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Available online at www.sciencedirect.com

Computers and Chemical Engineering 32 (2008) 2529–2535

An integrated model of supply network and production planningfor multiple fuel products of multi-site refineries

Young Kim a, Choamun Yun a, Seung Bin Park a, Sunwon Park a,∗, L.T. Fan b

a Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong,Yuseong-gu, Daejeon 305-701, Republic of Korea

b Department of Chemical Engineering, Kansas State University,Manhattan, KS 66506, USA

Received 5 May 2007; received in revised form 28 July 2007; accepted 31 July 2007Available online 15 August 2007

bstract

An integrated model of supply network and production planning is proposed for the collaboration among refineries manufacturing multiple fuelroducts at different locations. The simulation and optimization based on the model indicate the following. The distribution costs can be reducedy relocating distribution centers as well as by reconfiguring their linkages to various markets. Moreover, the multiple fuel products manufacturedeed to be segregated during storage and transportation to be able to satisfy the demands of the various markets. The production planning, therefore,

hould be an integral part of the supply-network planning, and vice versa. Specifically, the proposed integrated model is for the nationwide supplyf multiple fuel products manufactured by the individual refineries. The efficacy and usefulness of the integrated model is illustrated with anxample involving three refineries and four varieties of fuel products.

2007 Elsevier Ltd. All rights reserved.

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eywords: Supply network; Multi-site refineries; Collaborative production

. Introduction

Efficient supply networks have become indispensable forarketing diversified products to meet the varied demands

f global customers. A number of major oil refineries andhemical manufacturers producing various fuel and chemicalroducts in large quantities have forged a merger of their oper-tions to manufacture and/or market these products. Such aerger renders it possible to facilitate the acquisition of rawaterials, the distribution of intermediates and the delivery of

roducts.The planning of integrated production has been studied for

ulti-site refineries and petrochemical complexes where theroducts are delivered through the fixed networks of pipelines

Jackson & Grossmann, 2003; Neiro & Pinto, 2004; Schulz,iaz, & Bandoni, 2005). It is highly likely that further inte-ration of supply networks will reduce the distribution cost; this

∗ Corresponding author. Tel.: +82 42 869 3920; fax: +82 42 869 3910.E-mail address: sunwon@kaist.ac.kr (S. Park).

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098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2007.07.013

nvolves reconfiguring the linkages to markets through relocatedistribution centers (Melkote & Daskin, 2001; Wu, Zhang, &hang, 2006).

The linkages between distribution centers and markets shoulde planned separately for different fuel products. They needo be segregated during transportation and storage to satisfyhe demands of the various markets under different conditions.

eanwhile, the production rates of individual refineries dependn the properties of crude oil, the cut points of distillation units,nd the modes of blending operation (Brooks, Van Walsem, &rury, 1999; Jia & Ierapetritou, 2003; Li, Hui, & Li, 2005;endez, Grossmann, Harjunkoski, & Kabore, 2006; Moro,

anin, & Pinto, 1998). Accordingly, the production planninghould be integrated into supply-network planning to enablehe production to respond effectively to fluctuations in marketemand.

This study aims at establishing an integrated model of supply

etwork and production planning for fuel products. Specif-cally, the distribution centers are relocated according to a

ixed-integer model for profit maximization. Moreover, thisixed-integer model is coupled with the non-linear production

2530 Y. Kim et al. / Computers and Chemical E

Nomenclature

Indicesi refineriesj distribution centers (DC’s)k marketsp productss intermediate streams

SetsI set of refineriesJ set of DC’sK set of marketsP set of productsS set of intermediate streams

ParametersCap cdui capacity of CDU at refinery i (tonne/day)Dk,p demand for product p at market k (bbl/year)Fj unit fixed operating cost of DC j (won/bbl)G fcci weight transfer ratio of the gasoline stream from

FCC at refinery iOp cdui unit operating cost of CDU at refinery i

(won/tonne)Op fcci unit operating cost of FCC at refinery i

(won/tonne)Pcrude price of crude oil (won/tonne)PMTBE price of MTBE (won/tonne)Pp price of product p (won/bbl)Re fcci weight transfer ratio of the recycle stream from

