across two states southwest of the country, is the southwest of the country, is the area of our country where the area of our country where the apples and pears are grown.apples and pears are grown.
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Argentinean fruit industry relevant figures
• Fruit Industry : 700.000.000 u$s/year export value
• Apples and Peers : 350.000.000 u$s (50 %)
• HV Region : 330.000.000 u$s (95 %)
ARGENTINEAN FRUIT INDUSTRY IN FIGURESARGENTINEAN FRUIT INDUSTRY IN FIGURES
Apples: Apples: 10.086.000 10.086.000 tnstns
Pears: Pears: 520.000 520.000 tnstns
23 % for industrialization
(concentrate juice)
50 % apples for industrialization
(concentrate juice)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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During the 90During the 90’’s, companies made important capital investments s, companies made important capital investments on new machinery for efficiency improvement. on new machinery for efficiency improvement.
ARGENTINEAN FRUIT INDUSTRY DESCRIPTIONARGENTINEAN FRUIT INDUSTRY DESCRIPTION
In the last few years, due to new worldwide competitors from AsiIn the last few years, due to new worldwide competitors from Asia a South West, local economic problems and volatile international South West, local economic problems and volatile international markets, companies are compelled to improve even more their markets, companies are compelled to improve even more their competitiveness to keep on business. competitiveness to keep on business.
In this context, they have a need for better decision tools to In this context, they have a need for better decision tools to manage the whole supply chain.manage the whole supply chain.
There are a few large companies that operate along the entire frThere are a few large companies that operate along the entire fruit uit supply chain, and concentrate the largest part of the business isupply chain, and concentrate the largest part of the business in the HV n the HV region.region.
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Packaging plant
Juice plant
Own farms
Third party farms
Fruit markets
Juice markets
Third party cold
storage
Third party packaging
plant
G
B
H
N
E
A
F
CD
H: Fruit from storage to PPF: Fresh fruit from own farms to PPC: Fresh fruit from own farms to JPA: Fresh fruit from fruit suppliers to PP.G: Fresh fruit from fruit suppliers to JPN: Fruit from supplier’s PP.
B: Fresh fruit prepared and packed in different ways.
D: Fruit from PP that do not fulfill quality specification transferred to JP
E: Product streams of Concentrate Juice of 72°Brix and aroma.
ARGENTINEAN FRUIT INDUSTRY SUPPLY CHAINARGENTINEAN FRUIT INDUSTRY SUPPLY CHAIN
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Packaging warehouse
J
B
H
AFCA
F
K
D
Refrigeration chamber
AFG
H : Fruit from storage to PPF : Fresh fruit from own farms to PPA : Fresh fruit from fruit suppliers to PPAFG : Fruit sent to the processing line.AFC : Fruit directly sent to cold storage for later processing.K : Fruit to keep in cold storage for later selling.
D : Fruit from PP that do not fulfill quality specification transferred to JP
J : Fruit from cold storage to processing line.B : Fresh fruit prepared and packed in different
ways.
PACKAGING PLANTPACKAGING PLANT
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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G
CConcentrate
juice chamberIndustrial process
M
F
E
Fruit reception
N
D
L
D : Fruit from PP that do not fulfill quality specification transferred to JP.C : Fresh fruit from own farms to JPG : Fresh fruit from fruit suppliers to JPN : Fruit from supplier’s PP.E : Product streams of Concentrate Juice of 72°Brix and aroma.
CONCENTRATE JUICE PLANTCONCENTRATE JUICE PLANT
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Formulated as a Formulated as a midterm tactical planning problem, over , over oneone--year time horizon (divided in 12 monthly periods.year time horizon (divided in 12 monthly periods.
FRUIT SUPPLY CHAIN PLANNING MODELFRUIT SUPPLY CHAIN PLANNING MODEL
Time horizon coincides with the business cycle from harvest Time horizon coincides with the business cycle from harvest to harvest. During this cycle, many decisions have to be to harvest. During this cycle, many decisions have to be made along the SCmade along the SC..
Model parameters:Model parameters: cost of each variety of raw material, cost of each variety of raw material, selling prices for each product, fruit production and fruit selling prices for each product, fruit production and fruit variety, distances, packaging and juice plant capacities, variety, distances, packaging and juice plant capacities, demands for each product and market, cooling storage of demands for each product and market, cooling storage of fresh fruit and final products, etc.fresh fruit and final products, etc.
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Model description:Objective Function: max. of benefit along one-year operation.Model equations : mass balance and production equations at
farms, packaging plants and juice plantsConstraints : production limits at proprietary farms, bounds
on fruit supply, bounds on internal processingcapacities, demand satisfaction, stock limits atcold storage and storage at juice plants
MTHEMATICAL MODEL: MILPMTHEMATICAL MODEL: MILP
Model statistics: 14335 continuous variables and 3372 binary variables, 4421 equality and 7524 inequality constraints.
