A multiobjective optimization model for the waste ... - ScienceDirect

A multiobjective optimization model for the waste management of the petrochemical industry Abdulaziz

S. Alidi

King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

A multiobjective optimization model based on the goal programming approach is proposed in this paper to assist in the proper management of hazardous waste generated by the petrochemical industry. The analytic hierarchy process (AHP), a decision-making approach, incorporating qualitative and quantitatbe aspects of a problem, is incorporated in the model to prioritize the conflicting goals usually encountered when addressing the waste management problems of the petrochemical industry. The application of the model has been illustrated through a numerical example, using hypothetical but representative data. 0 1996 by Elsevier Science Inc. Keywords: hazardous process (AHP)

waste

management,

petrochemical

1. Introduction

The improper management of hazardous wastes (HW) generated by the chemical and petrochemical industries is considered to be one of if not the most pressing environmental problem all over the world. Based on the US Environmental Protection Agency’ definition a waste can be characterized as hazardous if it possesses any one of the following four characteristics: (a) ignitability; (b) corrosivity; (c) reactivity; or (d) toxicity. The mismanagement of HW has resulted in hundreds of documented cases of damage to life and the environment. Kiang and Metry* indicated that HW have been found to contaminate ground water supplies, rivers, lakes, and other surface waters, to pollute the air, to cause fires and explosions, and to cause serious illness by contaminating foodstuffs and by direct contact. These wastes are frequently bioaccumulated, very persistent in the environment, and often toxic at very low concentrations. The source of the vast majority of these cases may be traced back to some part of the petrochemical industry. Manufacturing of many petrochemicals and other types of products results in most cases in the generation of

Address reprint requests Petroleum and Minerals, Arabia. Received 1996

23 January

to Dr. Alidi at King Fahd KFUPM Box 1645, Dhahran

1995; revised

University of 31261, Saudi

3 July 1996; accepted

Appl. Math. Modelling 1996, Vol. 20, December 0 1996 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010

16 August

plants,

goal programming,

analytic

hierarchy

substantial quantities of hazardous/toxic materials. Much of the wastes are generated by the chemical and petrochemical industries, which produce different types of chemicals needed by any advanced society. Jain3 reported that there are more than 60,000 commercial chemicals on the market and that the chemical industry creates about 1,000 new chemicals each year. In addition there are currently available approximately 35,000 pesticides, 8,600 food additives, and many cosmetic and drug ingredients. Some of the chemicals, pesticides, food additives, and other items, in the long-run, may be hazardous to human health and/or the environment. The past mismanagement of HW has led to increased public concern about HW. Careful disposal of HW does not mean it is always the proper management option for getting rid of these wastes. In fact there is a range of other management options that must be considered. According to K.iang and Metry,2 in order of priority the desired options for managing HW are: (a) minimize the amount of waste generated by modifying the industrial process involved; (b) transfer the waste to another industry that may use the waste; (c) reprocess the waste to recover materials and energy; (d) separate hazardous and nonhazardous materials; (e) subject the waste to some process that will render the waste nonhazardous; and (f) dispose of the waste in a secure landfill. This research effort is directed towards the development and testing of a multiobjective planning model based on the goal programming approach for the proper treatment and disposal of HW generated by the petrochemical

0307-904X/96/$15.00 PII SO307-904X(96)00106-2

Petrochemical

waste

management:

A. S. Alidi

are shipped to a landfill, while hazardous/toxic wastes are incinerated using incineration facilities available at the treatment station. The flow scheme for this integrated HW management system is shown schematically in Figure

industry. The multiple goals and priority determinations are based on a decision-making methodology incorporating qualitative and quantitative aspects of a problem known as the analytical hierarchy process (AHP). The present model is an extension to Alidi’s modek4 and it can be used to address many of the issues related to facility utilization, recycling, treatment, and disposal of HW. The next section defines the problem, describes the structure of the petrochemical industry under study and develops the model. The use of the model has been illustrated using hypothetical but representative data pertaining to an integrated hazardous waste system of a petrochemical industry composed of several plants located at a certain geographical area such as the ones located in Al-Jubail Industrial City of Saudi Arabia. Finally, summary and concluding remarks are presented.

1.