FCC at refinery iSj annual throughput capacity of DC j (bbl/year)SDi stream days per year at refinery iTBp barrels per 1 tonne of product p (bbl/tonne)Vj unit variable operating cost of DC j (won/bbl)XCi,j unit transportation cost from refinery i to DC j

(won/bbl)YCj,k unit transportation cost from DC j to market k

(won/bbl)

VariablesMTBEi,p flowrate of MTBE that is added in the blending

of product p ∈ {G#93, G#90} (tonne/day)qFi,s flowrate of intermediate stream s at refinery i

(tonne/day)qFi,s,p flowrate of intermediate stream s split to produce

product p (tonne/day)qPi,p production rate of product p at refinery i (bbl/year)Wi integer variable for the number of operating

CDU’s at refinery ixi,j,p quantity of product p delivered from refinery i to

DC j (bbl/year)Xj binary variable for the establishment of DC jyj,k,p quantity of product p delivered from DC j to mar-

ket k (bbl/year)Z profit (won)Z′ profit of the integrated model (won)

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ngineering 32 (2008) 2529–2535

odel developed by Li et al. (2005). A real-world example isresented to demonstrate the usefulness of the integrated model.

. Development of integrated model

Linking the models of supply network and production plan-ing for manufacturing and marketing fuel products leads ton integrated model. Such a model can be deployed to deter-ine the optimal production rates at the refineries, the locations

f distribution centers and the transport routes to markets foraximizing profit.

.1. Network planning

In the first sector of a typical refinery-supply network as illus-rated in Fig. 1 with the one existing in South Korea, the fuelroducts are transported from the refineries to the distributionenters (DC’s) by different means including pipelines (P/L’s),essels (VSL’s), railroad train containers (RTC’s), and/or tankrucks (T/T’s). This gives rise to a network, comprising theefineries, DC’s and the linkages among them.

In the second sector, the fuel products are delivered from DC’so the markets where the aggregated or individual demands ofas stations reside. The delivery in this sector usually involves/T’s: they can readily reach the markets with diverse demands.

n either sector, the unit transportation cost depends on the meansf transportation and the delivery distance.

The network model is formulated as a mixed-integer prob-em of network reconfiguration where the locations of candidateC’s and the production capacities of the refineries involved

re known. The objective is to maximize the profit, which is

ig. 1. Network linking the multi-site refineries to the distribution centers (DC’s)n South Korea: three refineries denoted by plant icons ( ) and DC’s belongingo them denoted by red tanks ( ), white tanks ( ) and green tanks ( ).

Y. Kim et al. / Computers and Chemical Engineering 32 (2008) 2529–2535 2531

F ntermG , DC2

tt

Z

EsiDotpDYtucddvectac

N

Tf∑∑

Taiegp

ro∑

2

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rmt

ig. 2. Overview of the supply network for fuel products: crude oil producing i#90, D#−10 and D#0; and fuel products delivered to distribution centers DC1

he difference between the revenue from sales and the costs ofransportation and storage, i.e.,

Maximize:

=∑j,k,p

Pp · yj,k,p −∑i,j,p

XCi,j · xi,j,p −∑j,k,p

YCj,k · yj,k,p

−∑

j

Fj · Sj · Xj −∑

j

⎛⎝Vj

∑i,p

xi,j,p

⎞⎠ (1)

ach term1 on the right-hand side of the above expression repre-ents the respective sums of the following terms. The first terms the revenue from the delivery of product p to market k fromC j, yj,k,p, multiplied by the price of product p, Pp; the sec-nd term, the delivery cost from refinery i to DC j, which ishe product of the unit transport cost, XCi,j, and the quantity ofroduct p delivered, xi,j,p; the third term, the delivery cost fromC j to market k, which is the product of the unit transport cost,Cj,k, and the quantity of product p delivered, yj,k,p; the fourth

erm, the cost of establishing DC j, which is the product of thenit fixed operating cost of DC j, Fj, and its annual throughputapacity, Sj; and the fifth or last term, the variable operating costepending on its throughput, which is the amount of product pelivered from refinery i to DC j, xi,j,p, multiplied by the unitariable operating cost of DC j, Vj. Note that the unit deliv-ry costs, XCi,j and YCj,k, vary according to the lengths andonditions of optimal routes. The binary variable, Xj, signifieshe establishment or non-establishment of DC j; thus, the totalmount of all fuel products delivered from refinery i to DC j isonstrained as below:∑i,p

xi,j,p ≤ Sj · Xj, for j ∈ J

Xj ={

1 if DC j is established,

0 otherwise.