Implementation environment:The GAMS (Brooke et al., 1998) was used in order to implement the MILP optimization model and generate their solutions.
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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57618.69
16864.8127481.23
5591.58
107556.3
0
20000
40000
60000
80000
100000
120000
Tn/
year
From own farms(C+F)
From suppliers'farms (A+G)
From coldschamber (H)
From suppliers'packaging plants
(N)
Total ProcessedFruit
Fruit Processed
NUMERICAL RESULTS: Total fruit processedNUMERICAL RESULTS: Total fruit processed
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Packed Fruit SoldArgentina
44%
Europe/USA15%
Brazil41%
Argentina44%
Europe/USA15%
Brazil41%
Packed Fruit Sold
Juice Sold
Argentina48%
Europe / USA52%
Argentina48%
Europe/USA52%
Concentrate Juice Sold
NUMERICAL RESULTS: Fruit and juice sold in different marketsNUMERICAL RESULTS: Fruit and juice sold in different markets
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
15
0
10
20
30
40
50
60
Gal
x 1
03
1 2 3 4 5 6 7 8 9 10 11 12
Period
Europe / USA Local Customers
NUMERICAL RESULTS: Optimal plan for juice commercializationNUMERICAL RESULTS: Optimal plan for juice commercialization
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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0500
10001500200025003000350040004500
Kg
x 10
3
1 2 3 4 5 6 7 8 9 10 11 12
Period
Europe / USA Brazil Argentina
NUMERICAL RESULTS: Optimal plan for fresh fruit commercializationNUMERICAL RESULTS: Optimal plan for fresh fruit commercialization
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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0
20
40
60
80
100
120
Gal
x 1
03
1 2 3 4 5 6 7 8 9 10 11 12
Period
JP1 JP2
NUMERICAL RESULTS: Optimal juice storage profileNUMERICAL RESULTS: Optimal juice storage profile
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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0
2000
4000
6000
8000
10000
12000
14000
16000
Kg
x 10
3
1 2 3 4 5 6 7 8 9 10 11 12
Period
PP1 PP2 PP3 PP4
NUMERICAL RESULTS: Optimal fresh fruit storageNUMERICAL RESULTS: Optimal fresh fruit storage
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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A model was developed to optimize the SC planning A model was developed to optimize the SC planning of a typical fruit company in the HV area of of a typical fruit company in the HV area of Argentina.Argentina.
It optimally decides production plans for fruit and It optimally decides production plans for fruit and juice to satisfy customer orders, while it optimally juice to satisfy customer orders, while it optimally allocates sources or raw material, based on allocates sources or raw material, based on capacities and costs.capacities and costs.
The model realistically represents the current The model realistically represents the current economic scenario in the country.economic scenario in the country.
Current research is under way to complete Current research is under way to complete sensitivity analysis and incorporates uncertainties in sensitivity analysis and incorporates uncertainties in demands and harvest estimations.demands and harvest estimations.
NUMERICAL RESULTS: Optimal fresh fruit storageNUMERICAL RESULTS: Optimal fresh fruit storage
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
N. Petracci, A. BandoniN. Petracci, A. Bandoni
Case Study:
FRUTAS & JUGOS ARG co.
Case Study:
FRUTAS & JUGOS ARG co.
Planta Piloto de Ingeniería QuímicaPlanta Piloto de Ingeniería QuímicaCamino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Camino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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FarmsPlantsSea Port
FRUTAS Y JUGOS ARG Co. : Supply ChainFRUTAS Y JUGOS ARG Co. : Supply Chain
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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•• Villa ReginaVilla Regina
Packaging Plant, PPPackaging Plant, PP11
Concentrate Juice Plant, CJPConcentrate Juice Plant, CJP11
•• GralGral. . RocaRoca
Packaging Plant, PPPackaging Plant, PP22
Concentrate Juice Plant, CJPConcentrate Juice Plant, CJP22
FRUTAS Y JUGOS ARG Co. : Supply ChainFRUTAS Y JUGOS ARG Co. : Supply Chain
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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PP1V. Regina
CJP1V. Regina
PP2Gral. Roca
CJP2Gral. Roca
Plant 1
Plant 2
Market1Brazil
(Sao Pablo Seaport)
Market2USA
(San Antonio Seaport)
Market3Argentina
(Buenos Aires)
Farm 1 Cipolletti
Farm 2 Neuquén
Farm 3 Cinco Saltos
RC
RC
FFi,j,k
FOSfFi,j,k
PFFi,k,
m
PCJi,k,m
FOSi
,k
FFtSi,
k
CJtSi,
k
FFfSi,
k
FRUTAS Y JUGOS ARG Co. : Supply Chain SketchFRUTAS Y JUGOS ARG Co. : Supply Chain Sketch
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Goal of the studyGoal of the study: :
To design the supply chain that maximizes To design the supply chain that maximizes the gross benefit of the company, analyzing the gross benefit of the company, analyzing several possible scenarios. several possible scenarios.
