1-s2.0-037877889190022U-main

Energy and Buildings, 15 - 16 (1990/91) 537 - 551 537

A Linear Goal Programming Model for Urban Energy-Economy-Env i ronment Interaction

N. S. KAMBO and B. R. HANDA

Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016 (India)

R. K. BOSE

Tata Energy Research Institute, 7, Jot Bagh, New Delhi 110003 (India)

ABSTRACT

The last decade has witnessed a growing concern with the adequacy of energy resources and with the quality of the physical environ- ment. This concern stems from such factors as the unrelenting growth of energy use, the end of an era of abundant and cheap energy, adverse environmental effects of economic growth, and the increasing participation of governments in decisions pertaining to energy supply and envi- ronmental protection. Owing to the fact that a significant part of the shortfalls in environmen- tal quality in contemporary societies derives from energy use, issues of "trade-off" between additional energy supplies and environmental quality frequently arise. In the context of this intimate association between the economy, envi- ronment and energy, there has been a growing awareness that policy decisions on economic, environmental and energy-related issues need to be placed in the broader framework of con- flicting political priorities. These include: meet- ing energy demands for sectoral end-uses; maximizing energy conservation; checking air pollution; reducing the annualized economic cost of utilization of energy systems; reducing import of energy from neighbouring regions; and increasing the capacity for utilization of domestic appliances and different modes of transport.

Multi-objective decision models arise from the need to take into account the presence of a wide variety of conflicting objectives in ordinal ranking or priorities depending on the degree of importance one wants to assign to each objec- tive. The basic problem related to the existence of multiple objectives is the fact that decisions are normally interdependent, so that any deci- sion to increase production has a corresponding

impact on energy consumption, pollution emis- sion and vice versa. Pollutants considered for this study are carbon monoxide (CO), nitrogen oxides (NOx), sulphur dioxide (S02) and sus- pended particulate matter (SPM) which are the emissions caused by combustion or automation.

This paper provides a comprehensive and systematic analysis of energy and pollution problems interconnected with the economic structure, by using a multi-objective sectoral end-use model for addressing regional energy policy issues. The multi-objective model pro- posed for the study is a "linear goal program- ming (LG P)" technique of analysing a "reference energy system (RES)" in a frame- work within which alternative policies and technical strategies may be evaluated. The model so developed has further been tested for the city of Delhi (India) for the period 1985- 86, and a scenario analysis has been carried out by assuming different policy options.

Keywords: energy, economy, environ- ment, goal programming, reference en- ergy system, Delhi.

BACKGROUND

Urban izat ion is a relat ively recent but by far the most dominant social t ransformat ion of our times. The world has fast t ransformed itself into an urban society, and by 1985 near ly 2 bi l l ion people (41% of the total popu- lation) were l iving in urban sett lements [1].

This rapid pace of the urbanizat ion process and the different forms of urban growth present serious chal lenges to the energy sector in finan- cial, economic, technological and environ- mental terms. The impl icat ions of urbanizat ion

0378-7788/91/$3.50 ~ Elsevier Sequoia/Printed in The Netherlands

538

on the energy sector is therefore concerned with two major current debates in public pol- icy in affluent societies. One is the widespread concern with the quality of the natural envi- ronment, which is degrading. A second debate concerns the adequacy of energy resources to meet the requirements of the growing service needs in an urban economy. Increased energy consumption entails increased outputs of po- tentially polluting "residuals" (sulphur ox- ides, nitrogen oxides, particulates, carbon monoxide, etc.). Thus the production, distribu- tion, conversion and use of all forms of energy are inherently and heavily associated with environmental impacts. Since a significant part of the shortfalls in environmental quality in contemporary societies derive from energy use, issues of "trade-off" between additional energy supplies and environmental quality frequently arise. In the context of this inti- mate association between the economy, envi- ronment and energy, recent developments in energy and natural resources have raised a number of analytical issues that may be grouped into three classes [2]:

(1) the effects on the economy (and the policies) to facilitate the transition from cheap or abundant energy and a reliance on oil and gas to more expensive sources of en- ergy;

(2) the trade-off between additional or lower-cost energy for environmental quality;

(3) the incidence of the costs incurred in the trade-off decisions in different socio- economic groups in society.

SUSTAINABLE URBAN ENERGY SYSTEMS THROUGH MULTI-OBJECTIVE PROGRAMMING APPROACH

The basic question that now arises is how to plan an overall energy system in a city in terms of "optimum mix of energy sources to meet the growing service needs in different sectors" by which the following objectives (a part of which are conflicting in nature) can be addressed together:

- - maximize efficiency of energy use; - - m i n i m i z e the overall energy system

cost, i.e., both the capital cost of the energy- using devices and their operating cost should be minimized;

meet the service needs of the poor in an equitable manner;

- - minimize emission of air pollutants due to burning or automative processes of differ- ent fuels;

minimize import of energy supply from the neighbouring region.

It is very apparent that these objectives, which are conflicting in nature, cannot be met simultaneously. Therefore, a single objective like minimizing the energy system cost or rain- imizing emission of pollutants is less relevant in the actual decision environment.

In recent years the insight has grown that energy-economic and environmental decision- making has to be placed in a broader frame- work of multiple objectives. Multi-objective programming and planning is concerned with decision-making problems in which there are several conflicting objectives. Multi-objective analysis allows several noncommensurable effects to be treated without artificially combining them. According to Cohon [3], the analysis of energy problems, which is inextri- cably bound up with the environment, is a new area to which multi-objective analysis is applicable. This new view has induced the development of multi-objective decision- making tools. This multi-objective analysis technique has so far been used by Lesuis, Muller and Nijkamp [4] for studying the inter- relationships between economic structure, en- ergy consumption and pollution with an application to the Dutch economy. Accor- ding to Lesuis et al. [4], the other persons who have also done work in this field are Blair [5] and van Delft and Nijkamp [6]. The study by Samouilidis and Pappas [7] has im- plemented a similar technique for energy- forecasting of the Greek economy where the problem of pollution is not taken into ac- count. Another recent study by Hsu et al. [8] used a multi-objective programming approach to an input-output model for energy plan- ning in Taiwan.

