Evaluation of Synergy Effect in the Horizontal Merger of Companies in

Ind. Eng. Chem. Res. 2009, 48, 11017–11033

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Evaluation of Synergy Effect in the Horizontal Merger of Companies in a Petrochemical Complex Sung-Geun Yoon,† Sunwon Park,*,† Jeongseok Lee,‡ Peter M. Verderame,§ and Christodoulos A. Floudas§ Department of Chemical and Biomolecular Engineering, Korea AdVanced Institute of Science and Technology (KAIST), 373-1, Guseong-dong, Yuseong-gu, Daejeon 305701, Korea, Corporate R&D, LG Chem Ltd., 104-1, Moonji-dong, Yuseong-gu, Daejeon 305380, Korea, and Department of Chemical Engineering, Princeton UniVersity, Princeton, New Jersey 08544

Mergers and acquisitions (M&As) have been actively carried out in the petrochemical industry. However, the synergy created by the merger of petrochemical companies has seen relatively little study, despite being the primary goal of a merger. This study deals with the horizontal merger of petrochemical companies located within a single complex. Synergies considered in this work stem from integration of the process network and the utility plant, reduction of fixed costs, and contracts in purchasing and selling. A novel mathematical model that represents the operation of a process network and a utility plant and the decisions for purchasing and selling contracts is formulated. Four contracts for purchasing and selling are considered. The proposed model is applied to three Korean companies at a naphtha cracking center (NCC) located in the same industrial complex. The results show that synergy effects from integration of the process network and the utility system, reduction of fixed costs, and increased market share together increase profit by 50%. 1. Introduction The petrochemical industry produces chemical products using materials such as ethylene, propylene, and benzene that are manufactured by cracking naphtha, gas oil, ethane, and propane included in crude oil and natural gas. The petrochemical industry occupies an important position in many national economies, as most manufacturing industries use the products of the petrochemical industry as raw materials. Many countries have fostered the petrochemical industry in its early stages of industrialization, and nations such as the United States, Germany, and Japan, which all have strong manufacturing industries, have strong petrochemical industries. Recently, the center of the petrochemical market has shifted to Asia. Developing countries such as China and India are experiencing rapid growth in petrochemical demand, and Middle Eastern countries are also constructing numerous petrochemical plants using their abundant resources, whereas developed countries are faced with mature markets. Major petrochemical companies in developed countries have carried out M&As (mergers and acquisitions) as a strategic tool to sustain their market position. The Korean petrochemical industry has developed rapidly since the 1970s as a result of a strong development policy initiated by the Korean government. The Korean petrochemical industry is presently ranked fifth in the world in terms of ethylene production. Recently, the Korean petrochemical industry has experienced prosperity because of the rapid growth of the neighboring Chinese market. That China and Middle Eastern countries are rapidly developing their own petrochemical industries, however, poses a major threat to the Korean petrochemical industry. To sustain competitive* To whom correspondence should be addressed. E-mail: sunwon@ kaist.ac.kr. Tel.: +82-42-350-3960. Fax: +82-42-862-5961. † Korea Advanced Institute of Science and Technology (KAIST). ‡ LG Chem Ltd. § Princeton University.

ness, the Korean petrochemical industry has recently come to consider M&As as an important strategy. Major petrochemical companies and Japanese petrochemical companies have carried out many M&As to raise their competitiveness since the 1990s, whereas the Korean petrochemical industry has been party to only a few because of a financial crisis in late 1990s. At present, too many companies are still participating in the petrochemical industry. Companies and governments should therefore consider M&As as a necessary strategy to improve competitiveness. However, there is no blueprint for M&A strategies from a holistic view. Some companies have announced mergers of their subsidiary companies. The Korean government also has not provided direction regarding M&As. Many stakeholders are now debating on the M&A issue. The debate has focused on how much M&As will impact the petrochemical industry and the national economy. To assist stakeholders, in an earlier study, the present authors proposed an optimization model to quantify synergy in the merger of petrochemical companies in an industrial complex, considering purchasing and selling advantages.1 The results of the previous research indicate that strengthening market power can significantly increase profit. To reflect more realities in estimating synergy, this study improves on the previous model, which had some drawbacks. First, that optimization model identified little synergy from plant integration. Interactions between processes and utility systems were rarely considered in mathematical modeling. As a result, operations of individual companies and of the merged company were assumed to be very similar. However, a petrochemical company typically has a united utility plant system and process network, and the utility plants are affected by each other.2 Presently, it is necessary to identify synergy from the utility system because of rising utility costs. However, we considered only boiler operation for the utility system in the previous research. Second, the optimization model did not include investment costs incurred in the merger. The reason that the

10.1021/ie900802v CCC: $40.75  2009 American Chemical Society Published on Web 11/09/2009

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Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009

previous work ignored the investment costs was that it did not focus on control of a company (G1) and the cost of reconfiguring the process network was considered to be negligible compared to the profit, which was the objective function. However, it is meaningful to add an investment term, because construction costs have risen radically in recent years because of a boom in plant constructions in the Middle East and developing countries. Third, the previous model was developed for a single period. However, corporate M&As must have a long-term perspective. Therefore, the development of a multiperiod model is required, which increases the complexity of the model. In particular, the investment cost model needs to determine the timing of investments. Fourth, purchasing and selling terms need to more accurately reflect reality. The previous model considered only a bulk-discount contract, whereas petrochemical companies utilize various contract forms in purchasing and selling. Park et al. developed an MILP model for various contracts in the chemical industry, which is applied to this study.3 This work deals with the same target companies that were considered in our previous work. We propose a new and improved optimization model to better reflect realities. The model can quantify synergy from the case in which a target company has one utility plant. In addition, investment costs to enable the transport of chemicals and steam between individual companies are added to the optimization model. The singleperiod model is extended to a multiperiod model, and finally, four representative contracts for purchasing and selling are applied to the model. This article consists of six sections. Section reviews previous works on process and utility system integrations. Section defines the target problem. Section describes the optimization model, and the results follow in section 5. In section 6, we conclude this article. 2. Previous Works The goal of a M&A is to create synergy that is not attainable for a single company within the same period. Synergy in the merger of companies can be created from various elements. For example, there are synergies from raising market power, increasing production efficiency, eliminating duplicate work, and improving financial status, among others. This work concentrates on proposing a novel mathematical model to quantify synergy from the integration of a process network and a utility plant and contracts in purchasing and selling. Several studies have dealt with the petrochemical process network. Rudd introduced a linear programming (LP) model applicable for a short-range allocation problem in the intermediate chemicals industry.4 This model allowed for competing production paths, including new technologies for manufacturing a product. Among the competing paths, the LP model selected one or two processes to satisfy the demand. Many researchers have developed the model further. Stadtherr et al. extended the LP model to a long-range planning model allowing for perturbations in feedstock availability.5,6 They introduced the concept of a feedstock efficiency index (FEI), representing the ratio of theoretical carbon requirement for a chemical to its shadow price. The proposed model was applied to an industrial problem and minimized feedstock consumption. The resultant FEIs provided insight into the actual effects of perturbations in feedstocks. Jimenez et al. introduced a mixed-integer linear programming (MILP) model for the development of the Mexican petrochemical industry.7 The MILP model compared installing a process with importing its corresponding product on an