FRUTAS Y JUGOS ARG Co. : Goal of the studyFRUTAS Y JUGOS ARG Co. : Goal of the study
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Each site has a refrigeration chamber which may storage preEach site has a refrigeration chamber which may storage pre--classified classified fresh fruit and raw fruit to be processed by concentrated juice fresh fruit and raw fruit to be processed by concentrated juice plant.plant.
Global mass balances of the plants (packaging and concentrate juGlobal mass balances of the plants (packaging and concentrate juice ice plants).plants).
The operating cost evaluation involves the complete supply chainThe operating cost evaluation involves the complete supply chain, from , from farms to markets. Furthermore, terms like raw material cost, farms to markets. Furthermore, terms like raw material cost, transportation cost, production cost, etc., must be consideredtransportation cost, production cost, etc., must be considered
The The Plant’s production may be split in different ways to satisfy the demands, so it must be considered at the time to evaluate sales.
Company benefit is evaluated as a gross benefit (profit), i.e. the difference between sales and operating costs.
FRUTAS Y JUGOS ARG Co. : Bases for the studyFRUTAS Y JUGOS ARG Co. : Bases for the study
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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To produce packed fresh fruit and/or concentrate juice after croTo produce packed fresh fruit and/or concentrate juice after crop p time to fulfill the unsatisfied demand, using as raw material frtime to fulfill the unsatisfied demand, using as raw material fruit from uit from refrigeration chambers.refrigeration chambers.
The Company is committed to receive all the farm production. The Company is committed to receive all the farm production.
Considering the farm production uncertainty. Analyze the supply Considering the farm production uncertainty. Analyze the supply chain profit when one, two or three farms loose a given maximum chain profit when one, two or three farms loose a given maximum production percentage.production percentage.
According to the most important term of the total cost equation,According to the most important term of the total cost equation,suggest possible actions to improve the global profitsuggest possible actions to improve the global profit
Analyze the product price uncertainty.Analyze the product price uncertainty.
FRUTAS Y JUGOS ARG Co. : Possible scenariosFRUTAS Y JUGOS ARG Co. : Possible scenarios
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
27
A linear model has been developed to maximize the A linear model has been developed to maximize the gross profit of the company along the harvest time, gross profit of the company along the harvest time, January to May.January to May.
The model assign:The model assign:
plant operation levelsplant operation levels
amount and place where raw material should be amount and place where raw material should be obtainedobtained
and final product deliveryand final product delivery
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Based on:Based on:
demands from three major marketsdemands from three major markets
estimated fruit production estimated fruit production
economic information economic information
yield and availability of processing plantsyield and availability of processing plants
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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Objective Function:Objective Function:Maximize Gross ProfitMaximize Gross Profit
Model equations:Model equations:mass balance and production equations at mass balance and production equations at farms, packaging plants and juice plantsfarms, packaging plants and juice plants
Constraints:Constraints:production limits at proprietary farms, bounds on fruit supply, bounds on internal processing capacities, demand satisfaction.
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
kiPP
kikikiki
FFfSPFFFFtSFF
,
,,,, η
−+=
kiFFISLki ISLFFfSkiFF ,, *
,η=
kiPFFki MaxPFFFFtSki ,, *
,η=
PP Mass Balance
PP global balance
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
PPi,k Initial Stock
Fresh fruit send to stock
PPk Yield
PPk Maximum Production
( ) kiPPki FFFOSki ,, *1
,η−=
kiMaxPFFki MaxPFFPFFki ,, *
,η=
kikiCJP
kikiki FOStSPCJFOSfSFOSFOSfFki
,,,,, *1
,
+=++η
kiCJISLki ISLFOSfSkiCJ ,, *
,η=
kiki CJPkiPCJki MaxPCJFOStS,, ,, * ηη=
kiMaxPCJki MaxPCJPCJki ,, *
,η=
Out of Spec. fruit to Stock
PCJk Maximum Production
CJP Mass Balance
CJP global balance
PCJi,k initial stock
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
kikjiPPkji FFFF ,,,,, ∗=α
kikjiCJPkji FOSfFFOSfF ,,,,, ∗=α
1,, =∑j
kjiPPα
1,,=∑
jCJP kji
α
Fresh fr. out of Spec. from farm j to CJPk
Fruit Supplier’s Distribution
Fresh fr. from farm j to PPk
Normalization
kimkiPPmki PFFPFF ,,,,, ∗= β
kimkiCJPmki PCJPCJ ,,,,, ∗= β 1,, =∑m
mkiPPβ 1,,=∑
mCJP mki
β
mik
mkimi DPFFPFFusDPFF ,,,, −= ∑
mik
mkimi DPCJPCJusDPCJ ,,,, −= ∑
Packed fesh fr. delivered by plant k to market m.