One of the most promising techniques for multiple objective decision analysis is goal programming (GP), developed by Ijiri [9], Lee [10- 12] and Ignizio [13]. Goal programming is a powerful tool and provides a simultaneous solution to a complex system of competing objectives. It can handle decision problems having single or multiple goals with multiple subgoals [10]. In GP, instead of attempting to

maximize or minimize the objective criterion directly, the deviations between goals and what can be achieved within the given set of constraints are minimized, based on the rela- tive importance or priority assigned to each goal. Prioritizing the deviational variables in the objective function allows for the satisfy- ing of conflicting goals corresponding to their order of importance with the decision- maker. If overachievement of a certain goal is acceptable, deviational variable d from the goal can be eliminated from the objective function. On the other hand, if underachieve- ment of a certain goal is acceptable, devia- tional variable d- should not be included in the objective function. If the exact achieve- ment of the goal is desired, both d and d - must be represented in the objective function.

For the application of this model, it is es- sential to understand the overall energy sys- tem framework in the reference region. This is possible by using the process flow tech- nique known as the "reference energy sys- tem" (RES) network developed by Hoffman [14]. The RES presents a network description of the energy system in which the flow of energy sources from supply ends to each of the sectoral service demands is depicted. Each link in the network corresponds to a physical process and is characterized by con- version efficiency, capital and operating cost, and emission of air pollutants due to burning or automative processes of these fuels per unit of energy input.

OBJECTIVES

The broad objective of the study is to de- velop a linear goal programming (LGP) model by analysing the reference energy system (RES) for satisfying the "best" mix of fuels required to meet at least the basic demand of different economic sectors in an urban area of India. While doing so, three major goals are addressed in some ordinal preference by prior- itizing them under different scenarios. The three goals are to minimize:

(1) emission of pollutants in the atmo- sphere with respect to the National Ambient Air Quality Standards;

(2) energy system cost with respect to the budgetary limit of the total energy expendi- ture;

539

(3) level of import of different energy sources from the neighbouring region.

In the present paper an attempt has been made to develop this integrated optimization model for the city of Delhi. Delhi has been chosen due to its phenomenal growth of popu- lation at the rate of 4.69% annually during the last decade. The total population of Delhi city had swelled to 62.21akhs (92.7% of the total population of the Union Territory of Delhi) during 1981 [15]. Presently, Delhi ac- commodates 99% of the urban population and it is expected that by the year 2001, Delhi will overtake any other city in India if this rapid rate of growth continues.

The model so developed for the city of Delhi has been further tested by carrying out a scenario analysis using 1985-86 data as the reference year for the study.

THE MATHEMATICAL MODEL

The mathematical structure of the LGP model is formulated by analysing the RES for the city of Delhi during 1985-86 (Fig. 1), by considering the following indices, decision variables and parameters.

Indices The following indices take different values

and are defined in Table 1: i = energy source; j =end-use; S =sector; s =subsector; p= pollutants. From Fig. 1 and Table 1 we also define:

K

K(~)

K*(J)

K,(p)

set of feasible combinations of i and j, where i=1,2 . . . . 11 and j = 1,2 . . . . 16 set of feasible combinations (i,j) for fixed energy source i, where j= l , 2 . . . . 16 set of feasible combinations (i,j) for fixed end-use j, where i = 1, 2 , . . . 11 set of feasible combinations (i,j), i = 1, 2 . . . . 11 and j = 1, 2 . . . . 16, emit- ting pth pollutant

Decision variables For each feasible combination (i,j),

i=1 ,2 . . . . 11 and j= l , 2 . . . . 16, let us define

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Energy sources

FIrewood

Charcoal

Coke

Coal

LPG

Kerosene

Dieeel

Petrol

Furnace oll

Fuel oll

Electricity

End-use devices End-uses Sub-sectors Sectors

ove~lah :~ :~, Cooking t plate j j ~oking range ~ . Water heating yser tmeraion rod . J j , Space heating r cooler r conditioner loom heater - - 1~Space cooling .'an

LI family

, Domestic

can.bulb uor.bulb ~ MI family I/ashlng mach ine .~ Lighting ron "-'~-.~ ad Io.TV,VCR ~efrlgerator ~ Others HI family

two wheeler ~ Passenger Transport hree wheeler " ~ movement :vate oar ~/~ ubllo oar ~ \ / / Food products , \

i3uS ~ _ ,//i~ ' COttOn,textiles , , ,\ F urnaoe rooo. heat ? oiler ~ Motive power ~ Chemicals ./,i I Industry Iotor ~ j_ ~\ : Other, with I lght~ ~ //

Captive power ~ Metal & alloy ,:/ kenerstor ~\," Public lighting \,..~___~___Others J

Miscellaneous 0 ~~"- - ' - -~Serv lces & ~ooster pump Water works & sewage ~ / Commercial

IlscellaneoUShops ~_ - , Commercial

vthers . ~ . Others

Fig. 1. Reference energy system network for Delhi.