It is also assumed that the management of the integrated HW system has special goals to achieve such as minimizing the cost of managing the system and improving its operating efficiency. The management also would like to satisfy, as much as possible, the needs and multiple goals of several groups involved in the management of HW. Among these groups are the public, local government, and HW generators. These multiple goals could be related to environmental control aspects, objections to siting of HW treatment stations and landfills at certain locations, restrictions related to traffic flow of vehicles, and the need of HW generators to haul the HW away from their plants.

2. Problem description It is assumed that different types of HW are generated at several petrochemical manufacturing plants, located at a certain geographical area. The rate of generation of these wastes at each petrochemical plant varies with time due to the stochastic demand for the manufactured products. The future generation of these wastes can be estimated on a periodical basis for several future cycles using the methodology described by Alidi and Freedman.’ The wastes are hauled to a HW treatment station where recyclable materials can be recovered and sold to markets and the remainder of wastes are separated into two groups. Those wastes that can be disposed of safely

3. Model development The above-described problem can be considered as a multiple-objective optimization problem, since it seeks an optimal compromise between several conflicting objectives or the achievement of satisfying levels in the objectives. It is formulated as an optimization model based on the goal programming technique. The goal programming technique developed by Charnes and Cooper6 attempts to minimize the set of deviations from prespecified multiple goals, which are considered simultaneously but are weighted according to their relative importance.

PETROCHEMICAL PLANTS j = 1, 2, . . .. J

xijt ,__________________--~____~~~-~~~ t R%jt xij, MN,,, xti,

I

-_______________________________I

I

I

: I I

I

I 1 I

%

I

(=&4j,)

i I I I

4 MF, (MIN,i, xv,) i

Minimization Facilities

Recycling Facilities

a

Incineration Facilities

f. Treatment Station Boundaries ________________________________I

___^_______.____________________

V mt

wIn*

z mt

I

v

LANDFILLS m = 1, 2, . . .. M Figure 1.

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An integrated

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Vol. 20, December

industry.

I

I I I I ! 1 1 1 I

*

Petrochemical The priorities of the multiple goals are determined using the AHP approach. The AHP, developed by Saaty,’ is an efficient measurement and a multiobjective decision-making approach that employs pairwise comparisons to determine the weights and priorities of a variety of factors, attributes, elements, and alternatives. The basic assumption is that decision makers are able to structure a complex problem in the form of a hierarchy where each factor and alternative can be identified and evaluated with respect to other related factors. The application of the AHP to a complex problem usually involves four major steps: (a) break down the complex problem into a small number of constituent (decision) elements and then structure the elements in a hierarchical form; (b) make a series of pairwise comparisons among the elements according to a ratio scale as given by Saaty;’ (c> use the “eigenvalue” method to estimate the relative weights of the elements; and (d) aggregate these relative weights and synthesize them for the final measurement of given decision alternatives. Full details of these steps can be found in Saaty.’ Several researchers such as Gass,’ Bard,” and more recently Benjamin et al. ‘” have integrated multiobjective programming models with the AHP. It is assumed that the administrations of several petrochemical plants make use of the services of a private contractor to manage HW generated by their plants. To take into account the goals and needs of the various groups concerned with the handling and disposal of HW, the private contractor would like to achieve, as much as possible, the following eight goals. 3. I First goal: Hazardous waste removal from the petrochemical plants One of the main responsibilities of the private contractor is to remove the wastes generated by the various petrochemical plants. The contractor would like to remove as much as possible of these wastes using its own facilities and without resorting to a subcontractor to do this removal. Therefore the goal chosen here is to minimize the unremoved quantity of HW represented by the deviation variables d;;‘- from the plants. This goal can be expressed mathematically by the following set of constraints. zxijr+d;P-

-d$+

The transportation cost of any HW management system is considered to be one of the major costs. An attempt to control this cost can be made by minimizing the deviation variables d,?’ appearing in the following set of constraints.