Packed conc. juice delivered by plant k to market m.
Unsatisfied demand of packed fresh fruit
Unsat. demand of conc. juice
Demand distribution
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
( ) ( )∑∑ +=
=+=
kikii
kikii
FOSFF
FOSfFcFOSFFcFF TRFCTRFCTRFC
,,
,, **
( ) ( )∑∑ +=
=+=
kikiki
kikiki
FOSFF
FOSfScFOSfSFFfScFFfS TFfSCTFfSCTFfSC
,,,
,,, **
( ) ( )∑∑ +=
=+=
kjikjikj
kjikjikj
FOSFF
FOSfFdjtcFFFFdjtcFF TFPTrCTFPTrCTFPTrC
,,,,,
,,,,, ****
Raw fruit cost
Fruit from stock cost
Farms to plants fruit trans. cost
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
Costs
( ) ( )∑ ∑+=
=+=
ki kikikikiki
CJPPP
PCJpcCJPPFFpcPP TPCTPCTPC
, ,,,,, **
( ) ( )∑∑ +=
=+=
kiki
kiki
CJFF
FOStSrcCJFFtSrcFF TRCTRCTRC
,,
,, **
( ) ( )∑∑ +=
=+=
mkimkimk
mkimkimk
PCJPFF
PCJdmtcPCJPFFdmtcPFF TPMTrCTPMTrCTPMTrC
,,,,,
,,,,, ****
Total production cost
Total refrigeration cost
Total plants to market products transport cost
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
FRUTAS Y JUGOS ARG Co. : SC ModelFRUTAS Y JUGOS ARG Co. : SC Model
Costs
( )∑ ∗∗=mi
PFFmimi prfpPFFusDPFFusDPFFC,
,,
( )∑ ∗∗=mi
PCJmimi prfpPFFusDPCJusDPCJC,
,,
usDPCJCusDPFFCTPMTrCTRCTPCTFPTrCTFfSCTRFCCostTotal
+++++++=
Unsatisfied Demand PFF Cost
Unsatisfied Demand of Packed Conc. Juice
( ) ( )∑ ∑+=
=+=
mki mkimkimimkimi
CJPPP
PCJpPCJPFFpPFF SalesSalesSales
,, ,,,,,,,, **
TotalCostSalesProfit Gross −=
Gross Profit
Sales
Total plant cost
kiki MaxPFFPFF ,, ≤
kiki MaxPCJPCJ ,, ≤
kiFFki ISLFFfS ,, ≤
kiki MaxPFFFFtS ,, ≤
kiCJki ISLFOSfS ,, ≤
kiCJPkiki MaxPCJFOStS,,, η≤
mik
mki DPFFPFF ,,, ≤∑
mik
mki DPCJPCJ ,,, ≤∑
( )∑ ≤+k
jiFkjikji MaxFPFOSfFFFji ,,,,, *
,η
Inequality constraints
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
Planta Piloto de Ingeniería QuímicaPlanta Piloto de Ingeniería QuímicaCamino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Camino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
A. Blanco , G. Masini, N. Petracci, A. BandoniA. Blanco , G. Masini, N. Petracci, A. Bandoni
Operations Management of a Packaging Plant in the Fruit Industry
Operations Management of a Packaging Plant in the Fruit Industry
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
Journal of Food Engineering 70, 297-307 (2005)Journal of Food Engineering 70, 297-307 (2005)
35
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
36
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Fruit from farms
Drencher(washing)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
37
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
To processing line
To cold storage
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
38
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Non ProcessedFruit Storage
Own Cold Storage
Third Party Cold Storage
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
39
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Pre classification(damaged fruit)
Waste(to juice production)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
40
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Washing Waxing
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Quality Classification(1st, 2nd, 3rd quality)
Waste(to juice production)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
42
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Gauge Classification(weight or size)
Waste(to juice production)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
43
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Out of Specification Fruit
Processed Fruit
Packaging
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
44
DR PC WA WX QC GC PK
NPFS PFSOSF
TPFS
W1 W2 W3
X1
X3
X2
X10
X4
X9X5 X7X6 X8
XOS
X11
PACKAGING PLANTPACKAGING PLANT
Overseas, regionaland local markets
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• Regular income of fruit (apples and pears) during the whole harvest period (day 12 to day 157)
• Based on historical records it is possible to forecast an income profile in terms of amount, quality, waste and gauge (average value and standard deviation)
PACKAGING PLANTPACKAGING PLANT
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46
v Variety SD HP A(kg/day) SDev(kg/day) CR($/kg)v1 Williams pear 12 12 to 36 45560 2000 0.07v2 Beurre D´Anjou pear 45 45 to 69 27400 1500 0.1v3 Beurre Bosc pear 72 72 to 96 35960 2200 0.07v4 Red apple 1 78 78 to 102 24240 780 0.08v5 Packams Triumph pear 91 91 to 115 33200 2100 0.09v6 Red Delicious apple 95 95 to 119 38600 3000 0.08v7 Red apple 2 123 123 to 147 39040 2800 0.07v8 Granny Smith apple 133 133 to 157 48360 3500 0.08