TABLE ]

Definition of various indices considered in the model

Energy sources i Pollutants p End-uses j Subsectors s Sectors S

1. Firewood 1. SO2 1. Cooking 1. Low-income family 1. Domestic 2. Charcoal 2. CO 2. Water heating 2. Middle-income family 3. Coke 3. NOx 3. Space heating 3. High-income family 4. Coal 4. SPM 4. Space cooling 5. LPG 5, Lighting 4. Low-income family 2. Passenger 6. Kerosene 6. Other electric 5, Middle-income family transport 7. Diesel appliances 6. High-income family 8. Petrol 9. Furnace oil

10, Fuel oil 7. Passenger movement ]l. Electricity 7. Food products 3. Manufacturing

8. Cotton textiles industry 9. Chemicals

10. Metal and alloy 11. Others

8. Process heating 9. Motive power

10. Others including lighting

11. Captive power 12. Public lighting 13. Public water works

and sewage pumping 14. Miscellaneous 15. Commercial 16. All other end-uses

together in urban establishments

12. Services and 4. Services and commercial commercial

x!;) =

-annual per-capita requirement of the ith energy source for the jth end-use demand expressed in 103 kcal/person in the s th subsector; s = 1, 2 , . . . 6, 12

annual requirement of the /th energy source per unit of value added (va) for the j th end-use demand expressed in 103kcal/Re va in the s th subsector; s =7,8 . . . . 11

Parameters For each feasible combinat ion (i, j), i =

1, 2 . . . . 11 and j = 1, 2 . . . . 16, let us denote by a!~ ) the energy demand coefficient correspond- ing to the decision variable xl~ ). Depending upon a part icu lar subsector, these coefficients are defined differently as given below:

device or appl iance efficiency ex- pressed as a fraction, used to meet the j th end-use demand by util izing the i th

a(8) energy source; s = 1, 2, 3, 7, 8 . . . . 12 i j ~-

inverse of the "operat ing energy in- tensity"* expressed in passenger km/ kcal of different modes of t ransport when used to meet the passenger travel demand ( j = 7) by util izing the ith energy source; s = 4, 5, 6

"annual per capita useful energy de- mand** of the j th end-use expressed in 10akcal/person in the s th subsector;

u(8) s = 1, 2 . . . . 6, 12 j ---

annua l useful energy demand per unit of value added of the j th end-use ex- pressed in 10 3kcal/Re va in the s th subsector; s -- 7, 8 . . . . 11

-total person populat ion expressed in 10 6 persons in the s th subsector; s =1,2 . . . . 6,12

t (s ) =

annual value added expressed in 10 6 Rupees value added in the s ts subsec- tor; s=7,8 , . . .11

Note that t (1) = t (4), t (2) = t (5) and t (3) = t (s).

*Operating energy intensity [16] in a way represents the efficiency of different modes of vehicles. It measures the amount of energy needed to move one person over 1 km by a given vehicle. It is an average concept, which conceals wide variations in energy intake in operating conditions and will be expressed in kcal/passenger km (pkm) units. **"Useful" energy refers to the amount consumed net of conversion losses.

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For each feasible combinat ion (i, j), let us denote by bi. j the annual capacity of utiliza- t ion of the ith energy source to meet the jth end-use demand. In the definition of bi~ the suffix i for 8 and 11 will be further split at the second level*. The definition of bii is given below:

- annual uti l ization of six domestic elec- tr ical appliances, namely, immersion rod, geyser, water cooler, air-condi- t ioner, incandescent bulb and fluores- cent tube expressed in 109 kcal; {(i,j) = (11.1, 2), (11.2, 2), (11.4, 4),

bij -- (11.5, 4), (11.6, 5), (11.7, 5)} annual uti l ization of five different ve- hicles, namely, bus, two wheeler, three wheeler, car and taxi, expressed in 109 pkm; {(i,j) = (7, 7), (8.1, 7), (8.2, 7),

(8.3, 7), (8.4, 7)}

ri =annua l avai labi l i ty of the ith fuel pressed in 109 kcal; i = 1, 2 . . . . 11

ex-

Let _(8) denote the cost coefficient corre- {: i j sponding to the decision variable ..(8) Depend- X i j ing on a part icular subsector, these coefficients are defined differently, as given below:

- l eve l i zed annual cost of domestic ap- pl iances per unit of gross heat input, expressed in Rs/10 a kcal, required to meet the j th end-use by the ith energy

(8) source in the s th subsector; s = 1, 2, 3

c ij = levelized annual cost of different modes of vehicles to meet the passen- ger travel demand ( j = 7) expressed in Rs/pkm by the ith energy source in the s th subsector; s = 4, 5, 6

market price of the i th energy source expressed in Rs/103kcal in the s th subsector; s = 7, 8 . . . . 11

Denote by e (8), the annual energy expen- diture in the s th subsector. Depending on a

*i Vehicles i Appliances

8.1 2-wheeler 11.1 Immersion rod 8.2 3-wheeler 11.2 Geyser 8.3 Car 11.4 Water cooler 8.4 Taxi 11.5 Air-conditioner

11.6 Incan. bulb 11.7 Fluor. bulb

542

part icular subsector, these coefficients are defined differently, as shown below:

F annual per-capita energy expenditure |expressed in Rs/person in the s th sub-

sector; s = 1, 2, 4, 5

e('~)= |annua l energy expenditure per unit of |va lue added expressed in Rs/Re va in Lthe s th subsector; s = 7, 8 . . . . 11

The parameters giving emission factors of pol lutants are defined next:

q(P'~) = emission factor of the pth pol lutant ex- ij pressed in g/103 kcal due to the burn- ing or automative process of the i TM energy source for the jth end-use in the s TM subsector.

Finally,

v(P)= annual permissible or al lowable loading level of the pth pol lutant expressed in tonnes.

CONSTRAINTS

1. Useful energy demand by sectoral end-use The useful energy demand for each end-use

in different sectors which is exogenously esti- mated will be met.