+

J,t=1,2

t = 1,2,...,T

3.3 Third goal: Operations funds control The private contractor responsible for the treatment and disposal of HW seeks not to exceed the allocated budget for operating the equipment of the treatment station. This goal can be accomplished by attempting to minimize the deviation variables dpc+ appearing in the following set of constraints.

i 1,2 ,...,

_ d=c+ = TC I dTcI I

where, M = number of landfill sites Bijr = unit transportation cost of ith HW transported from jth petrochemical plant in tth period C,, = unit transportation cost of incineration waste transported to mth landfill in tth period ZImt = unit transportation cost of recycling waste transported to mth landfill in tth period E,, = unit transportation cost of other disposable processed HW transported to mth landfill in tth period of incineration waste transported to mth Z m, = quantity landfill in tth period of recycling waste transported to mth landW mr = quantity fill in tth period L1,f = quantity of other disposable processed HW transported to mth landfill in tth period dTc+ = additional transportation cost needed in tth peI riod, to be minimized drc- = savings in transportation cost in t th period r’C, = total transportation cost available for tth period.

hxijt[Gijl+Z’(ZNCi,,) j

j=

A. S. Alidi

3.2 Second goal: Transportation cost control

=Aj,

+Q(REC,,,)

+S(MIN,,,)]

i

,..., T

where, I = number of types of HW J = number of petrochemical plants T = number of future periods X r,, = quantity of ith HW removed from jth petrochemical plant in tth period A, = total quantity of HW contracted to be removed from jth petrochemical plant in tth period d,f - = underachievement of HW removal from jth petrochemical plant in tth period, to be minimized d,f - = overachievement of HW removal from jth petrochemical plant in tth period.

waste management:

+

do’I

- df”+

= OC,

t = 1,2,...,T

where Gij, = unit handling cost of ith HW removed form jth plant in tth period P = unit incineration cost Q = unit recycling cost S = unit minimizing cost of disposable processed HW ZNCilt = percentage of the quantity of ith HW removed from jth plant in tth period to be incinerated ZUXij, = percentage of the quantity of ith HW removed from jth plant in tth period to be recycled

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MZNij, = percentage of the quantity of ith HW removed from jth plant in tth period to be only processed and minimized dpc’ = additional operations funds needed in tth period, to be minimized dfC- = savings in allocated operations funds in tth period OC, = total allocated operations funds for tth period. 3.4 Fourth goal: Utilization of facilities

The proposed integrated HW management system is mainly composed of facilities for waste minimization, incineration, recycling, and landfilling. These facilities should be utilized to the maximum possible extent for economical operation, if their use is cost effective. It is assumed that the private contractor will seek the minimization of the underutilization of the system facilities. This goal can be represented by the following set of constraints. Minimization:

Landfilling:

m=l,2

,... M, t=1,2

,...,

T

where, dR”of mth landfill capacity in tth f?l, = underachievement period, to be minimized dR”+ of mth landfill capacity in tth mr = overachievement period RU,, = designed capacity of mth landfill in tth period. 3.5 Fifth goal: Energy production

In any integrated HW management system energy is expected to be produced as a result of incineration. The energy produced could be in the form of electricity, which may be sold to the local electrical company. It is assumed that the private contractor would like to have a constant supply of this energy to meet its obligations to the local electrical company. Therefore it will always seek to minimize the deviation variables dfP- appearing in the following set of constraints.

t = 1,2,...,T ET,

where, dyUm = underachievement

of HW minimizing capacity in t th period, to be minimized dc”+ = overachievement of HW minimizing capacity in * t th period GU, = designed HW minimizing capacity in tth period. Incineration:

~INCij,nijt +d,H”- - d;“+

i I

= HU,

f: f: Ih’Cij,xijr j

+ d,EP- - dFP+ = EP,

i

t=l,2

,...’ T

where, dEP= underachievement of energy production in tth I period, to be minimized dEPf = overachievement of energy production in tth pe, riod EP, = desired energy production level in tth period ET, = energy production level in tth period as a percentage of the amount of HW incinerated.

i t = 1,2,...,T

where, dH”= underachievement of incineration capacity in tth 1 period, to be minimized dHU+ = overachievement of incineration capacity in tth 1 period HU, = designed incineration capacity in tth period. Recycling:

3.6 Sixth goal: Waste minimization

It is assumed that the private contractor would like to achieve, as much as possible, a desired level of waste minimization. Therefore it will seek the minimization of the deviation variables d,MF- appearing in the following set of constraints. f: MIIV~~,X,~,+ dyFm - d,MF+ = ML,

MF, i j

&ECijrxrjt +dr”- -d,up+

i j

=pu

t= 1,2,...,T

I

i

t= 1,2,...,T where, of recycling capacity in tth period, to be minimized dp”+ = overachievement of recycling capacity in tth peI riod PU, = designed recycling capacity in tth period.

dp”t

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where, dMF= underachievement of minimization level in tth L period, to be minimized d IMF+ = overachievement of minimization level in t th period ML, = desired waste minimization level in tth period MF, = minimization level in t th period as a percentage of the amount of HW minimized.