FRUIT INCOMEFRUIT INCOME
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47
v q1 q2 q3 q1 q2 Q3
v1 0.58 0.27 0.15 0.063 0.045 0.025v2 0.58 0.26 0.16 0.094 0.045 0.02v3 0.5 0.35 0.16 0.077 0.045 0.019v4 0.58 0.27 0.15 0.07 0.03 0.029v5 0.58 0.34 0.08 0.106 0.057 0.013v6 0.4 0.27 0.33 0.043 0.049 0.038v7 0.58 0.29 0.13 0.092 0.041 0.023v8 0.45 0.32 0.23 0.091 0.055 0.023
A(%) SDev(%)
FRUIT QUALITYFRUIT QUALITY
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48
v DPC DQC DGC DPC DQC DGCv1 0.11 0.05 0.06 0.014 0.003 0.007v2 0.14 0.03 0.06 0.011 0.004 0.006v3 0.12 0.03 0.07 0.012 0.005 0.005v4 0.13 0.04 0.06 0.014 0.004 0.007v5 0.1 0.05 0.07 0.011 0.003 0.006v6 0.11 0.04 0.07 0.011 0.005 0.006v7 0.13 0.04 0.05 0.013 0.004 0.007v8 0.12 0.03 0.07 0.013 0.003 0.006
A(%) SDev(%)
WASTEWASTE
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
49
v g1 g2 g3 g4 g5 g1 g2 g3 g4 g5
v1 0.12 0.11 0.23 0.14 0.4 0.004 0.004 0.008 0.005 0.015v2 0.11 0.16 0.19 0.24 0.3 0.005 0.008 0.009 0.009 0.012v3 0.2 0.12 0.18 0.21 0.29 0.009 0.005 0.008 0.009 0.009v4 0.18 0.12 0.22 0.22 0.26 0.008 0.005 0.008 0.009 0.012v5 0.3 0.22 0.2 0.21 0.09 0.009 0.007 0.008 0.007 0.003v6 0.21 0.26 0.12 0.26 0.16 0.01 0.012 0.005 0.011 0.007v7 0.1 0.23 0.16 0.13 0.38 0.004 0.008 0.005 0.005 0.012v8 0.27 0.16 0.16 0.14 0.28 0.012 0.007 0.005 0.005 0.011
A(%) SDev(%)
GAUGEGAUGE
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
50
• One permanent labor staff the whole year (eight hour working shift)
• Temporary labor staff may be required to cover two or three additional eight hour working shifts during certain periods in order to satisfy commercial commitments
LABOR POLICYLABOR POLICY
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51
• Different markets demand different products
• Products are classified according to:– Fruit variety (v1, …, v8)– Waxing (waxed or not waxed)– Fruit quality (1st, 2nd, 3rd))– Gauge (g1, …, g5)– Crate (only one in the present work)
FINAL PRODUCTSFINAL PRODUCTS
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52
v1 v2 v3 v4 v5 v6 v7 v8 w1 w2 q1 q2 q3 g1 g2 g3 g4 g5 p1 PP ($/kg)P1 1 1 1 1 1 0.33P2 1 1 1 1 1 0.39P3 1 1 1 1 1 0.26P4 1 1 1 1 1 0.28P5 1 1 1 1 1 0.24P6 1 1 1 1 1 0.34P7 1 1 1 1 1 0.27P8 1 1 1 1 1 0.29P9 1 1 1 1 1 0.32P10 1 1 1 1 1 0.36P11 1 1 1 1 1 0.28P12 1 1 1 1 1 0.31P13 1 1 1 1 1 0.28P14 1 1 1 1 1 0.29P15 1 1 1 1 1 0.29P16 1 1 1 1 1 0.29P17 1 1 1 1 1 0.29P18 1 1 1 1 1 0.26P19 1 1 1 1 1 0.31P20 1 1 1 1 1 0.31Set SPVP WP QP GP
PACKAGING PRODUCTSPACKAGING PRODUCTS
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53
Overseas P1, P2, P6, P9, P14, P15, P19, P20Regional P4, P7, P8, P13, P16, P17Local P3, P5, P10, P11, P12, P18
PRODUCTS AND DELIVERY DATES FOR DIFFERENT MARKETSPRODUCTS AND DELIVERY DATES FOR DIFFERENT MARKETS
Overseas Regional Local25 30 3150 60 5480 90 78
110 120 102140 150 126170 180 150190 210 174215 240 198
270 222300 246330 270360 294
318342360
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54
Deterministic income fruit scenario generation by means of Monte Carlo Simulation for each parameter:
PLANNING MODELPLANNING MODEL
amount of fruit per varietyquality of fruit per varietygauge of fruit per varietywaste of fruit per variety
Mass Balances
DrencherPreclassificationWaxing moduleQuality classification moduleGauge classification modulePackaging stage
Packaging plant Cold storageNon processed fruit (total and per variety)Processed fruit (total and per product)Out of specification fruitTotal mass balanceThird party storage
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
55
• Maximum Processing Capacity is given by the amount of fruit that can be handled at the Pre Classification module
• It depends on the number of working shifts and the processing capacity per shift
• Objective function : profit oriented mode
PLANNING MODELPLANNING MODEL
Total Profit = sales income - raw material cost -labor costs - cooling costs
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
56
• A plan that maximizes the production of each particular product is obtained
• The resulting plan constitutes a “forecast”of the processing capacity of the facility