~] _(8) _(~) " (~) (1 ) tt ij " ij ~ U j

i e K*( J )

where (j, s) takes values according to the fol- lowing:

Domestic sector

( j , s) E~ = {(j, s): (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (6, 1), (6, 2), (6, 3)} (2)

Transport sector

(j, s) E2 = {(j, s): (7, 4), (7, 5), (7, 6)} (3)

Industrial sector

(j, s) E3 = {(j, s): (8, 7), (8, 8), (8, 9), (8, 10), (8, 11), (9, 7), (9, 8), (9, 9), (9, 10), (9, 11), (10, 7), (10, 8), (10, 9), (10, 10), (10, 11), (11, 7), (11, 8), (11, 9), (11, 10), (11, 11)} (4)

Services and commercial sector

(j, s) E4 = {(j, s): (12, 12), (13, 12), (14, 12), (15, 12), (16, 12) I (5)

We thus have 45 constrained inequalities in eqn. (1) of which 17 correspond to the domes- tic sector in eqn. (2), 3 for transport in eqn. (3), 20 for industries in eqn. (4) and the last five inequalit ies in eqn. (5) are for the services and commercial sector.

In the LGP setup the constraint eqn. (1) is to be written as

u-(~)u ~-(~)i: + d~ - dfs = _ju (~) (6) i E K*(J)

where dj~ (or dj +) denotes the under- (or over-) achievement of the jth end-use energy demand in the s TM subsector.

2. Capacity utilization of selected appliances and vehicles

The annual use pattern of some selected domestic electrical appliances, namely, immer- sion rod, geyser, water cooler, air-conditioner, incandescent bulb, f luorescent tube and differ- ent modes of passenger vehicles, namely, bus, two wheeler, three wheeler, car, taxi, are fully utilized. In other words, the capacity utiliza- tion factor of these specified devices/modes should be 100% utilized.

(~) t(~)xl~ ~

(9) are for different types of passenger vehi- cles. In the LGP setup the constraint eqn. (7) is to be written as

(s) t(s)~c(s) aij - --ij +d* - = bij (10) s

where d*- denotes the under-utilization of the appliance/mode of transport using the ith energy source for the jth end-use.

Here it may be mentioned that in the in- equality, eqn. (7), only a negative deviational variable is added to transform it into a LGP framework in eqn. (10). This is due to the fact that the capacity utilization factor of any device/mode of transport cannot exceed 100% utilization factor.

3. Energy resources avai lable Total annual demand of the i th energy

source for different sectoral end-uses is to be met with respect to the total availability of the i th energy source in the region. 12

~ -t(s)y(s)'-ij < ri i = 1, 2, . . . 11 (11) s=l j K ( i )

There are 11 constrained inequalities in eqn. (11), each of which corresponds to the availability of the 11 different types of fuels used in Delhi.

In the LGP setup the constraint eqn. (11) is written as 12

~ ~(s)~(s) . . . . . + - - i j q- d i - d , = r i (12)

s=l j e I';[(i)

where dT- (or d7 +) denotes the surplus (or deficit) of the i th energy source in the region of study.

4. Energy expendi ture The energy demand for domestic end-uses

and for transportation purposes is to be met within the current level of energy expenditure budget in only low- and middle-income house- holds. Similarly, the industrial end-use de- mands are to be met within the current level of energy expenditure. It may be noted here that an energy budget is not taken as a con- straint in the high-income households, as the percentage share of energy expenditure of the total income in the high-income household is very small as compared to the low- and mid- dle-income households.

~, ~ _(s) (s) e(S) Uij X i j ~ (13)

j i e K*(J)

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where, depending on the value of s ( = 1, 2, 4, 5, 7, 8, 9, 10, 11), the summation index j belongs to either set E9 or El0 or Ell as defined below.

Energy budget: domestic

fo rs=l , 2; j~Eg=(1 ,2 ,3 . . . . 6) (14)

Energy budget: transport

for s = 4, 5; j e El0 -- (7) (15)

Energy budget: industries

for s=7,8,9,10,11; jeEaa=(8,9 ,10,11) (16)

There are nine constrained inequalities in eqn. (13), of which two correspond to the do- mestic energy budget in eqn. (14), two to the transport energy budget in eqn. (15) and the last five to the industrial energy budget in eqn. (16).

In the LGP setup, the constraint eqn. (13) is written as

(~) (s) + d*- - d *+ = e (s) (17) Z Z c,j x ij j i K*(J)

where, d*- (or d *+) denotes the energy under- (or over-) expenditure in the s th sector.

5. A i r pol lut ion loading The total annual emission of the pth pollu-

tant due to the burning or automotive pro- cesses of different fuels is to be kept as low as possible with respect to its permissible or safe loading level in the atmosphere annually. In other words, total emission of the pth-pollu- tant annually should be minimized with re- spect to the annual safe loading level.

12

qij p = 1, 2, 3, 4 s = l (i,j) K'(P)

(18)

There are four constrained inequalities in eqn. (18), each of which corresponds to the four different pollutants SO2, CO, NO~ and SPM.

In the LGP setup, the constraint eqn. (18) is to be written as

12 ~, .~a!e'~)t(~)~ ~ _,j + d'p- - d'p = v (p) (19)

s = 1 (i, j) K'(P)

where d~- (or d~ +) denotes the under- (or over-) loading of the pth pollutant in the atmo- sphere.

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6. Non-negativity constraint We have here the natural constraints

x (s) i j ~>0 for all i , j ands (20)

Also, all the positive and negative deviational variables are non-negative.

GOAL FORMULATIONS

Let us classes:

G1

G2

G3

consider the following six goal

useful energy demand of sectoral end-uses is to be met; minimize over-utilization of energy after G1 is completely attained; annual capacity of utilization of some se- lected domestic electrical appliances, and different types of passenger vehicles should be fully utilized;

G 4 minimize energy import from neighbour- ing region;

G5 minimize over-expenditure on energy while meeting the domestic end-uses as well as travel demand in low- and middle- income households. Also, over-expendi- ture on energy in the five types of industries considered are minimized while meeting the industrial end-uses demand;

G6 minimize pollution loading of four pollu- tants SO2, CO, NOx and SPM due to the burning or automotive processes of differ- ent fuels with respect to their safe or permissible loading level.