Petrochemical 3.7 Seventh goal: Waste recycling If the private contractor is interested in achieving a certain level of materials recycling, then it should seek the minimization of the deviation variables drTm appearing in the following set of constraints.

+dpT-

- dpT+ = RT, t=l,2

,..., T

where, dRT= underachievement of recycling level in tth period, f to be minimized dRT+ = overachievement of recycling level in tth period dq = desirable quantity of recyclable materials in tth period RE, = anticipated recycling level in tth period as a percentage of the amount of HW recycled. 3.8 Eighth goal: Vehicle routing restrictions It is assumed that the transportation of wastes by vehicles through some of the paths of the integrated HW management system network is restricted. This restriction is imposed to control air pollution, minimize traffic congestion, and/or control noise due to vehicles movements. xijt + dPX(,T,- dPXi$ = XRijt

for each i, j, and t

z,, + dPZ,, - dPZ,+, = ZR,,

for each m and t

w,,,, + dPW,; - dPW,: = WR,,

for each m and t

u,,,, + dPV,; - dPV,: = I/R,,

for each m and t

where, dPXL;I,= underachievement of the quantity of ith HW allowed to be transported from jth petrochemical plant to the treatment station in tth period dPXGt = overachievement of the quantity of ith HW allowed to be transported from jth petrochemical plant to the treatment station in tth period, to be minimized XRijt = maximum quantity of ith HW allowed to be transported from jth petrochemical plant to the treatment station in tth period dPZi, = underachievement of the quantity of incineration waste allowed to be transported from the treatment station to mth landfill in tth period dPZz, = overachievement of the quantity of incineration waste allowed to be transported from the treatment station to mth landfill in tth period, to be minimized ZR,, = maximum quantity of incineration waste allowed to be transported from the treatment station to mth landfill in tth period dPW,; = underachievement of the quantity of recycling waste allowed to be transported from the treatment station to mth landfill in tth period

waste management:

A. S. Alidi

dPW,: = overachievement of the quantity of recycling waste allowed to be transported from the treatment station to mth landfill in tth period, to be minimized II%,, = maximum quantity of recycling waste allowed to be transported from the treatment station to mth landfill in tth period dPV,; = underachievement of the quantity of minimized waste allowed to be transported from the treatment station to mth landfill in tth period dPV,: = overachievement of the quantity of minimized waste allowed to be transported from the treatment station to mth landfill in tth period, to be minimized I/R,, = maximum quantity of minimized waste allowed to be transported from the treatment station to mth landfill in tth period. 3.9 Overall material balance requirement As mentioned earlier, the various types of wastes collected from the petrochemical plants are treated either by incineration, recycling, or just minor processing and minimization. Therefore the material balance requirement at the treatment station has to be preserved. The following set of constraints will take care of this requirement.

-(ET,INCij,)]

- f(z,,+w~~+~,~~)=O m t= 1,2,...,T

The determination of the priorities of the various goals should not be based only on the perception of the private contractor, since there are other groups who have their own goals regarding the management of HW. As an alternative, the various goals can be assigned a certain priority using the AHP. The strength of the AHP approach is that it has the capability of addressing both objective criteria, such as the need to remove HW from the petrochemical plants, as well as subjective criteria, such as the impact of public attitudes toward environmental issues. In order for the private contractor to make use of the AHP approach to assign priorities to the various goals, it must develop a dialogue among all concerned groups to obtain a variety of strategic and tactical information and ensure that as many points of view as possible are considered. If, for example, the results of the AHP indicate that the goal of removing the HW from the petrochemical plants has the highest ranking, then it should be given the first priority, and hence the model will attempt to minimize the deviation variables d,f first. The mathematical representation of the objective function may be expressed, depending on the results of the

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Petrochemical AHP ranking

waste management:

of the priorities

Minimize Z = P;d$-

A. S. Alidi

of the goals, as follows:

+ P2+dTC+ + P3+dpc+

+ P,-d,GUm+ P,-d,NU- + P,-drU+ P,d$-

+ P;d;pm

+ PljdfT-

+ P:,dPX;,

+ P:,dPW,:

+ P;d,MF+ P:,dPZ,+,

+ P:,dPV,:

where Z is the sum of all deviations from the goals specified and P; to PA are priorities assigned to the goals. The use of the model is illustrated using hypothetical but representative data pertaining to an integrated HW system of a petrochemical industry composed of several plants such as the ones located in Al-Jubail Industrial City of Saudi Arabia. The results of model solution will provide the private contractor, plants managers, and other concerned groups with information about (a) the extent of HW removal from the various petrochemical plants, (b) the level of savings in financial resources allocated to run the transportation fleet and operate the HW treatment facilities, (cl the extent of facilities utilization, energy production, and level of recycling, and finally (d) HW vehicles’ movement throughout the entire transportation network. Additionally the results of the postoptimality analysis will make it possible to assess the effects of changes in the model parameters and to take the necessary actions.

4. An overview of hazardous Saudi Arabia

waste management

in

The rapid industrialization of Saudi Arabia, as pointed out in Ref. 11, has produced the same risks to human life and the environment that have affected other industrialized nations. However, Saudi Arabia is fortunate in that environmental concerns were recognized at an early stage of industrial development. This resulted in the establishment of agencies such as the Meteorological and Environmental Protection Agency (MEPA) and the Royal Commission for Al-Jubail and Yanbu to regulate industry so that environmental dangers are minimized. Saudi Arabia is still in a dangerous position, however, from the viewpoint of hazardous waste control, as industrialization is occurring rapidly and few facilities currently exist to manage the waste streams generated. This would also probably be true of other Gulf states. Regulations in Saudi Arabia concerning the transfer, transportation, treatment, and disposal of HW are in draft form and have yet to be promulgated. Several surveys were made in Saudi Arabia a few years ago to determine the types and quantities of HW produced by the petrochemical industry. The estimates arrived at were made by analyzing the process flows of each industry or type of industry based on information supplied by the industry itself or through the information available on similar types of industries elsewhere. The surveys indi-

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cated that there was clearly a need for a HW facility to manage the quantities of wastes that were being generated. In many instances it was believed that these wastes were being improperly disposed of, for instance, in illegal dumps in the desert. Government agencies in Saudi Arabia support the following hierarchy of waste management: (a) waste reduction, i.e, avoid producing the waste in the first place; (b) waste recycling, i.e., reuse the waste for other purposes, either directly, indirectly by converting to other useful materials, or producing energy; and (c) dispose of the waste safely by effective treatment, destruction, and disposal techniques. However, these agencies nonetheless realize that despite the best efforts at promoting waste reduction and recycling, there would inevitably be a need for safe disposal of a large amount of HW. Al-Jubail Industrial City, located in eastern Saudi Arabia, is the site of twelve major petrochemical plants producing considerable quantities of HW as a result of manufacturing processes. Presently there is a main private contractor that collects HW from the plants and disposes of them at a landfill site after subjecting them to special treatments. However, most of the collected HW is presently being stored in special containers at a remote section of the landfill. At the present time the private contractor is constructing a HW treatment station to dispose of the waste in the proper way through incineration, waste minimization, and recycling. The increase in HW generation due to capacity expansions and additions of new facilities at the petrochemical plants dictated the construction of such a facility. An illustrative example is presented in the next section to show how the private contractor can make use of the proposed model to assist in making appropriate decisions regarding the management of HW at Al-Jubail Industrial City.

5. An illustrative

example

Due to the lack of actual data at the present time hypothetical but representative data is used as feed data. To reduce the dimensional&y of the illustrative example it is assumed that there are only two petrochemical plants (1 = 2), each of which generates two types of HW (I = 2), and one landfill site (M = 1). The model is simulated for only one future period (T = 1). Although the illustrative example is small in terms of its dimensional@, the proposed model can handle a large number of petrochemical plants, types of HW, landfill sites, and future periods, depending on the computing capabilities of the linear programming computer software used to solve it. It is also assumed that the groups concerned with the management of HW in Al-Jubail Industrial City are as follows: (a) a private contractor who is in charge of collection, processing, and ultimate disposal of HW; (b) the administrations of the petrochemical plants; and finally (c) the people of the city represented by the Royal Commission of Al-Jubail Industrial City. Three conflicting