• Valuable for managers to establish next year sales commitments
PLANNING MODEL: Profit oriented modePLANNING MODEL: Profit oriented mode
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57
PLANNING MODEL: ResultsPLANNING MODEL: Results
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
58
• Profit = $ 3,331,623• Sales income = $ 58,423,785• Raw material cost = $ 33,242,063• Operating cost = $ 21,783,926• Cooling cost = $ 111,171
PLANNING MODEL: ResultsPLANNING MODEL: Results
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59
Provided a historical profile of fruit income and an established sales program, generate a processing plan in order to maximize total profit, while penalizing non satisfaction of sales commitments in terms of volume of fruit and delivery deadlines.
PLANNING MODEL: Sales oriented modePLANNING MODEL: Sales oriented mode
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
Planta Piloto de Ingeniería QuímicaPlanta Piloto de Ingeniería QuímicaCamino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
Camino La Carrindanga, Km. 7 (8000) Bahía BlancaArgentina
G. Durand, A. BandoniG. Durand, A. Bandoni
A Novel Method to Reduce Event Variables in Continuous-time
Formulation for Short-term Scheduling
A Novel Method to Reduce Event Variables in Continuous-time
Formulation for Short-term Scheduling
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
7th World Congress of Chemical EngineeringGlasgow, Scotland
July 10-14, 2005
7th World Congress of Chemical EngineeringGlasgow, Scotland
July 10-14, 2005
61
INTRODUCTION – MULTIPURPOSE BATCH PLANTS OPTIMIZATIONINTRODUCTION – MULTIPURPOSE BATCH PLANTS OPTIMIZATION
How to achieve the maximum production, the maximum profits and/or the minimum costs?
How to achieve the maximum production, the maximum profits and/or the minimum costs?
• total operation time (time horizon)
• process recipe
• quantity and capacity of units
• products’ demand
• total operation time (time horizon)
• process recipe
• quantity and capacity of units
• products’ demand
Knowing:Knowing:
SOLUTION: Schedule optimizationSOLUTION: Schedule optimizationDetermining:Determining: • the sequence and the timing of tasks taking place in
each unit
• the batch size of tasks (i.e. the processing time and the required resources/utilities)
• the amount of final products sold and raw materials consumed
• the sequence and the timing of tasks taking place in each unit
• the batch size of tasks (i.e. the processing time and the required resources/utilities)
• the amount of final products sold and raw materials consumed
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SCHEDULE OPTIMIZATION – STATE TASK NETWORKSCHEDULE OPTIMIZATION – STATE TASK NETWORK
T1 T2 T3 T4 T5F1 S1 S2 INT1 S3 P1
T6P2
WS
0.98
0.02
T10P3
T7S5F2
T8
S4
INT2T9
S60.9
0.10.50.5
A framework for graphical representation and mathematical formulation of recipes (processes) for product manufacturingA framework for graphical representation and mathematical formulation of recipes (processes) for product manufacturing
Uses materials (states) and tasks as building blocks for the process description, with each task consuming and producing materials while using equipment
Uses materials (states) and tasks as building blocks for the process description, with each task consuming and producing materials while using equipment
raw materialsraw materialsintermediatesintermediates
final productsfinal productstaskstasks
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63
MODELLING FOR SCHEDULE OPTIMISATION – STN/RTN FORMULATIONSMODELLING FOR SCHEDULE OPTIMISATION – STN/RTN FORMULATIONS
Gantt chartGantt chart
Unit1
t
units
Tf2BTf
1BTf1A,Ts
1B
Ts1A
Tf2ATs
2A
Unit2
Task A Task B
Gives smaller problemsand better LP relaxationsGives smaller problems
and better LP relaxationsDecoupling task events
and unit events(Ierapetritou & Floudas, 1998)
Gantt chartGantt chart
Periods of constantand equal lengthPeriods of constantand equal length
MILP formulation.Too many periods neededto model in a realistic way
MILP formulation.Too many periods neededto model in a realistic way
Discrete time representation (STN)(Kondili et al., 1993)
Task1A
Uni
t2
t
tasks
Uni
t1
Task1B
Task2A
Task2B
Gantt chartGantt chartEvent: period of different lengthfor each occurrence of a taskEvent: period of different lengthfor each occurrence of a task