economic basis. At that time, Mexico sought to develop a petrochemical industry. The decision of whether to import or build was greatly motivated by economic incentives. Jimenez et al. extended the MILP model so as to detect an optimal development sequence.8 The model provides the sequence of short steps needed to achieve a specified long-range development plan. Recently, research was carried out in Middle Eastern countries with the objective of using the region′s inexpensive resources.9,10 Al-Sharrah et al. proposed an MILP model for the development of the petrochemical industry with an objective defined by sustainability and quantified by added value and a health index.7 The model was inherently multiobjective. They provided a strategy for treating a multiobjective problem and applied the model to the Kuwait petrochemical industry. Alfares et al. proposed an MILP model for planning and screening investment opportunities in the petrochemical industry in Saudi Arabia.8 Piecewiselinear functions for the investment cost and the production cost were introduced to reflect economies of scale. Optimization studies were carried out under variations of investment budget and available raw materials. Optimization of the utility system has been an important issue since the inception of the petrochemical industry. The petrochemical industry is an energy-intensive industry in the same manner as the steel industry and cement industry. The oil crises in the 1970s and 1980s spurred researchers to address the issue of saving energy. This issue has recently been highlighted again because of high energy prices. Energy optimization of a process has become systematic since Linnhoff et al. identified the pinch point of a process.11 The methodology suggested by Linnhoff et al. has been used to optimize the heat exchanger network of a process. The pinch design method was subsequently proposed,12 and a mathematical model was developed to find the optimal heat exchanger network.13,14 The pinch methodology is a heuristic way to optimize the heat exchange network, whereas the mathematical model suggests a deterministic approach. Tjoe et al. extended the pinch methodology for a grassroots design to a retrofit design problem.15 Floudas et al. suggested an automated methodology to optimize a heat exchanger network using a superstructure.16-18 There are many industrial cases where these methodologies have been applied to reduce energy consumption. A fluid catalytic cracking plant,19 a pulp and paper plant,20 a nitric acid plant,21 a crude distillation plant,22 and an ethyl benzene plant23 are a few examples. The utility system optimization problem was extended from optimizing the energy consumption of a process to optimizing the utility plant of one site. Linnhoff et al. suggested a technique for optimizing a utility plant using the pinch methodology.24 Papoulias et al. developed a mixed-integer linear programming (MILP) model to optimize a utility plant including various steam grades and several steam turbines generating electricity.25 Park developed the MINLP model for optimal use of power drivers among steam turbines and electricity motors.26 Mavromatis et al. suggested methodologies to optimize a steam turbine network in a chemical plant.27,28 Marechal et al. developed an MILP model to optimize a utility plant using an expert system and then extended the model to consider multiple periods.29,30 Eliceche et al. dealt with a utility plant optimization problem considering the life-cycle impact on the environment.31 Yeo et al. proposed a rule-based optimization system for a steam distribution network based on the experience of plant engineers.32-34


A problem involving a single utility plant can be extended to utility plants in multiple sites. Hirata et al. suggested a methodology for integrating two utility plants that are in close proximity.35 Soylu et al. developed an MILP model for integrating two different companies’ utility systems when the two companies cooperate to operate the utility system.36 The MILP model identified synergy and the investment costs of cooperation. In the petrochemical industry, the relation between companies is contractual. To identify synergy in purchasing and selling, we have applied a model of different purchasing and selling contracts. A different aspect of contract modeling is different types of contracts that a company sets up during its planning process. The result of such contracting modifies the objective function of the optimization model, leading to a more complicated but also more realistic function. Park et al. developed a novel mathematical model for different types of contracts in purchasing and selling.37 This work develops an optimization model to identify chemical transportation between companies and to calculate investment costs based on the transportation. We also add a utility plant model to the previous model. Each company has an individual utility plant including boilers and steam turbines. Steam transportation between utility plants and investment costs due to the steam transportation are also identified by the model. The contract model is applied to the optimization model to identify synergy from purchasing and selling. 3. Problem Definition This work considers three companies, A, B, and C, having a naphtha cracking center (NCC) within a complex in Korea. The process networks and utility plant diagrams of the three companies are shown in Figure 1. Each company has NCC and BTX (benzene, toluene, and xylene extraction) processes and different downstream processes. Each company has one utility plant having one boiler, one superheated-steam (SS) turbine, and one high-pressure (HP) steam turbine. The capacities of the boilers and turbines are different. Steam and electricity transportation between the process network and the utility plant is available. Some processes generate steam, which is transported to the utility plant. The utility plant produces steam and electricity and then transports them to the process network according to the steam grade and electricity demands of each. NCC companies can sell steam to other companies. Sometimes NCC companies sell electricity generated by their steam turbine to a regional power company. If the three companies are merged, the new merged company can operate all process networks and utility plants of the three companies. We assume that company D is the aggregate of companies A, B, and C. The process network and utility plant diagram of company D are shown in Figure 2. 4. Mathematical Modeling A novel MILP model is developed herein for optimization of a process network and a utility plant. This model maximizes the profits of target companies under given price and parameter data. The sets, parameters, and variables in the model are listed in the Nomenclature section. The equations for operation of the process network, contracts of purchasing and selling, and utility plant are presented first, followed by the mixed-integer nonlinear objective function.