(2)

1 The complete list of definitions of variables and parameters is provided inomenclature.

odsu

l

ediates GO, HN, LD, HD and BR; intermediates yielding fuel products G#93,, . . ., DCJ, followed by the delivery to markets M1, M2, . . ., MK.

he mass balances at refineries and DC’s are, respectively, asollows:

j

xi,j,p ≤ qPi,p · TBp, for i ∈ I, p ∈ P (3)

k

yj,k,p ≤∑

i

xi,j,p, for j ∈ J, p ∈ P (4)

he production rate of product p at refinery i, qPi,p, can be givens a constant or estimated in production planning delineatedn the succeeding section. Following convention, production isxpressed in terms of tonnes while the quantities distributed areiven in barrels in the above expressions; thus, TBp, the barrelser tonne of product p, is introduced to consolidate the basis.

In the second sector of distribution, the quantities of productseaching each market should not exceed the estimated demandf the market, Dk,p; hence,

j

yj,k,p ≤ Dk,p, for k ∈ K, p ∈ P (5)

.2. Production planning

Fig. 2 depicts the overall view of a typical supply network foruel products ranging from exploiting the crude oil to distribut-ng the products. The streams connecting the layers of supplynits indicate that the supply-network planning needs to be com-ined with the production planning to estimate the necessaryroduction capacities of refineries.

The production processes of multi-site refineries can be rep-esented by the available model (Li et al., 2005) with minimumodification, thus resulting in Eqs. (6)–(10). The model con-

ains the five intermediate streams from CDU, including grossverhead (GO), heavy naphtha (HN), light distillate (LD), heavyistillate (HD) and bottom residual (BR) streams. The heaviest

tream, BR, is treated further in the fluidized catalytic crackingnit (FCC) to manufacture gasoline and other light components.

The two lightest streams, GO and HN, together with the gaso-ine stream from FCC, yield the premium and regular gasoline,

2532 Y. Kim et al. / Computers and Chemical Engineering 32 (2008) 2529–2535

Table 1Pre-tax prices and market demands for the fuel products

Product, p Barrels per tonne, TBp (bbl/tonne) Price-tax, Pp (wona/L) Market demand, Di,p (bbl/year)

i = A i = B i = C

G#93 8.45 828 66,395 20,276,819 15,176G#90 8.45 608 20,276,819 17,380,131 4,634,702DD

irstsDAib

∑

wd

wbrWh∑

etsr

q

wph

q

2

rieab(

Z

AdhttttatombciM

#−10 7.8 623#0 7.5 594

a Korean currency (US$ 1 = 930 won).

.e., G#93 and G#90, respectively, with the numerical values rep-esenting the octane numbers. These two grades of gasoline areubsequently blended with methyl tertiary butyl ether (MTBE)o increase their octane numbers. The middle streams in Fig. 2,treams LD and HD, are blended to produce two grades of diesel,#−10 and D#0, numerically differentiated by their pour points.ccordingly, the mass balances in the gasoline and diesel blend-

ng units can be given in Eqs. (6) and (7), respectively, as givenelow.∑s

qFi,s,p + MTBEi,p

=qPi,p, for i ∈ I, s ∈ {GO, HN, BR}, p ∈ {G#93, G#90}(6)

s

qFi,s,p = qPi,p, for i ∈ I, s ∈ {LD, HD},

p ∈ {D# − 10, D#0} (7)

here qFi,s,p is the flowrate of the substream split from interme-iate stream s to produce product p at refinery i.