For notational convenience, let us replace all the goal deviations in eqns. (6), (10), (12), (17) and (19) by d~-(~>0) for negative devia- tions and d[ (~>0) for positive deviations. Thus, goal deviations corresponding to goal classes:

G1 is d i ;

G2 is d[;

G~ is dT;

G4 is d [ ;

G~ is d/~;

G 6 is d[;

= 1,2 . . . . 45

= 1,2 . . . . 45

= 46,47 . . . . 56

= 57,58 . . . . 67

= 68,69 . . . . 76

= 77,78,79,80.

With this, G1 and G2 have 45 subgoals each; Ga and G4 have 11 subgoals each; G5 has 9 sub- goals and G 6 has 4 subgoals.

Now, the objective function of LGP can be formulated only after the following are deter- mined:

(i) prioritizing ordinal ranking of the six goal classes G1 to G6, and

(ii) assigning weighting factors to the goal deviation of each of the subgoals within a goal class.

Prioritization of goal classes The primary objective of the model would

be to determine the optimum mix of fuels required to meet G1 completely in the pres- ence of Gz and to see its overall impact on G2, G4, G~ and G G. It is important to mention here that the goal G3 has a special significance in the overall LGP framework. Without Ga it is very likely that the model might represent a very unrealistic situation. For instance, with- out G~ it is very likely that, to meet the passenger travel demand, the model may sug- gest use only of Delhi Transport Corporation (DTC) buses and not of personal vehicles, mainly because buses are more economically efficient as compared to personal vehicles. But, under the existing situation this is not possible as the fleet strength of DTC buses is limited and also because personal vehicles are actually being used. From the nature of the goal classes it can be noted that, excepting G~ and Ga, all the other four goals are non-com- mensurable or incompatible. It therefore fol- lows that G~ and G3 are to be assigned P1 and the other goal classes are assigned low-order priorities. Since the goal classes G 2, G4, G 5 and G6 cannot be met simultaneously, each of them have been assigned different levels of priorities P2, P~, P4 and/)5 depending on the ordinal ranking of these goals.

In this paper, let us consider the three scenarios given in Table 2 where each time

TABLE 2

Ordinal ranking of the goals

Priorities

Scenario P1 P2 Pa P4 P5

I Ga > G1 G~ G6 G4 G,~ II G:3 > G~ G~ G~ G 4 G 2 III G:, > G~ G4 Gs G6 G2

For G~ > Gj under P1 means both G i and Gj are assigned first priority but between them G i is assigned more impor- tance than Gj.

the ordinal ranking of the goals is considered differently.

Objective weighting within priority grouping After assigning priorities to all the six goal

classes (Table 2) the next step is to assign differential values of weights to the goal devi- ations of subgoals within a goal class. Assign- ing weights to the goal deviations is purely on the basis of our judgements and will vary from person to person.

Let us denote the differential weights as wE(>~0) or w~(>~0). These differential weights are assigned to the negative or posi- tive goal deviation dT(~>0) or d~(~>0) for i = 1, 2 . . . . 80, respectively.

Let us define

45

A- = ~ wTdF = weighted deviation of the i= I 45 subgoals in G~

45

A+= E w;d; = i= l

56

B-= ~ w[-di- = i = 46

67

C += ~ w?-dJ- = i =57

76

D+= E w~-d?-= i = 68

8O

E+= E w?-d~- i =77

weighted deviation of the 45 subgoals in G2

weighted deviation of the 11 subgoals in G3

weighted deviation of the 11 subgoals in G4

weighted deviation of the 9 subgoals in G~

= weighted deviation of the 4 subgoals in G6

where

45 56

w/-+ ~ w/ -=1 i = 1 i=46

45 67 76 80

E w; = E w~+ = E w~-= E w~+ =1 i=1 i=57 i=68 i=77

Objective function The structures of the objective function un-

der three different scenarios after assigning weights to the goal deviations in Table 2 are:

Scenario I

Minimize Z = PI (A - + B - ) + P2D +

+ P3E + + P4C + + PsA + (21)

545

Scenario H

Minimize Z = PI (A - + B - ) + P2E +

+ P3D+ + P4C+ + P~A + (22)

Scenario I I I

Minimize Z = P , (A - + B - ) + P2C +

+ P3D + + P4 E + P~A + (23)

Thus, under the three scenarios, the LGP model consists of finding the values of deci- sion variables and deviational variables which minimize Z given by eqns. (21), (22) and (23) subject to the constraints expressed in eqns. (6), (10), (12), (17) and (19).

The mathematical structure of the LGP, after analysing the RES for Delhi city during 1985-86, has a total of 80 linear equations in 136 decision variables. Also, the total number of deviational variables is 149, of which 80 are negative deviations corresponding to each of the 80 equations and only 69 are positive devi- ations, as no positive deviational variable is allowed in eqn. (10).

The solution set of LGP is determined by using a FORTRAN program developed by Lee [17]. Of the total 285 variables (136 decision and 149 deviation), only a maximum of 80 non-zero variables are the basic variables which will be determined in the optimum solu- tion set; and the balance of 205 variables being non-basic have zero values.

SCENARIO RESULTS

P1 = 0, in all the scenarios. This means G1 and G 3 are fully met. In other words, each of the sectoral end-use energy demands have at least been met, in the presence of full utiliza- tion of the selected domestic electrical appli- ances and different modes of vehicle available in Delhi during 1985-86.

Ph ~ 0 for h = 2, 3, 4, 5 in all the scenarios. This indicates none of the other four goals G2, G4, G~ and GG are fully met.

Now to understand which subgoals in G2, G4, G5 and G~ are responsible for under-attain- ment of these goals in all the three scenarios, Table 3 presents a detailed analysis. From the definition of goal types, any positive devia- tional variable, if it is non-zero for the goal G2, is a gain in the overall system. Whereas, any negative deviational variable, if it is a

TA

BL

E

3

Un

de

r-a

tta

inm

en

t o

f g

oa

ls un

de

r th

ree

dif

fere

nt s

ce

na

rio

s sh

ow

ing

pe

rce

nta

ge

g

ain

or

loss

in e

ac

h go

al

Eq

n.