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Then, the transformation of the mixed-integer nonlinear objective function into an equivalent mixed-integer linear form is explained, and the complete mixed-integer linear programming model is presented. 4.1. Equations for Process Operation and Chemical Mass Balance. Xnit

rnit )

Xnit

,

∀n, i, t

rnit e bnit e 2rnit,

∑ qo

nqpnjt +

nijt

i

(1)

∀n, i, t

(2)

0 e Xnit e Xnit, ∀n, i, t

(3)

ainijXnit ) qinijt, ∀n, i, j, t

(4)

aonijXnit ) qonijt, ∀n, i, j, t

(5)

+

∑ ct

n′njt

n′

) nqsnjt +

∑ qi

nijt

+

i

∑ ct

nn′jt,

∀n, j, t

(6)

n′

∑ ct

n′njt

e Myctinjt, ∀n, j, t; M ) large positive value

n′

(7)

∑ ct

nn′jt

e Myctonjt, ∀n, j, t; M ) large positive value

n′

(8) yctinjt + yctonjt e 1, ∀n, j, t

(9)

ctn′njt e Myctnn′jt, ∀n, n′, j, t; M ) large positive value (10) yctnn′jt + yctn′njt e 1, ∀n, n′, j, t

(11)

Equation 1 represents the operating ratio of the process. Equation 2 is for activating the binary variable of the process and for forcing the minimum operating ratio of the process to be 50%. An industrial process is not able to operate below a certain operating ratio because an operating ratio that is too low can cause equipment trouble. We assume the minimum operating ratio of the process to be 50%. If a process is activated, the process must operate at over 50% according to eq 2. Equation 3 represents the range of process input. Equations 4 and 5 calculate the amounts of chemicals consumed and produced by a process. The equations are the products of material balance coefficients, ainij and aonij, and process input, Xnit. Equation 6 is the material balance for chemical j in company n. The sum of the amount of chemical purchased, nqpnjt; the amount of chemical produced by the processes, ∑iqonijt; and the amount of chemical transported from other companies, ∑n′ctn′njt, is equal to the sum of the amount of chemical sold, nqsnjt; the amount of chemical consumed by the processes, ∑iqinijt, and the amount of chemical transported to the other companies, ∑n′ctnn′jt. Equations 7-9 are constraints on ∑n′ctn′njt and ∑n′ctnn′jt. That is, for chemical j in company n, transportation from the other companies and to the other companies cannot occur simultaneously. The large positive value of M ) 107 was used in this study. Equations 10 and 11 restrict mutual transportation of same chemical j between companies. As the mass balance equations are applied to individual companies, the variable for chemical transportation, ctnn′jt, is forced to be zero.

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4.2. Contracts for Purchasing and Selling. Qpjt )

∑ nqp

njt,

∀j, t

(12)

∑ nqs

njt,

∀j, t

(13)

n

Qsjt )

n

0 e Qpjt e Mypjt, ∀j, t; M ) large positive value (14) 0 e Qsjt e Mysjt, ∀j, t; M ) large positive value (15) ypjt + ysjt e 1,

∀j, t

(16)

Equations 12 and 13 calculate the amounts of chemicals purchased and sold, Qpjt and Qsjt, by the merged company. Equations 14-16 are constraints on Qpjt and Qsjt. For all chemicals, Qpjt and Qsjt cannot take on positive values simultaneously. 4.2.1. Purchasing Contracts. The types of contracts for purchasing include (1) fixed price, (2) discount after a certain amount, (3) bulk discount, and (4) fixed duration. Equations to determine purchasing cost for the various types of contract are as follows PURjt )

∑ PUR

hjt,

∀j, t

(17)

h

Qpjt )

∑ qpc

hjt,

∀j, t

(18)

h

0 e qpchjt e Mbqpchjt,

∀h, j, t; M ) large positive value (19)

∑ bqpc

hjt

e 1 ∀j, t

(20)

h

h ∈ H ) {f, d, b, l} where f represents a fixed-price contract, d represents a contract with a discount after a certain amount, b represents a bulkdiscount contract, and l represents a fixed-duration contract. Equation 17 means that PURjt, the cost of purchasing chemical j at time t, is defined as the sum of PURhjt over all contracts h. Equation 18 indicates that Qpjt, the amount of chemical j purchased at time t, is the sum of over all contracts h of qpchjt, the amount of chemical j purchased in contract h at time t. Equation 19 activates the binary variable for qpchjt. The number of contracts that can be made at time t is constrained by eq 20. 4.2.1.1. Fixed-Price Contract. A fixed-price contract means that a company purchases raw materials in any amount at the current market price. The purchasing cost of raw materials at the fixed price, PURfjt, is defined by the equations PURfjt ) Pfjtqpcfjt, ∀j, t

(21)

qpcfjt e PFUjt, ∀j, t

(22)

where Pfjt is the chemical price in the fixed-price contract. qpcfjt is the amount purchased in the fixed-price contract and has the upper bound given in eq 22. 4.2.1.2. Contract with a Discount after a Certain Amount. A contract with a discount after a certain amount requires the purchase of a minimum quantity of chemical j at

time t (PDLjt). In this type of contract, if the amount of chemical purchased by a company exceeds PDLjt, it purchases the amount of PDLjt at the price of Pd1jt and the excess amount at the lower price Pd2jt. Equations for this type of contract are as follows PURdjt ) Pd1jtqpd1jt + Pd2jtqpd2jt, ∀j, t

(23)

qpcdjt ) qpd1jt + qpd2jt, ∀j, t

(24)

qpd1jt ) qpd11jt + qpd12jt, ∀j, t

(25)

0 e qpd11jt e bqpd1jtPDLjt, ∀j, t

(26)

qpd12jt ) bqpd2jtPDLjt, ∀j, t

(27)

0 e qpd2jt e Mbqpd2jt, ∀j, t; M ) large positive value (28) bqpd1jt + bqpd2jt ) bqpcdjt, ∀j, t

(29)

qpcdjt e PDUjt, ∀j, t

(30)

The purchasing cost of raw materials in a contract with a discount after a certain amount, PURdjt, is defined by eq 23. Equation 24 indicates that the amount purchased in this type of contract is the sum of the amounts purchased in the two contract divisions, 1 and 2. If qpcdjt exceeds PDLjt, qpd1jt is determined for PDLjt by eqs 25-27. Equation 28 is for the binary variable bqpd2jt. Equation 29 determines the division of qpcdjt if qpcdjt is activated. Equation 30 specifies the upper bound of qpcdjt. 4.2.1.3. Bulk-Discount Contract. A bulk-discount contract requires the purchase of a minimum quantity of chemical j at time t (PBLjt). In this contract, if the amount of chemical purchased by a company exceeds PBLjt, it purchases the whole amount of chemical at the price of Pb2jt, which is lower than Pb1jt. Equations for the bulk contract are as follows PURbjt ) Pb1jtqpb1jt + Pb2jtqpb2jt, ∀j, t