The sum of the flowrates of intermediate streams, qFi,s’s,hich is identical to the load to CDU at refinery i, is constrainedy its capacity, Cap cdui. By assuming that the individualefineries possess CDU’s of the same size, the integer variable,

i, is introduced to represent the number of operating CDU’s;ence,

s

qFi,s ≤ Cap cdui · Wi, for i ∈ I (8)

The operation of FCC at refinery i is assumed to be fixed toxclude the consideration of all the other outlet streams excepthe gasoline stream; the weight transfer ratios of the recycletream and gasoline stream are set to be Re fcci and G fcci,espectively. Consequently, the load to FCC at refinery i is

Fi,BR(1 + Re fcci), for i ∈ I (9)

hile the flowrate of stream BR, qFi,BR, and the sum of theroduction rates of the recovered gasoline streams, qFi,BR,p’s,ave the following relation;

Fi,BR · G fcci=∑p

qFi,BR,p, for i ∈ I, p ∈ {G#93, G#90}(10)

m

ih

15,071,321 12,918,275 3,444,87350,300,576 43,114,779 11,497,274

.3. Integration

The integration of supply network and production planningequires that both the production and distribution costs be takennto account in maximizing the profit. The non-linear prop-rty relations in the models for CDU’s and blenders (Li etl., 2005) demand that the profit of the integrated network, Z′,e maximized through mixed-integer non-linear programmingMINLP); therefore,

Maximize:

′ =⎡⎣∑

j,k,p

Pp · yj,k,p −∑i,j,p

XCi,j · xi,j,p −∑j,k,p

YCj,k · yj,k,p

−∑

j

Fj · Sj · Xj −∑

j

⎛⎝Vj

∑i,p

xi,j,p

⎞⎠

⎤⎦

−⎡⎣Pcrude ·

∑i,s

SDi · qFi,s−PMTBE ·∑i,p

SDi · MTBEi,p

⎤⎦

−[∑

i

Op cdui · Cap cdui · SDi · Wi

]

−[∑

i

Op fcci · SDi · qFi,BR(1 + Re fcci)

](11)

s can be discerned from the variables and parameters defined ineriving Eq. (1), the terms in the first square bracket on the right-and side of the above expression signify the difference betweenhe revenue and distribution costs; the second square bracket,he raw-material costs comprising the cost of crude oil given ashe price of crude oil, Pcrude, multiplied by the amount loadedo CDU’s, which is the sum of intermediate streams, qFi,s’s,nd the cost of MTBE given as its price, PMTBE, multiplied byhe quantity of MTBE, MTBEi,p; the third square bracket, theperating cost of CDU given as the unit operating cost, Op cdui,ultiplied by its capacity, Cap cdui; and lastly, the fourth square

racket, the operating cost of FCC given as the unit operatingost, Op fcci, multiplied by the load to the FCC unit, expressedn Eq. (9). Note that all the quantities on a daily basis, i.e., qFi,s’s,

TBEi,p and Cap cdui, are converted into the yearly basis by

ultiplying them with the number of stream days per year, SDi.In the integrated network, the fixed operating cost of DC j

s assumed to be shared based on the pay-by-volume policy;ence, the fixed operating cost of individual refinery i for all the

Y. Kim et al. / Computers and Chemical Engineering 32 (2008) 2529–2535 2533

Table 2Prices of raw materials

Raw material Price (won/tonne)

C a −1

M

p

∑

wobt

3

arcuarttcr

3

eTrfbr

3r

a

TU

U

DCF

No

Table 4Unit transport costs from refineries to DC’s and the annual throughput capacitiesof DC’s

DC, j Unit transport cost fromrefinery i to DC j, XCi,j (won/L)

Annual throughput capacityof DC j, Sj (103 bbl/year)