Pa

ram

ete

r de

scri

pti

on

U

nit

G

oa

l S

ce

na

rio

I S

ce

na

rio

II

No

. S

ce

na

rio

III

d

d +

d

- d ~

d

d*

Sc

en

ari

o I

Sc

en

ari

o I1

Ga

in

Lo

ss

Ga

in

Lo

ss

(%)

(%)

(%)

(%)

Sc

en

ari

o IlI

Ga

in

Lo

ss

(%)

(%)

5

Wa

ter h

ea

t: M

I: d

om

esti

c

10 a k

ea

l/p

ers

on

4

2

0

0

0

6

Wa

ter h

ea

t: H

I: d

om

esti

c

10 a k

ca

l[p

ers

on

9

0

0

244

0

9

Sp

ace

co

ol:

LI:

do

me

sti

c

103 kc

al/

pe

rso

n

27

0

0

0

11

Sp

ace

co

ol:

HI:

do

me

sti

c

10 a k

ca

l/p

ers

on

3

80

0

762

0

13

Lig

hti

ng

: MI:

do

me

sti

c

103 kc

al]

pe

rso

n

14

0

0

0

14

Lig

hti

ng

: HI:

do

me

sti

c

103 kc

al/

pe

rso

n

26

0

0.3

6

0

18

Pa

sse

ng

er kin: LI:

tra

nsp

ort

10 a p

km

/pe

rso

n

4

0

0

0

20

Pa

sse

ng

er km

: HI:

tra

nsp

ort

10 a p

km

/pe

rso

n

4

0

2

0

57

Fir

ew

oo

d

109 kca

l 1608

1608

0

1608

58

Ch

arc

oa

l 10 s k

ca

l 3

55

355

0

35

5

59

So

ft c

ok

e

109 kc

al

707

0

2311

707

60

Co

al

109 ke

al

535

535

0

535

61

LP

G

109 kc

al

1340

0

373

0

62

K

ero

se

ne

109 kc

al

1940

0

1601

68

8

63

Die

sel

109 kc

al

6253

5170

0

5170

64

Pe

tro

l 109 kca

l 2286

0

97

6

0

65

Fu

rna

ce

oil

10 s k

ca

l 1514

1514

0

1514

66

Fu

el o

il

109 kc

al

30

3

0

0

30

67

Ele

ctr

icit

y

10 a k

ca

l 3353

0

5532

0

68

Ex

pe

nd

itu

re: LI:

do

me

sti

c

Rs[p

ers

on

242

0

19

0

69

E

xp

en

dit

ure

: MI:

do

me

sti

c

Rs/p

ers

on

4

48

0

285

0

70

Ex

pe

nd

itu

re: Lh

tra

nsp

ort

R

s/p

ers

on

3

65

0

0

0

71

Ex

pe

nd

itu

re: MI:

tra

nsp

ort

R

s/p

ers

on

943

0

0

0

72

Ex

pe

nd

itu

re: fo

od

: in

du

str

y

Rs/

Re

va

0.5

1

0

0.2

0

0

73

Ex

pe

nd

itu

re: co

tto

n: in

du

str

y

Rs/

Re

va

0

.68

0

0.4

2

0

74

Ex

pe

n.:

ch

em

ica

l: ind

ustr

y

Rs/

Re

va

0

.47

0

0.1

0

0

75

Ex

pe

nd

itu

re: m

eta

l: in

du

str

y

Rs/

Re

va

0.8

1

0

0.3

1

0

76

Ex

pe

nd

itu

re: oth

er:

ind

ustr

y

Ils]R

e v

a

0.1

3

0

0.2

1

0

77

SO

2 p

oll

uta

nt lo

ad

ing

103 to

nn

e

16

0

11

0

78

CO

po

llu

tan

t loa

din

g

103 to

nn

e

255

91

0

131

79

NO

~ p

oll

uta

nt lo

ad

ing

103 to

nn

e

42

0

.04

0

0

80

SP

M p

oll

uta

nt lo

ad

ing

10 a to

nn

e

22

0

13

0.9

3

237

0

0

0

0

164

2193

0

2193

0

0

0

2

0

0.0

1

0

0

0

6

0

6

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

6128

0

0

0

0

0

0

48

16

0

853

0

825

0

0

0

0

0

0

5057

0

55

23

7523

0

7526

798

0

479

4671

0

87

68

359

477

0

0.2

9

0

0.4

1

0.7

2

0

0.6

2

0.1

5

0

0.1

3

0.6

3

0

0.6

8

0.2

9

0

0.2

5

4

0

11

0

92

0

0

0

2

0

0

41

270

201

1

38

100

100

100

83

100

100

36

0.1

0

327

28

83

43

165

8

64

39

62

21

38

168

69

62

569

8071

17

127

100

100

100

100

35

83

100

100

51

45

7

37

151

3112

178

1218

38

57

106

32

78

22

3

24

182

8071

0.0

7

127

77

5]

36

36

165

3113

107

2405

80

91

28

84

192

71

5

190

All

th

e fi

gu

res h

av

e be

en

rou

nd

ed

off

to

th

e n

ea

rest in

teg

er v

alu

e ex

ce

pt fo

r fi

gu

res le

ss th

an

un

ity

.

TA

BL

E

4

Sc

en

ari

o re

su

lts

on

an

nu

al

mix

of

en

erg

y s

ou

rce

s fo

r d

iffe

ren

t en

d-u

se

s in

th

ree

inc

om

e ca

teg

ori

es

in t

he

do

me

sti

c

se

cto

r o

f D

elh

i d

uri

ng

19

85

- 8

6

En

d-u

se

E

ne

rgy

A

pp

lia

nc

e

Un

it

Sc

en

ari

o I

Sc

en

ari

o II

S

ce

na

rio

III

so

urc

e

LI*

M

I H

I L

I M

I H

I L

I M

I H

I

Co

ok

ing

F

ire

wo

od

k

g]p

ers

on

.