(31)

qpcbjt ) qpb1jt + qpb2jt, ∀j, t

(32)

0 e qpb1jt e bqpb1jtPBLjt, ∀j, t

(33)

bqpb2jtPBLjt e qpb2jt e Mbqpb2jt, ∀j, t; M ) large positive value

(34)

bqpb1jt + bqpb2jt ) bqpcbjt, ∀j, t

(35)

qpcbjt e PBUjt, ∀j, t

(36)

Equation 31 defines the purchasing cost in the bulk-discount contract, PURbjt. The sum of amounts in purchasing divisions 1 and 2 is equal to qpcbjt in eq 32. Equations 33-35 determine the purchasing division of qpcbjt, if qpcbjt is activated. Equation 36 constrains qpcbjt to be lower than an upper bound. 4.2.1.4. Fixed-Duration Contract. The fixed-duration contract determines the length of the time that contracts are valid for given prices, Plljτ, and the minimum quantity of the chemical to be purchased, PLLljτ. In this type of contract, if a contract with length l is made at time τ, a company can purchase the chemical at the price Plljτ in time period t (τ < t) with a minimum quantity of chemical purchased of PLLljτ. Equations for the fixed-duration contract are as follows PURljt )

∑ ∑ Pl

ljτqplljτt,

l

τ

∀j, t

(37)


qpcljt )

∑ ∑ qpl

ljτt,

l

∀j, t

PLLljτbqplljτt e qplljτt e PLUljτbqplljτt, ∀l, j, τ, t

∑ ∑ bqpl l

ljτt

(38)

τ

e bqpcljt, ∀j, t

(39) (40)

τ

Equation 37 defines the purchasing cost in the fixed-duration contract, PURljt. Equation 38 determines the amount purchased

Figure 1. Process networks and utility plant diagrams of the target companies.

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in the contract length l, qplljτt, which has the upper and lower bounds in eq 39. Equation 40 represents the decision for a contract of length l for the chemical j at time t. 4.2.2. Selling Contracts. In the same way as for purchasing contracts, a company can sell chemicals through different types of contracts. The types of contracts for selling include (1) fixed price, (2) discount after a certain amount, (3) bulk discount, and (4) fixed duration. Equations to determine sales revenue for the various types of contract are as follows

Figure 2. Process network and utility plant diagram of company D.

11022 Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009


REVjt )

∑ REV

∀j, t

hjt,

(41)

h

Qsjt )

∑ qsc

∀j, t

hjt,

(42)

h

0 e qschjt e Mbqschjt,

∀h, j, t; M ) large positive value (43)

50-52 represent the general mass balance model for a steam turbine. Equation 53 calculates the electricity generated by a steam turbine. A linear model for an actual turbine was used to calculate electricity generation. tanmo and tbnmo are coefficients that were estimated by linear regression of turbine operating data. 4.5. Electricity. TEt + SEt )

hjt

e 1 ∀j, t

(44) TEt )

h

nmt

where f represents a fixed-price contract, d represents a contract with a discount after a certain amount, b represents a bulkdiscount contract, and l represents a fixed-duration contract. Equation 41 means that REVjt, the sales revenue from chemical j at time t, is defined as the sum of REVhjt over all contracts h. Equation 42 indicates that Qsjt, the amount of chemical j sold at time t, is the sum over all contracts h of qschjt, the amount of chemical j sold in contract h at time t. Equation 43 activates the binary variable for qschjt. The number of contracts that can be made at time t is constrained by eq 44. Detailed models for each contract have exactly same forms as those for the purchasing contracts.3 4.3. Boiler. BXnkot ) Befnko

fuelnkot , DHSo

∀n, k, o, t

CO2nkot ) CO2cnkofuelnkot, BXnkot BXnkot

∀n, k, o, t

∀n, k, o, t

,

∀n, k, o, t

0.4bbnkot e brnkot e bbnkot,

∀n, k, o, t

∀t

nitEdni,

(54)

(55)

i

0 e SEt e Mbset, ∀t; M ) large positive value (56) 0 e PEt e Mbpet, ∀t; M ) large positive value (57) bpet + bset e 1

(58)

(45)

Equation 54 is an electricity balance equation. The sum of the electricity demand of the process network, TEt, and the electricity sold, SEt, is equal to the sum of the electricity generated by turbines, ∑n∑mTEGnmt, and the electricity purchased, PEt. Equation 55 defines the electricity demand of the process networks. Equations 56-58 are constraints that electricity purchasing and selling cannot occur simultaneously. 4.6. Steam Header.

(46)

∑X

nitsgcnio

i

∑ BX + ∑ Tout + ∑ st + - ( ∑ Tin + LD + ∑ X sdc + ∑ st + stms ) ) 0, ∀n, o, t

+

nkot

k

LDno′t

nmot

nmot

n′

not

nit

m

(47)

n′not

m

nio

i

nn′ot

0 e BXnkot e BXnkot,

+ PEt, ∀t

m

∑ ∑X n

h ∈ H ) {f, d, b, l}

brnkot )

∑ ∑ TEG n

∑ bqsc

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not

(59)

n′

(48) (49)

∑ st

n′not

e Mystinot, ∀n, o, t; M ) large positive value

n′

(60) Equation 45 calculates the steam generation in boiler k, BXnkot, which is the product of boiler efficiency, Befnko, and the fuel consumption, fuelnkot, divided by the heat load to heat water to the SS steam, DHSo. CO2 discharge from boiler k is calculated by eq 46. Equation 47 defines the operating ratio of boiler k. Equation 48 represents the range of boiler operating levels. Equation 49 determines the activation of the binary variable for boiler operation and sets the minimum operating ratio at 40% of capacity. 4.4. Steam Turbine.