i = A i = B i = C

S1 8.83 0.35 9.09 9,000S2 8.83 0.21 9.09 9,000S3 10.71 0 12.85 14,100S4 8.83 0.21 9.09 14,000S5 7.1 1.09 7.71 10,000S6 9.03 0.49 9.26 1,000S7 6.39 1.83 5.68 2,000S8 8.79 2.49 9.45 1,000S9 7.36 3.1 8.95 1,000S10 5.61 6.55 12.42 1,000S11 5.55 6.39 9.01 1,000S12 5.61 6.55 12.42 3,400S13 6.53 4.1 8.46 5,000S14 4.72 3.98 4.01 1,000S15 4.72 3.62 4.01 1,000S16 4.72 3.96 4.01 1,300S17 6.01 2.15 5.3 1,000S18 7.91 4.8 4.72 1,000S19 7.3 5.01 3.9 2,000S20 7.91 4.8 4.72 1,000S21 7.52 5.19 2.25 3,000S22 7.02 6.91 2.81 2,000S23 7.02 6.91 2.81 5,100S24 4.54 8.61 0.15 1,000S25 5.13 8.83 0.49 1,000S26 6.78 7.95 0.73 1,000S27 8.04 7.35 3.56 1,000S28 12.85 12.85 0 25,000S29 7.9 7.35 3.42 2,600S30 8.16 9.05 4.28 1,000S31 8.16 9.05 4.28 700S32 1.64 8.47 6.6 3,000S33 1.56 8.53 6.29 1,000S34 1.62 7.18 5.38 3,200S35 1.64 8.47 6.6 3,000S36 2.16 7.18 5.38 1,000S37 3.6 7.63 2.13 1,000S38 4.2 8.26 1.12 1,000S39 2.7 8.64 3.34 1,000S40 2.52 8.6 3.39 2,200S41 1.5 9.69 4.46 2,000S42 1.84 9.38 4.12 2,000S43 1.5 9.69 4.46 1,000S44 1.49 9.19 4.41 4,000

rude oil, Pcrude 392,788 (US$ 57.44 bbl )TBE, PMTBE 623,100 (US$ 670 tonne−1)

a 1 bbl = 0.136 tonne.

roducts can be given separately as

j,p

Fj · Sj · Xj · Di,p∑i,pDi,p

, for i ∈ I (12)

here Di,p is the demand for product p of refinery i. The benefitf the supply network integration for individual refineries cane evaluated by comparing the costs of separate networks andhat of the integrated network.

. Illustration

The efficacy and utility of the proposed integrated modelre illustrated with a real-world supply network comprising 3efineries, 46 DC’s and 124 markets; specifically, 3 cases areonsidered. The first involves the supply network of the individ-al refineries; the second, the collaborative supply network ofll the refineries; and the third, the integrated network of all theefineries. The pertinent data are presented in Tables 1–4. Notehat the market demands, given in Table 1, are estimated fromhe total nationwide annual demand and the population of 124ities. It is assumed that the sales limit is imposed on each of theefineries in any of the cities according to their market shares.

.1. Case 1: Separate planning of the individual refineries

It is rational to assume that the refineries are individuallyarning the maximum possible profits from the present networks.hus, the profits and distribution costs of the three individual

efineries, supplying the nationwide market with fuel products,orm the basis. Network planning can be carried out separatelyy applying the proposed model to the individual refineries. Theesults are summarized in Tables 5 and 6.

.2. Case 2: Collaborative network planning by all the

efineries

This case deals with the supply networks for the optimal oper-tive use of distribution facilities; the three refineries coordinate

able 3nit operating costs and size parameters

nit Unit operating cost (won/tonne) Size parameter

C, j Fj = 300, Vj = 300 Sj: see Table 4DUa Op cdui = 2413 Cap cdui = 400 tonne/dayCCa Op fcci = 13,272 Re fcci = 0.404

otes: Fj and Vj—fixed and variable operating costs of DC; Cap cdui—capacityf CDU; Re fcci—weight transfer ratio of the recycle stream in FCC.a From Li et al. (2005).

S45 0 12.85 12.85 30,000S46 12.85 8.83 5.54 500

Table 5Production cost and profit of individual refinery in Cases 1 and 2

Refinery Production costa (million won) Profit (million won)

Case 1 Case 2 Case 1 Case 2

A 53,947 53,947 741,837 743,114B 10,016 10,098 168,815 170,694C 46,014 46,014 632,294 643,969

a The sum of the operating costs of CDU and FCC.