..

..

.

63

.11

-

So

ft c

ok

e

kg

/pe

rso

n

- -

14

2.3

9

9.7

8

LP

G

kg

/pe

rso

n

65

.18

2

3.6

3

46

.77

6

5.1

8

28

.14

2

.13

Ke

ros

en

e

litr

es

/pe

rso

n

38

.98

7

7.1

6

- -

10

1.3

3

Ele

ctr

icit

y

kW

h]p

ers

on

-

- -

12

2.5

1

Wa

ter

he

ati

ng

L

PG

k

g/p

ers

on

-

- -

21

.08

-

Ke

ros

en

e

litr

es

/pe

rso

n

2.2

8

9.7

4

-

Ele

ctr

icit

y:

imm

ers

ion

rod

k

Wh

/pe

rso

n

- 1

45

.29

-

78

.23

-

- 7

8.2

3

-

Ele

ctr

icit

y:

ins

tan

t g

ey

se

r k

Wh

/pe

rso

n

37

2.1

5

13

.34

1

31

.44

1

23

.59

1

3.3

4

10

.91

3

48

.19

Sp

ac

e h

ea

tin

g

Ele

ctr

icit

y

kW

h/p

ers

on

-

44

.12

1

28

.97

4

4.1

2

12

8.9

7

- 4

4.1

2

12

8.9

7

Sp

ac

e c

oo

lin

g

Ele

ctr

icit

y:

fan

k

Wh

/pe

rso

n

37

.16

1

13

.33

.

..

.

Ele

ctr

icit

y:

wa

ter

co

ole

r k

Wh

/pe

rso

n

- 3

99

.36

-

11

3.3

3

18

8.2

2

11

3.3

3

18

8.2

2

Ele

ctr

icit

y:

air

-co

nd

itio

ne

r k

Wh

/pe

rso

n

- -

11

62

.43

3

03

6.8

7

33

1.2

9

30

36

.87

3

31

.29

Lig

hti

ng

K

ero

se

ne

li

tre

s/p

ers

on

-

53

.09

-

Ele

ctr

icit

y:

inc

an

de

sc

en

t bu

lb

kW

h/p

ers

on

-

43

.29

3

11

.55

8

3.1

4

19

4.6

1

- 8

3.1

4

16

6.9

7

52

.77

Ele

ctr

icit

y:

flu

ore

sc

en

t tu

be

k

Wh

/pe

rso

n

46

.19

6

8.6

5

14

1.4

3

- 1

41

.43

Oth

ers

**

E

lec

tric

ity

k

Wh

/pe

rso

n

57

.08

1

60

.21

3

07

.59

5

7.0

8

16

0.2

1

30

7.5

9

57

.08

1

60

.21

3

07

.59

*LI

= L

ow

-in

co

me

ho

us

eh

old

wit

h a

nn

ua

l fa

mil

y i

nc

om

e u

p t

o R

s. 1

8 0

00

.

MI

= M

idd

le-i

nc

om

e ho

us

eh

old

wit

h a

nn

ua

l fa

mil

y in

co

me

be

twe

en

Rs.

18

00

0 a

nd

Rs.

54

00

0.

HI

= H

igh

-in

co

me

ho

us

eh

old

wit

h a

nn

ua

l fa

mil

y in

co

me

ov

er

Rs.

54

00

0.

**

"Oth

ers

" in

clu

de

th

e u

se

of

su

ch

ele

ctr

ica

l ap

pli

an

ce

s a

s i

ron

s,

TV

s,

rad

ios

, re

frig

era

tors

, wa

sh

ing

ma

ch

ine

s, e

tc.,

th

at

are

no

t in

clu

de

d u

nd

er

the

sp

ec

ific

en

d-u

se

s

me

nti

on

ed

ab

ov

e.

TA

BL

E

5

Sc

en

ari

o re

su

lts

on

an

nu

al m

ix o

f e

ne

rgy

so

urc

es

for

me

eti

ng

tra

ve

l de

ma

nd

for

pa

ss

en

ge

r km

by

dif

fere

nt m

od

es

of

tra

ns

po

rt in

th

ree

inc

om

e c

ate

go

rie

s in

th

e t

ran

spo

rt

se

cto

r

En

erg

y

Ve

hic

le m

od

e

Un

it

Sc

en

ari

o I

Sc

en

ari

o II

S

ce

na

rio

II|

so

urc

e

LI

MI

HI

LI

MI

HI

L!

Mt

Ht

Die

se

l B

us

li

tre

s/p

ers

on

1

7.9

4

16

.37

1

0.9

9

14

.62

1

9.1

0

16

.98

1

4.7

1

Pe

tro

l 2

wh

ee

ler

litr

es

/pe

rso

n

7.4

1

41

.42

1

60

.30

--

7

2.6

5

12

.79

P

etr

ol

3 w

he

ele

r li

tre

s/p

ers

on

-

34

.88

1

23

.54

1

.16

3

4.5

9

Pe

tro

l C

ar

litr

es

/pe

rso

n

25

.96

2

2.4

2

34

.66

2

32

.96

P

etr

ol

Ta

xi

litr

es

/pe

rso

n

14

.30

7

.68

-

51

.85

TA

BL

E

6

Sc

en

ari

o re

sult

s on

an

nu

al m

ix o

f e

ne

rgy

sou

rce

s fo

r fo

ur

ma

jor e

nd

-use

s in f

ive

ty

pe

s of m

anufa

cturi

ng

indust

ries in

De

lhi d

uri

ng

19

85

- 86

En

d-u

se

En

erg

y

Un

it

Sc

en

ari

o I

Sc

en

ari

o II

Sc

en

ari

o Ill

SO

UrC

e

Fo

od

C

ott

on

C

he

mic

al

Me

tal

Oth

ers

F

oo

d

Co

tto

n

Ch

em

ica

l M

eta

l O

the

rs

Fo

od

C

ott

on

C

he

mic

al

Me

tal

Oth

ers

Pro

ce

ss

Ch

arc

oa

l k

g/R

e v

a

0.1

1

0.1

5

he

ati

ng

C

ok

e

kg

/Re

va

0

.12

0

.43

0

.06

0

.46

0

.11

Co

al

kg

/Re

va

0

.62

0

.07

0.