∑ Tin

nmot

o

)

∑ Tout

nmot,

∀n, m, o

0 e Tinnmot e TinCnmo, 0 e Toutnmot e ToutCnmo, TEGnmt )

∑ ta

nmoTinnmot

o

∀n, m, t

(50)

o

-

∑ tb

∀n, m, o

nmoToutnmot,

(51) (52) ∀n, m, t

o

(53) Equation 50 represents the mass balance of a steam turbine. The inlet and outlet streams of the steam turbine are constrained by eqs 51 and 52, respectively. In general, a steam turbine has one inlet stream and two or more outlet streams. Equations

∑ st

nn′ot

e Mystonot, ∀n, o, t; M ) large positive value

n′

(61) ystinot + ystonot e 1, ∀n, j, t

(62)

stn′not e Mystnn′ot, ∀n, n′, o, t; M ) large positive value (63) ystnn′ot + ystn′not e 1, ∀n, n′, o, t

(64)

Equation 59 represents the mass balance of a steam header for steam grade o. Inputs to the steam header are steam purchased, stmpnot; steam generated in a process, Xnitsgcnio; steam production in a boiler, BXnkot; turbine outlet, Toutnmot; and letdown from a steam header having a higher steam grade, LDno′t. o′ is a steam grade just higher than o. For example, HP′ steam is SS steam, and SS′ steam is forced to zero. Outputs from the steam header are turbine input, Tinnmot; letdown to a lower-grade steam header, LDnot; process demand, Xnitsdcnio; and steam sold, stmsnot. Equations 60-62 are constraints on ∑n′stn′not and ∑n′stnn′ot. For steam o in company n, transport from the other companies and transport to the other companies cannot occur simultaneously. Equations 63 and 64 restrict mutual transportation of steam o between companies. As the mass balance

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equations are applied to an individual company, the variable for steam transportation, stnn′ot, is forced to be zero. 4.7. Investment. Chemical and steam transportation entails investment costs. An important aspect to calculate the investment costs is that the investment at time t affects the investment after time t. For example, if an investment is carried out for transportation of a certain amount of chemical at time t, investment for transportation of only excess amounts of chemical is required at time t + 1. Mathematical equations developed for investment costs are as follows invctnn′jt ) icann′jtbcpnn′jt + icbnn′jtcpnn′jt, ∀n, n′, j, t

Table 1. Model Statistics for the MILP Problems

company

no. of equations

no. of continuous variables

no. of binary variables

solution time (s)

no. of iterations

A B C D

24158 24158 24158 49773

18936 18936 18936 36826

6905 6905 6905 11860

0.406 0.343 0.234 3.000

618 368 397 5220

Table 2. Optimization Results

profit (106 $)

A B C sum D

individual companies

(65) 0 e cpnn′jt e Mbcpnn′jt, ∀n, n′, j, t; M ) large positive value (66) 0 e cnnn′jt e Mbcnnn′jt, ∀n, n′, j, t; M ) large positive value (67) bcpnn′jt + bcnnn′jt e 1, ∀n, n′, j, t

(68)

yctnn′jt g bcpnn′jt, ∀n, n′, j, t

(69)

k

ctnn′jt )

∑ cp

nn′jt

synergy (106 $) synergy effect (%) investment (106 $)

4.8. Objective Function. The objective function can be described as maximize (chemical sales - chemical purchasing - operating costs - investment costs)

∑ ∑ ∑ REV - ∑ ∑ ∑ PUR ∑ ∑ ∑ [U (0.4b + 0.6r ) + F ]X ∑ ∑ ∑ FP fuel - ∑ PE ep + ∑ SE es + ∑ ∑ ∑ stms stmp - ∑ ∑ ∑ ∑ invct ∑ ∑ ∑ ∑ invst (77)

maximize z )

- cnnn′jt,

∀n, j, k ∈ t

(70)

Equation 65 calculates the investment costs for chemical transportation. The investment cost equation consists of the fixed-cost term, which is independent of the amount of the transportation, and the variable-cost term, which is related to the amount. Parameters for the equations depend on the distances between companies and the species of chemical and steam. In this section, the distance between companies is assumed to be the same and every chemical is assumed to have the same investment parameter. It is important to note that the investment cost model is based on the work of Soylu et al.23 Positive slack variables, cpnn′jt and cnnn′jt, are introduced to reflect the sequential effects of investments. Binary variables for the slack variables are defined by eqs 66 and 67. Only one slack variable can be activated by eq 68. If bcpnn′jt is activated, then yctnn′jt must be activated by eq 69. By eq 70, an initial amount for transportation at time t and an additional amount for transportation are assigned to cpnn′jt. Equation 65 calculates the investment costs using cpnn′jt. In the same way as for investment costs for chemical transportation, investment costs for steam transportation were calculated using the equations invstnn′ot ) isann′otbspnn′ot + isbnn′otspnn′ot, ∀n, n′, o, t (71) 0 e spnn′ot e Mbspnn′ot, ∀n, n′, o, t; M ) large positive value (72) 0 e snnn′ot e Mbsnnn′ot, ∀n, n′, o, t; M ) large positive value (73) bspnn′ot + bsnnn′ot e 1, ∀n, n′, o, t

(74)

ystnn′ot g bspnn′ot, ∀n, n′, o, t

(75)

k

nn′ot

hjt

- snnn′ot,

∀n, o, k ∈ t

(76)

y)1

The objective function is discussed next, including an explanation of each term in the objective function.

h

n

t

nit

n

n

j

nit

nkt

t

k

nit

nit

t

t

t

not

t

h

i

nkt

t

hjt

j

nit

t

∑ sp

1,851.46 49.60 4.51

t

y)1

stnn′ot )

merged company

1,333.93 1,093.84 1,305.13 3,732.89 5,584.36

t

t

ot

nn′jt

o

t

n

n′

j

nn′ot

t

n

n′

o

That is, the objective is to maximize the net present value (NPV) of the profit. The profit is calculated by subtracting chemical purchasing, operating costs, and investment costs from the chemical sales. 4.8.1. Chemical Sales. chemical sales )

∑ ∑ ∑ REV

hjt

t

h

j

The chemical sales term is the sum of the sales revenue, REVhjt, of chemical j in contract h at time t for all j, h, and t. 4.8.2. Chemical Purchasing.

∑ ∑ ∑ PUR

chemical purchasing )

t

h

hjt

j

This term represents the cost of purchasing chemicals. It is the sum of the purchasing cost, PURhjt, of chemical j in contract h at time t for all j, h, and t. 4.8.3. Operating Cost. operating cost )

∑ ∑ ∑ [U (0.4b + 0.6r ) + ∑ ∑ ∑ FP fuel + ∑ PE ·ep ∑ SE es - ∑ ∑ ∑ stms stmp nit

t

Fnit]Xnit +

n

nit

nkt

t

n

nit

i

nkt

t

k

t

t

t

t

t

not

t

n

ot

o

The operating cost terms consist of the utility costs other than those for steam and electricity, Unit(0.4bnit + 0.6rnit)Xnit; the fixed cost, FnitXnit; the fuel cost for steam generation in the boiler, FPnktfuelnkt; the electricity sales revenue, SEtest; the purchasing cost, PEtept; and the steam sales revenue, stmsnotstmpot. The


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Figure 3. Profits of the companies.