2534 Y. Kim et al. / Computers and Chemical Engineering 32 (2008) 2529–2535

Table 6Distribution costs and the profits in Cases 1–3

Cost or profit (million won) Separate networks, Case 1a Cost reduction by integration

Case 2a (%) Case 3b (%)

Delivery cost 65,497 52,567 (−19.7%) 41,890 (−36.0%)Fixed operating cost of DC’s 53,730 53,730 (0) 18,910 (−64.8%)Variable operating cost of DC’s 20,078 20,099 (0.11%) 18,759 (−6.57%)

P 1,557,777 1,591,436

tutnep

tcrr

3

rbtonCt

4

p

Ft

Fi

ppsnafoe

s

rofit 1,542,946

a No. of DC’s = 46.b No. of DC’s = 29.

he operation of DC’s, while the production planning is individ-ally executed for the segregated demands. Only the change inhe configuration is, therefore, allowed to assess the effective-ess of collaboration. The sales of fuel products in the market byach refinery are not allowed to exceed the demand for the fuelroducts from an individual refinery, which is given in Table 1.

The results listed in the third column of Table 6 indicate thathe collaborative network planning reduces the overall deliveryost by as much as 19.7%. Share of the total profit gain byefinery C is 78.72%; that by refinery B, 12.67%; and that byefinery A, 8.61%. These results are depicted in Fig. 3.

.3. Case 3: Network integration among all the refineries

This case describes the total integration among the threeefineries; the supply networks of a single company constitutedy merging the three companies. This total integration involveshe collaborative production planning; the cooperative operationf DC’s; the consolidation of market demand; and the coordi-ation of the establishment of DC’s as well as the operation ofDU’s exclusively among the present facilities. The results of

he three case studies are compared in Figs. 4 and 5.

. Discussion

The three case studies presented amply demonstrate theotential benefits resulting from the collaborative planning for

ig. 3. Shares of the overall profit increase by the individual refineries based onhe pay-by-volume policy: Case 2.

pcpeat

wM&

ig. 4. Reductions in the annual distribution costs with increasing levels ofntegration.

roduction and distribution of fuel products based on the pro-osed integrated model among multiple refineries or within aingle refinery. The results indicate specifically that the supplyetwork and production of different fuel products need to be sep-rately planned to determine the most efficient delivery routesrom the multi-site sources to the various markets; the flexibilityf a supply network is enhanced; and any market change and itsffects on the entire supply network can be exactly evaluated.

The results of Cases 2 and 3 imply that the coordination ofupply networks allows each plant to improve its profit by sup-lying the more profitable products to its closer markets. If theandidate locations of the plants are taken into account in theroposed model, the relocation of refineries needs to be consid-red. To make such a decision, the delivery costs of raw materialsnd other resources need to be taken into account. This will behe subject of our future work.

The solutions for the three case studies have been obtainedith GAMS via DICOPT solver (Brooke, Kendrick, &eeraus, 1988; Grossmann, Viswanathan, Vecchietti, Raman,Kalvelagen, 2002) where the optimally planned operating

Fig. 5. Comparison of the itemized annual distribution costs.

ical E

ctetTl

tw2r

5

nrowm

A

KK

A

f2

R

B

B

G

J

J

L

M

M

M

N

S

Y. Kim et al. / Computers and Chem

onditions for production available in the literature serve ashe initial values. Case 3, involving 46,545 variables and 1351quations, requires the maximum computational time amonghe three cases; it amounts to 438 s on a 3.4 GHz Pentium D PC.he number of iterations and the total accumulated time are both

imited to 106.When the unit delivery costs, the most significant parame-

ers, are reduced by 20%, the choice of two DC’s are reversed,hile the results remained invariant when they are increased by0%. The computing time increased from 438 to 825 and 1653 s,espectively.

. Conclusion

An integrated model of supply network and production plan-ing has been proposed to reduce the distribution costs byeconfiguring the network of distribution centers. The efficacyf deploying this integrated model is demonstrated with a real-orld example involving three refineries supplying a nationwidearket with four fuel products.

cknowledgements

This work was supported by the Brain Korea 21 project,orea, and the Institute for Systems Design and Optimization,ansas State University, U.S.A.

ppendix A. Supplementary data

Supplementary data associated with this article can beound, in the online version, at doi:10.1016/j.compchemeng.007.07.013.

W

ngineering 32 (2008) 2529–2535 2535

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