Petrochemical

The objectives of the private contractor may be summarized so as to (a> increase profitability, (b) enhance the productivity of facilities, (c) minimize public opposition to the movement of vehicles and siting of facilities, and (d) offer the best service to HW generators. The objectives of the Royal Commission of Al-Jubail Industrial City may be listed so as to (a) minimize environmental harm, (b) promote peace and tranquillity in daily life, (c) maximize Al-Jubail Industrial City land use and development, (d) protect and improve the regional economy, and (e) ensure that governmental regulations and standards, set for the proper handling of HW generated by the petrochemical plants, are followed. The administrations of the petrochemical plants have their own objectives, such as to (a) control the budget allocated for HW removal from the plants, (b) minimize vehicles’ movement from and to the plants, and (cl establish good relations with the local community. By reducing the problem into its elements and grouping these elements at different levels, a hierarchy is formed, as illustrated in Figure 2.

5.1 Step 1: Construction of the AHP hierarchy The AHP hierarchy of the example problem is composed of four levels. Level 1 is associated with the focus, which is related to the projected outcome (the ranking of the three goals). In level 2 the three groups involved in the management of HW at Al-Jubail Industrial City are listed. Level 3 is composed of the various objectives of the three groups. The three goals to be ranked are contained within level 4.

1: Projected

Focus

Level

A. S. Alidi

5.2 Step 2: Identification of the groups’ objectives

goals are assumed, namely, HW removal, which is demanded by the administrations of the petrochemical plants, environmental pollution control within the City (for example, control of HW vehicles movement), which is required by the Royal Commission of Al-Jubail Industrial City, and managing HW with the minimum financial resources, which is desired by the private contractor. The AHP, which provides an organized framework for systematically ranking goals relative to their overall importance along with a variety of dimensions, is used to rank the priorities of the three goals. The ranking procedure of the three goals of the example problem is described as follows:

Level

waste management:

Outcome

2:

Groups

Petrochemical Plants (0.626)

Private Contractor (0.238)

Royal Commission (0.136)

Profitability (0.017)

Environment (0.007)

Budget (0.270)

Productivity (0.140)

Peace (0.008)

Vehicles Movement (0.060)

Avoiding Opposition (0.028)

Land Use (0.012)

Good Relations (0.270)

Best Service (0.065)

Economy (0.071)

Iavel 3: Objectives

Standards (0.052)

Level

4:

Goals

Figure

2.

Hierarchy

for conflict

Hazardous Wastes Removal (0.309) in the management

Pollution Control (0.331) of hazardous

waste

Appl.

with

cost Minimization (0.360) computed

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Weights that reflect the relative standing power of each group and the importance of objectives can then be assigned by performing pairwise comparisons at each level in the hierarchy. These weights reflect the judgment of the three groups’ representatives on the relative importance or preference of the elements in the hierarchy. Since the representatives can be error prone and often inconsistent, the AHP allows for some degree of error and inconsistency. According to a rule of thumb suggested by Saaty,’ a consistency ratio (CR) of 0.10 (10%) or less is considered acceptable. Determination of the relative weights and the CR can be made using an AHP computer program such as Criterium, version 1.1, HIPRE3 + , and the PC-based Expert Choice program.

results of the illustrative example solution are presented in Table I. As shown in Table I the private contractor will be able to remove all types of HW from plant 1, while it will be able to remove only 16 units out of the 32 units needed to be removed from plant 2. As also shown in Table 1 the quantities of incineration and recycling wastes to be hauled to the landfill are 4 units and 1 unit, respectively. As indicated in Table 1 for the period under consideration all HW removed from the two plants have to either be incinerated or recycled.

6. Summary 5.3 Step 3: Establishment of weights for the objectives The Expert Choice program is a decision support system that enables the decision maker to visually structure a multifaceted problem in the form of a hierarchy and then allows him/her to provide pair-wise judgments in an interactive, verbal mode. Based on input data obtained from Reid and Christensen’* and using the Expert Choice program, the weights for the three groups are: 0.626 for the group of administrations of the petrochemical plants, 0.238 for the private contractor, and 0.136 for the Royal Commission. Additionally the importance rankings of the projected outcome-related objectives can be obtained through the AHP pairwise comparison. The relative weights of the various objectives associated with this evaluation process are 0.270 for budget, 0.270 for good relations, 0.140 for productivity, 0.071 for economy, 0.065 for best service, 0.060 for vehicles’ movement, 0.052 for standards, 0.028 for avoiding opposition, 0.017 for profitability, 0.012 for land use, 0.008 for peace, and 0.007 for environment.