Figure 4. Revenues of the companies.

utility cost (except for steam and electricity) per unit product varies with the process operating ratio.25 The higher the operating level, the lower the utility cost per unit product. It is difficult to find a general formula representing the relation between the operating ratio of utility equipment and the utility cost. We used the formula of SRI International, which has various experience in industrial cost estimation. By using this formula, the proposed mathematical model can reflect the costs more realistically than a simple utility cost model that does not include an operating cost that varies with the operating ratio of the utility equipment. The binary variable term forces the utility cost to be zero when the operating level is zero. The fixed cost occurs when a plant is installed, so the operating level does not affect the fixed cost. This is why petrochemical companies intend to keep their operating ratio high. The fixed-cost term is the product of Fnit and Xnit, which are not related to the process input. The fuel cost term is the product of unit price of fuel, FPnkt, and the fuel consumption, fuelnkt. The electricity purchas-

ing cost is the product of the amount of electricity purchased, PEt, and the unit electricity purchasing price, ept. The electricity sales revenue is the product of amount of electricity sold, SEt, and the unit electricity selling price, est. The reason for distinguishing electricity selling and purchasing prices is that the power grid used in selling electricity is the property of the regional electricity company. The steam sales revenue is the product of the amount of steam sold, stmsnot, and the selling price of the steam, stmpot, for each steam grade o. 4.8.4. Investment Cost. investment cost )

∑ ∑ ∑ ∑ invct + ∑ ∑ ∑ ∑ invst nn′jt

t

n

n′

j

nn′ot

t

n

n′

o

The investment cost corresponds to chemical and steam transportation between companies. The above term is the sum

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Figure 5. Purchasing costs of the companies.

Figure 6. Operating costs of the companies.

of the investments for chemical transportation, invctnn′jt, and for steam transportation, invstnn′ot.

The resulting MILP problems were solved on a PC with a 2.93 GHz Core2 CPU and 2 GB of RAM. Model statistics for the MILP problems of case 1 are listed in Table 1.

5. Optimization Study

The mathematical model needs various parameters for the process, utility plant, price, and cost. The parameters for the process are the material input and output coefficients, capacity data, operating cost data, electricity demand data, and steam demand and generation data. The parameters for the utility plant are capacity data for the boiler and turbine and cost data for steam generation in the boiler. The parameters for price and cost are price data of the chemicals and utilities and investment

In this section, we apply the proposed mathematical model to the individual companies, A-C, and the merged company, D. The synergy of merging is defined as the difference between the profit of company D and the sum of profits of companies A-C. The case study is based on five 1-year time periods. The interest rate used in the optimization is 5%.


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Figure 7. Fuel uses in boilers of the companies.

Figure 8. Carbon discharges from the companies.

cost data. This study uses the parameter data provided in the previous work and additional data obtained from a literature survey and interviews with plant engineers. The optimization results provide the NPVs of the profits of the three individual companies and the merged company, and synergy was calculated using these results. Table 2 reports the results and synergy. The results show that the merger of the three NCC companies creates a synergy of $1,851 million. The synergy increases the profit by almost 50%. The investment for chemical and steam transportation is $4.51 million, which is much smaller than the synergy created. Figure 3 shows the profits of the target companies in each time period. The merger creates synergies in time periods 1-4. In time period 5, the merged company, D, achieves less profit than the sum of the profits of the individual companies, but the difference is negligible. This result can occur because the objective is to maximize the NPVs of the profits of five periods. Figure 4 shows the revenues of the companies in each time period. Revenues tend to increase through the time periods as a

result of rising prices of chemicals. The revenues of the individual companies B and C are similar to but lower than those of A. Company A has the largest NCC process among the three companies and sells the largest amount of chemicals. The merged company, D, achieves slightly higher revenue than the sum of revenues of companies A-C in each time period. The tendency of revenues to increase is different from that of profits. This means that the revenue increase is not a sole factor of the synergy of the merged company. Figure 5 shows the purchasing costs of the companies. The purchasing costs of companies B and C are similar to but lower than those of company A. Company A purchases more naphtha than company B or company C because of its larger capacity. The purchasing costs of company D are lower than sum of the purchasing costs of companies A-C in time periods 1, 2, and 4 but higher in time periods 3 and 5. Figure 6 represents the operating costs of companies A-D. The operating cost includes the utility cost and the fixed cost. The operating cost of D is lower than the sum of the operating costs of companies A-C. Reduction of the operating cost of

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Figure 9. Investment costs for steam and chemical transportation.

Figure 10. Synergies in each time period.

company D is caused by reduction of the fixed cost and integration of the utility system. The integration of the utility systems of the three companies reduces the fuel used in the steam boiler. This results in a reduction of carbon dioxide discharges. In these days, greenhouse gases are an important issue for manufacturing industries. It is difficult to achieve an increase of profit and a reduction of carbon dioxide emissions simultaneously. Figures 7 and 8 show the results in terms of fuel consumption and carbon discharge for the companies. The results indicate that the merger reduces emissions of carbon by about 300 tons for five time periods while increasing the profit. The 300 tons of carbon correspond to 106 tons of carbon dioxide. A merger needs rationalization in terms of production facility. For petrochemical companies, the rationalization means integration of process networks and utility systems. These integrations require capital investments for chemical and steam transport. Figure 9 shows the investment costs for chemical and steam transport. The investment for steam transportation is much larger than that for chemical transportation. Most of the investment is made in time period 1. The synergies in each time period are shown in Figure 10. Except for time period 5, a positive synergy is created in every time period. This study considers four kinds of synergy factors: process network integration, utility system integration, fixed-

cost reduction, and contracts for purchasing and selling. The contributions of the four factors to the synergy need to be analyzed. Figures 4-6 show the revenues and purchasing and operating costs of the companies. However, it is difficult to discover how much synergy each factor creates from Figures 4-6. To identify the contributions of the individual factors, optimization studies were carried out without fixed-cost reduction and chemical and steam transport. The chemical transportation represents the contribution of process network integration to creating synergy. The steam transportation represents the contribution of utility system integration to creating synergy. The contribution of contracts was calculated by subtracting the contributions of fixed-cost reduction, process network integration, and utility system integration from the total synergy. Table 3 reports the results of the optimization studies and the contribution of each factor. The results indicate that contracts in purchasing and selling contribute the most to synergy. Contracts affect the revenue and the purchasing costs in Figures 4 and 5, which are related to the amounts of chemicals sold and purchased. Further analyses are needed to identify how much synergy each contract creates. The next figures show the amounts and unit prices of naphtha, ethylene, and propylene. Naphtha represents raw materials. Ethylene and propylene represent products. Figures 11 and 12