Produces smaller problems andmodels the time in a more realistic way
Produces smaller problems andmodels the time in a more realistic way
Continuous time representation (RTN)(Schilling & Pantelides, 1996)
t
tasks
Tf2BTf
1BTf1A,Ts
1B
Ts1A
Tf2ATs
2A
Task1A
Uni
t1
Task1B
Uni
t2
Task2A
Task2B
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
64
SCHEDULE OPTIMISATION IS AN NP-HARD PROBLEMSCHEDULE OPTIMISATION IS AN NP-HARD PROBLEM
Solution performance vs. Problem sizeCase Study I
0
100200
300400
500
600700
800900
1000
8 9 10 11 12 13 14 15
Qty. of events
CPU
Tim
e [s
]
0
1000020000
3000040000
50000
6000070000
8000090000
100000
Itera
tions
CPU time [s] Iterations
STN/RTN formulations have, in general, a practical(*) size limit of 15-20 events
STN/RTN formulations have, in general, a practical(*) size limit of 15-20 events
(*)Practical: solvable in less than 3600 seconds in a 1GHz/256MB system(*)Practical: solvable in less than 3600 seconds in a 1GHz/256MB system
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IMPROVEMENTS FOR RTN FORMULATION – 1IMPROVEMENTS FOR RTN FORMULATION – 1
Decomposition approaches(Basset, Pekny and Reklaitis, 1996 – Khmelnitsky, Kogan, and Maimon, 2000 – Gupta and Maranas,
1999 – Wu and Ierapetritou, 2003)
One large problemOne large problem
Unit1
t
units
Unit2
Task A Task B
Unit1
t
units
Unit2
Task A Task B
Unit1
t
units
Unit2
Several smaller subproblemsSeveral smaller subproblems
How to model this?OR
How to give to the solver the possibility of choosing this solution?
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
66
IMPROVEMENTS FOR RTN FORMULATION – 2IMPROVEMENTS FOR RTN FORMULATION – 2
Reducing problem size in other dimensions(Maravelias & Grossmann , 2003)
• Tasks’ starting times can only take place at determined time points (TN), thus reducing the number of time ordering equations.
• Storage is not modelled as a task, therefore reducing the number of binary variables.
• Tasks’ starting times can only take place at determined time points (TN), thus reducing the number of time ordering equations.
• Storage is not modelled as a task, therefore reducing the number of binary variables.
Task A Task B Task C
Gantt chartGantt chart
Unit1
t
units
Unit2
Unit3
TN1 TN2 TN3 TN4Tf3C Tf
2B Tf2B
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
67
PROCESS RECIPE MODELLING IN RTNPROCESS RECIPE MODELLING IN RTN
Two sets of constraints (equations) model the process recipe in RTN:Two sets of constraints (equations) model the process recipe in RTN:
Material balances
Each task can only consume states that are being produced or were produced by its corresponding preceding task/s (and/or raw materials).
Material balances
Each task can only consume states that are being produced or were produced by its corresponding preceding task/s (and/or raw materials).
Time ordering
If a task consumes states produced by other tasks, it has to start after those tasks have started (continuous) or after they have finished (batch)
Time ordering
If a task consumes states produced by other tasks, it has to start after those tasks have started (continuous) or after they have finished (batch)
( ) ( ) SsNnnjiBpnjiBps is i Ii Jj
cccsi
Ii Jj
pppsi ∈∈∀=−− ∑ ∑∑ ∑
∈ ∈∈ ∈
,0,,1,,
( ) ( ) ( ) ( )[ ]NnIiIiJjj
niwvniwvHnjiTnjiT
pc jp
jcpc
pcppfccs
∈∈∈∈∀
−−−−−≥
,,,,1,,21,,,,
Bs and Ts are continuous variables
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
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MODELLING THE PROCESS RECIPE THRU BINARY VARIABLESMODELLING THE PROCESS RECIPE THRU BINARY VARIABLES
task i task i’
intermediatestates
intermediatestates
NnYY niin ∈∀= '
One-to-one pairs of tasksOne-to-one pairs of tasks
Both tasks continuous OR task i continuous/task i’ batchBoth tasks continuous OR task i continuous/task i’ batch
NnNnYY niin ≠∈∀= + ,1'
Task i batch/task i’ continuousTask i batch/task i’ continuous
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
69
MODELLING THE PROCESS RECIPE THRU BINARY VARIABLESMODELLING THE PROCESS RECIPE THRU BINARY VARIABLES
One-to-many pairs of tasksOne-to-many pairs of tasks
All tasks continuous ORtask i continuous/tasks i’ batch
All tasks continuous ORtask i continuous/tasks i’ batch
Task i batch/tasks i’ continuousTask i batch/tasks i’ continuous
task i
task i’1intermediatestates
intermediatestates
task i’2
task i’k