Expert judgments are used to rank the three goals relative to each of the objectives under the private contractor, the Royal Commission, and the petrochemical plants. The results of the subsequent synthesizing procedure indicate that the three goals are ranked as 0.309 for HW removal, 0.331 for pollution control, and 0.360 for cost minimization. Therefore the goal of cost minimization, which actually is what the private contractor is interested in, should be given the highest priority when attempting to solve the developed model, and the goal of HW removal should be given the least priority. The developed goal programming model can be solved using the modified simplex procedure, and any available linear programming code can be used to solve it. The solution procedure entails the partitioning of the objective function according to priority levels and the sequential solution of the resultant linear programming models. The solution obtained at each priority level is used as a constraint at the lower level. This sequential goal programming algorithm is outlined by Ignizio and Perlis.13 The

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remarks

Substantial quantities of hazardous and toxic wastes are generated every day by the chemical and petrochemical

Table

1.

Typical

results

of model solution

Variable

Definition Quantity

x111

from from

10

of 1 st type of HW to be removed of 2nd type of HW to be removed

10

1 st plant in 1 st period

Quantity

x121

Value

1 st plant in 1 st period

Quantity

x211

12

of 1 st type of HW to be removed

from 2nd plant in 1 st period Quantity

x221

of 2nd type of HW to be removed

4

from 2nd plant in 1 st period Quantity

211

of incineration

to 1 st landfill Quantity

Wll

Quantity

&I-

waste

transported

10

in 1 st period

of recycling

1 st landfill

waste

to

1

from 2nd plant

16

transported

in 1 st period

of HW unremoved

in 1 st period dlC1

Amount

of savings

in transportation

cost

821

in 1 st period doC1

5.4 Step 4: Ranking the alternative goals relative to all objectives

and concluding

Amount

of savings

in operations

funds

in

476

in 1 st

2.6

1 st period

d,G”-

Unutilized

capacity

of HW handling

period

dR”i 1

Overutilized

capacity

of landfill

1

in 1 st

period

dEP 1

Level of energy

production

underachieved

4

in 1 st period

dRT+ 1

Level of recycling

overachieved

in

2

1 st period

dW,

I

Quantity allowed

of 1 st HW less than the quantity to be transported

from

4

1 st plant

in 1 period

d’%,

,

Quantity

of 2nd HW less than the quantity

allowed to be transported in 1 st period

dWz

t

Quantity allowed

from

of 2nd HW less than the quantity to be transported

6

1 st plant 13

from 2nd plant

in 1 st period

dP’% ,

Quantity

of incineration

the quantity

allowed

the treatment

d’=“,_,1

of minimized

quantity

allowed

the treatment Note: other

facility

Quantity

variables

waste

less than

to be transported to 1 st landfill waste

facility

to 1 st landfill

have zero values.

in 1 st

less than the

to be transported

2

from

from in 1 st

4

Petrochemical

industries, which Produce different types of chemicals needed by any advanced society. The improper management of HW generated by these industries is considered to be one if not the most pressing environmental problem all over the world. Multiple goals with different priorities must be taken into consideration when managing and planning HW systems. In this paper a multiobjective optimization model based on the goal programming approach and the analytic hierarchy process is proposed to aid in the proper management of integrated HW systems. The model can be used to address many of the problems and issues associated with the management of HW systems such as the need for HW removal from the various petrochemical plants, the efficient utilization of facilities, systems cost control, and the control of environmental pollution. The use of the model has been demonstrated, through an example problem, by showing how it can be utilized to assist in the management of HW generated by the petrochemical industry. The results obtained show that the model is a viable tool and can be used to assist in making appropriate decisions regarding the management of HW.

waste management:

A. S. Alidi

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Acknowledgments The author would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals during the preparation of this paper. He also would like to thank the anonymous referees for their constructive comments that greatly improved the quality and readability of the paper.

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