Ind. Eng. Chem. Res., Vol. 48, No. 24, 2009 Table 3. Contributions of Four Factors profit of the merged company, D (106 $) with with with with with

all synergy factors only contract changes only fixed cost reduction only process network integration only utility system integration

5,584.36 5,220.63 3,890.02 3,893.81 3,778.57 contribution (106 $)

fixed cost reduction process network integration utility system integration contracts

157.13 (8.49%) 160.92 (8.69%) 45.68 (2.47%) 1487.74 (80.35%)

show the amounts of naphtha purchased and the unit costs of naphtha for the companies. Figures 13 and 14 show the amounts of ethylene sold and the unit price of ethylene. Figure 11 shows that the amount of naphtha purchased by company D is larger than the sum of the amounts purchased by the individual companies. The unit naphtha purchasing cost of company D is lower than those of the individual companies, on average, in Figure 12. The amount of ethylene sold by

Figure 11. Amounts of naphtha purchased by the companies.

Figure 12. Unit naphtha purchasing costs of the companies.

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company D is larger than the sum of the amounts sold by companies A-C in Figure 13. The unit selling price of ethylene, however, is almost the same for all four companies. According to the results, the larger amount of naphtha purchased by the merged company leads to a better price of naphtha and then produces more products. This result is consistent with real data. Figure 15 shows the unit naphtha purchasing costs and ethylene capacities of Korean NCC companies.37 Each point represents an average cost on a 10-year average. The ethylene capacities represent the amounts of naphtha purchased. As one can see, larger amounts purchased lead to better naphtha prices in Figure 15. The case study also shows that a petrochemical company can consider a M&A with a company in a different complex to achieve a purchasing advantage. The results coincide with the M&A record of major petrochemical companies, which have carried out many “out-of-complex” M&As. 6. Conclusions This work proposes a novel mathematical model to quantify various synergies in the merger of petrochemical companies

11030


Figure 13. Ethylene selling amounts of the companies.

Figure 14. Unit ethylene selling prices of the companies.

Figure 15. Unit naphtha costs and ethylene capacities for Korean NCC companies.


within a complex. We focus on the synergy from contracts in purchasing and selling, process network integration, utility system integration, and fixed-cost reduction. The model has been improved to express more detailed synergies than were applied in a previous work. The investment term is included to calculate the costs to implement chemical and steam transportation. The proposed model integrates the planning of contracts for purchasing and selling and the operation of the process network and utility system with M&As of petrochemical companies. Specific planning for the post-merger situation leads to precise estimation of the synergy. The optimization study was carried out on Korean NCC companies. The results show that a merger would increase profit by 50% for the modeled companies. The purchasing contract contributes 80% of the synergy created. The larger amount purchased leads to a lower unit cost for naphtha. These results mean that a petrochemical company can consider M&As with a company in a different complex to achieve a purchasing advantage. The Korean petrochemical industry seriously needs to consider mergers as a growth strategy. Nomenclature Sets d ) division in bulk and discount contracts h ) contracts i ) processes j ) chemicals k ) boiler l ) contract length for a fixed-duration contract m ) superheated-steam (SS) turbine N ) companies o ) steam grade p ) high-pressure (HP) steam turbine t ) time domain τ ) time at which a fixed-duration contract is made Parameters ainij ) material balance coefficient of chemical j input to process i in company n anm ) electricity generation coefficients of SS turbine m of company n aonij ) material balance coefficient of chemical j output to process i in company n Befnk ) efficiency of boiler k of company n BXnkt ) capacity of boiler k of company n at time t (ton/year) bnm ) electricity generation coefficient of SS turbine m of company n cnm ) electricity generation coefficients of SS turbine m of company n CO2cnk ) CO2 discharge coefficient of boiler k of company n DHS ) heat load to heat water to SS steam (toe/ton) dnm ) electricity generation coefficients of SS turbine m of company n Ednit ) electricity demand for process i in company n at time t (MWh/year) enp ) electricity generation coefficient of HP turbine p of company n ept ) electricity purchasing price at time t ($/MWh) est ) electricity selling price at time t ($/MWh) Fnit ) fixed cost of process i in company n at time t ($/ton) fnp ) electricity generation coefficient of HP turbine p of company n FPnkt ) fuel price of boiler k of company n at time t ($/toe) gnp ) electricity generation coefficient of HP turbine p of company n