Nn
YY
YYYY
YYYY
niin
niin
niin
nininiin
k
K
∈∀
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
≥
≥≥
+++≤
'
'
'
'''
2
1
21
M
K
NnNn
YY
YYYY
YYYY
niin
niin
niin
nininiin
k
K
≠∈∀
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
≥
≥≥
+++≤
+
+
+
+++
,
1'
1'
1'
1'1'1'
2
1
21
M
K
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
70
Nn
YYYYYY
YYYY
nininini
nini
nini
nini
K
K
∈∀
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
≥+++≤
≤≤
'
'
'
'
21
2
1
K
M
MODELLING THE PROCESS RECIPE THRU BINARY VARIABLESMODELLING THE PROCESS RECIPE THRU BINARY VARIABLES
Many-to-one pairs of tasksMany-to-one pairs of tasks
All tasks continuous ORtasks i continuous/task i’ batch
All tasks continuous ORtasks i continuous/task i’ batch
Tasks i batch/task i’ continuousTasks i batch/task i’ continuous
task i’
task i1 intermediatestates
intermediatestates
task i2
task ik
NnNn
YYYYYY
YYYY
nininini
nini
nini
nini
K
K
≠∈∀
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
≥+++≤
≤≤
+
+
+
+
,
1'
1'
1'
1'
21
2
1
K
M
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
71
CASE STUDY I – Multiproduct Plant (15 products/11 units/34 tasks)CASE STUDY I – Multiproduct Plant (15 products/11 units/34 tasks)
Modelled with:Ierapetritou & Floudas formulation (1998)I & F form. with proposed constraints
Modelled with:Ierapetritou & Floudas formulation (1998)I & F form. with proposed constraints─ One-to-one pairs─ One-to-one pairs ─ One-to-many pairs─ One-to-many pairs
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Stopping criterion: Integrality gap <10%Hardware: AMD Duron 996Mhz – 240Mb RAM memory Software: GAMS 21.2/CPLEX 8.1Stopping criterion: Integrality gap <10%Hardware: AMD Duron 996Mhz – 240Mb RAM memory Software: GAMS 21.2/CPLEX 8.1
CASE STUDY I – RESULTSCASE STUDY I – RESULTS
Optimal schedule (obtained with proposed modifications)Optimal schedule (obtained with proposed modifications)
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina
73
CASE STUDY II – Multiproduct Plant (3+1 products/6 units/10 tasks)CASE STUDY II – Multiproduct Plant (3+1 products/6 units/10 tasks)
Modelled with:Maravelias & Grossmann formulation (2003)M & G form. with proposed constraints
Modelled with:Maravelias & Grossmann formulation (2003)M & G form. with proposed constraints─ One-to-one pairs─ One-to-one pairs
T1 T2 T3 T4 T5F1 S1 S2 INT1 S3 P1
T6P2
WS
0.98
0.02
T10P3
T7S5F2
T8
S4
INT2T9
S60.9
0.10.50.5
BMAX in tons, α in hr, γ in kg/hr, δ in kg/hr*tonBMAX in tons, α in hr, γ in kg/hr, δ in kg/hr*ton
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74
CASE STUDY II – RESULTSCASE STUDY II – RESULTS
Stopping criterion: Integrality gap <10%Hardware: AMD Duron 996Mhz – 240Mb RAM memory Software: GAMS 21.2/CPLEX 8.1Stopping criterion: Integrality gap <10%Hardware: AMD Duron 996Mhz – 240Mb RAM memory Software: GAMS 21.2/CPLEX 8.1
Optimal schedule (obtained with proposed modifications)Optimal schedule (obtained with proposed modifications)
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75
CONCLUSIONSCONCLUSIONS
A new set of constraints for modeling the process recipe for scheduling problems is presented.
They are an additional method, reinforcing the task relations expressed thru material balances and time ordering.
They can be applied to several RTN representations.
The proposed modifications allow finding better values of the objective function in less time than the original formulation where they are applied.
The improved performance comes from the effective elimination of binary variables and faster integer cuts.
A new set of constraints for modeling the process recipe for scheduling problems is presented.
They are an additional method, reinforcing the task relations expressed thru material balances and time ordering.
They can be applied to several RTN representations.
The proposed modifications allow finding better values of the objective function in less time than the original formulation where they are applied.
The improved performance comes from the effective elimination of binary variables and faster integer cuts.
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76
Planta Piloto deIngeniería QuímicaPlanta Piloto deIngeniería Química
PASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, ArgentinaPASI Program on Process System Engineering, August 16-25, 2005, Iguazú Falls, Argentina