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HPEnpt ) maximum electricity generation in HP turbine p of company n at time t (MWh/year) HPTinnpt ) maximum input of HP turbine p of company n at time t (ton/year) HPToutlnpt ) maximum low-pressure (LP) steam passout in HP turbine p of company n at time t (ton/year) HPToutmnpt ) maximum medium-pressure (MP) steam passout in HP turbine p of company n at time t (ton/year) icann′jt, icbnn′jt ) investment cost coefficients for chemical transportation isann′ot, isbnn′ot ) investment cost coefficients for steam transportation Pbdjt ) price of chemical j in bulk-contract division d at time t ($/ton) PBLjt ) purchasing lower bound of chemical j for a bulk contract at time t (ton/year) PBUjt ) purchasing upper bound of chemical j for a bulk contract at time t (ton/year) Pddjt ) price of chemical j in discount-contract division d at time t ($/ton) PDLjt ) purchasing lower bound of chemical j for a discount contract at time t (ton/year) PDUjt ) purchasing upper bound of chemical j for a discount contract at time t (ton/year) Pfjt ) price of chemical j in a fixed contract at time t ($/ton) PFUjt ) purchasing upper bound of chemical j for a fixed contract at time t (ton/year) Plljτ ) price of chemical j in a fixed-duration contract of length l at time t ($/ton) PLLljτ ) purchasing lower bound of chemical j for a fixed-duration contract of length l at time t (ton/year) PLUljτ ) purchasing upper bound of chemical j for a fixed-duration contract of length l at time t (ton/year) SBLjt ) selling lower bound of chemical j for a bulk contract at time t (ton/year) SBUjt ) selling upper bound of chemical j for a bulk contract at time t (ton/year) sdcnio ) demand for steam grade o for process i in company n (ton/year) SDLjt ) selling lower bound of chemical j for a discount contract at time t (ton/year) SDUjt ) selling upper bound of chemical j for a discount contract at time t (ton/year) SFUjt ) selling upper bound of chemical j for a fixed contract at time t (ton/year) sgcnio ) generation of steam grade o for process i in company n (ton/year) SLLljτ ) selling lower bound of chemical j for a fixed-duration contract of length l at time t (ton/year) SLUljτ ) selling upper bound of chemical j for a fixed-duration contract of length l at time t (ton/year) SSEnmt ) maximum electricity generation in SS turbine m of company n at time t (MWh/year) SSTinnmt ) maximum input to SS turbine m of company n at time t (ton/year) SSToutcnmt ) maximum condensate passout in SS turbine m of company n at time t (ton/year) SSToutlnmt ) maximum LP steam passout in SS turbine m of company n at time t (ton/year) SSToutmnmt ) maximum MP steam passout in SS turbine m of company n at time t (ton/year) stmpot ) steam selling price of grade-o steam at time t ($/ton) stmsnot ) steam selling of grade-o steam in company n at time t (ton/year)

11032


Unit ) utility costs, other than steam and electricity, for process i in company n at time t ($/ton) Xnit ) process i capacity in company n at time t (ton/year) Variables bbnkt ) binary for BXnkt bcnnn′jt ) binary for cnnn′jt bcpnn′jt ) binary for cpnn′jt bnit ) binary for Xnit bPEt ) binary for PEt bqpbdjt ) binary for qpbdjt bqpchjt ) binary for qpchjt bqpddjt ) binary for qpddjt bqplljτt ) binary for qplljτt bqsbdjt ) binary for qsbdjt bqschjt ) binary for qschjt bqsddjt ) binary for qsddjt bqslljτt ) binary for qslljτt brnkt ) operating ratio of boiler k at time t bSEt ) binary for SEt bsnnn′ot ) binary for snnn′ot bsstnmt ) binary for SSTinnmt bstnn′ot ) binary for spnn′ot BXnkt ) operating level of boiler k at time t (ton/year) cnnn′jt ) slack variable for invctnn′jt CO2nkt ) CO2 discharge from boiler k at time t (ton of C/year) cpnn′jt ) slack variable for invctnn′jt ctnn′jt ) chemical j transportation from company n to company n′ at time t (ton/year) fuelnkt ) fuel consumption in boiler k in company n at time t (ton/ year) HPEnpt ) electricity production at HP turbine p of company n at time t (MWh/year) HPTinnpt ) HP steam input to HP turbine p of company n at time t (ton/year) HPToutlnpt ) LP steam output from HP turbine p of company n at time t (ton/year) HPToutmnpt ) MP steam output from HP turbine p of company n at time t (ton/year) invctnn′jt ) investment cost for chemical j transportation from company n to company n′ at time t ($) invstnn′ot ) investment cost for steam grade o transportation from company n to company n′ at time t ($) LDnot ) steam letdown from grade o in steam header of company n at time t (ton/year) nqpnjt ) amount of chemical j purchased by company n at time t (ton/year) nqsnjt ) amount of chemical j sold by company n at time t (ton/ year) PEt ) electricity purchasing at time t (MWh/year) PURhjt ) purchasing cost of chemical j in contract h at time t ($/ year) qinijt ) amount of chemical j consumed in process i of company n at time t (ton/year) qonijt ) amount of chemical j produced in process i of company n at time t (ton/year) qpbdjt ) amount of chemical j purchased in bulk-contract division d at time t (ton/year) qpchjt ) amount of chemical j purchased in contract h at time t (ton/year) qpd1djt ) division of qpd1jt into boundary and nonboundary values qpddjt ) amount of chemical j purchased in discount-contract division d at time t (ton/year)

Qpjt ) amount of chemical j purchased in a merged company at time t (ton/year) qplljτt ) amount of chemical j purchased in contract length l at time t (ton/year) qsbdjt ) amount of chemical j sold in bulk-contract division d at time t (ton/year) qschjt ) amount of chemical j sold in contract h at time t (ton/year) qsd1djt ) division of qsd1jt into boundary and nonboundary values qsddjt ) amount of chemical j sold in discount-contract division d at time t (ton/year) Qsjt ) amount of chemical j sold in a merged company at time t (ton/year) qslljτt ) amount of chemical j sold in contract length l at time t (ton/year) REVhjt ) sales revenue of chemical j in contract h at time t ($/ year) rnit ) operating ratio of process i of company n at time t (ton/year) SEt ) electricity selling at time t (MWh/year) snnn′ot, spnn′ot ) slack variables for invstnn′ot SSEnmt ) electricity production at SS turbine m of company n at time t (MWh/year) SSTinnmt ) SS steam input to SS turbine m of company n at time t (ton/year) SSToutcnmt ) condensate output from SS turbine m of company n at time t (ton/year) SSToutlnmt ) LP steam output from SS turbine m of company n at time t (ton/year) SSToutnmt ) MP steam output from SS turbine m of company n at time t (ton/year) stnn′ot ) transportation of steam grade o from company n to company n′ at time t (ton/year) TEt ) electricity demand at time t (MWh/year) Xnit ) amount of input to process i of company n at time t (ton/ year) yctinjt ) binary for chemical j transportation into company n at time t (ton/year) yctnn′jt ) binary for ctnn′jt yctonjt ) binary for chemical j transportation out from company n at time t (ton/year) ynqpnjt ) binary for nqpnjt ynqsnjt ) binary for nqsnjt ypjt ) binary for Qpjt ysjt ) binary for Qsjt ystinot ) binary for steam grade o transportation into company n at time t ystnn′ot ) binary for stnn′ot ystonot ) binary for steam grade o transportation out from company n at time t

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ReceiVed for reView May 16, 2009 ReVised manuscript receiVed October 19, 2009 Accepted October 26, 2009 IE900802V

Evaluation of Synergy Effect in the Horizontal Merger of Companies in

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