(17

LP

G

kg

/Re

va

0

.05

0

.17

0

.03

0

.18

0

.05

F

urn

. oil

li

tre

s/R

e va

0

.14

0

.05

F

ue

l oil

li

tre

s/R

e va

0

.01

Mo

tiv

e

Ele

ctr

icit

y

kW

h/R

e v

a

0.4

5

0.4

4

0.4

4

0.4

1

0.1

5

0.4

5

0.4

4

0.4

4

0.4

1

0.1

5

0.4

5

0.4

4

0.4

4

0.4

1

0.1

5

po

we

r

Oth

er a

nd

E

lec

tric

ity

k

Wh

/Re

va

0

.05

0

.05

0

.05

0

.05

0

.02

0

.05

0

.05

0

.05

0

.05

0

.02

0

.05

0

.05

0

.05

0

.05

0

.02

li

gh

t

Ca

pti

ve

D

iese

l li

tre

s/R

e va

0

.01

n

eg

. n

eg

. 0

.00

3

0.0

02

0

.01

n

eg

. n

eg

. 0

.00

3

0.0

02

0

.01

n

eg

. n

eg

. 0

.00

3

0.0

02

p

ow

er

549

TABLE 7

Scenario results on annual mix of energy sources for different end-uses in the services and commercial sector in Delhi during 1985- 86

End-use Energy Unit Scenario source

I I I I I I

Street lighting Electricity kWh/person 8.00 8.00 8.00 Water works and Electricity kWh/person 39.81 39.81 39.81 sewage pumping Miscellaneous Electricity kWh]person 8.90 8.90 8.90 Commercial Electricity kWh/person 120.11 120.11 120.11 Others* Firewood kg/person - 0.03

LPG kg/person 2.86 2.86 - Kerosene litres/person - 5.90

*"Others" include (i) hotels and restaurants, (ii) hospitals, (iii) laundries, and (iv) any other establishment where all types of fuels are consumed. Where in the case of all other end-uses only electricity is consumed.

non-zero for the goal G1, is a loss. Both the goals G, and G2 are expressed in the same equation numbers 1 to 45. The appearance of a non-zero value for a positive deviational variable is a gain for goals G4, G5 and G~. These are expressed in equation numbers 46 to 80.

The optimum mix of different fuels required to meet G1 in the presence of G3 in the four major economic sectors of Delhi city, namely, domestic, passenger transport, manufacturing industry and services and commercial is esti- mated and presented separately in Tables 4- 7, respectively.

DISCUSSION AND CONCLUSIONS

The optimum annual requirements of eleven different fuels to meet the desirable sectoral end-use energy needs under the three scenar- ios are estimated and are presented in Table 8. Table 8 also gives the actual utilization of these fuels annually in Delhi during 1985-86.

The following major conclusions can be drawn from Tables 3 and 8: - - Actual utilization of diesel during 1985 - 86 in Delhi was 579 x 103kl which included diesel consumption by both passenger and freight vehicles, and also for captive genera- tion. But as the freight transport is not con- sidered in the model owing to limited data, it is estimated that for meeting only the passen- ger travel demand and captive power genera- tion, the diesel requirement across three scenarios ranges between 17% and 23%.

- -E lec t r i c i ty and petrol are required in greater quantities with respect to their actual utilization pattern in all the three scenarios. Actual utilization of electricity in Delhi dur- ing 1985- 86 was nearly 3.9 TWh. According to the model results, the annual requirement of electricity across scenarios is nearly 2.5 to 2.7 times more than the actual amount used. Sim- ilarly, annual utilization of petrol during 1985-86 was 205 x 103kl. But the scenario results show an excess requirement of petrol which is nearly 1.4 times more than was actually utilized.

- - According to scenario I, when energy budget goal G5 is assigned greater importance than pollution loading goal G6 followed by the other two goals, namely, energy import and over-utilization (denoted by G4 and G2 respec- tively), only six out of eleven fuels (actually used in Delhi during 1985- 86) are required for achieving sectoral end-use energy demand goal G1 completely in the presence of capacity goal G~. Moreover, the energy budget avail- able for transportation in low- and middle- income households is used up for meeting their travel demand. But an additional expen- diture is required by low- and middle-income households for fulfilling their domestic end- use energy demands. The same holds true in all the five types of industries considered in Delhi, where additional expenditure is re- quired for meeting the industrial end-uses. As far as the pollution loading is concerned, CO and NOx are below the safe loading level, and, in the case of SO2 and SPM, the safe loading level is crossed.

550

TABLE 8

Actual availability vis-a-vis optimum annual requirements* of different fuels under three different scenarios

Energy Unit Actual Scenario Source consumption

in 1985-86 I II III

Firewood tonne 340 0 0 340 (8.07) (7.50)

Charcoal tonne 51 0 0 51 (1.78) (1.65)

Soft coke tonne 109 465 0 109 (3.55) (14.04) (3.30)

Coal tonne 121 0 0 121 (2.69) (2.49)

LPG tonne 114 146 635 114 (6.73) (7.97) (34.98) (6.25)

Kerosene klitres 177 323 114 177 (9.74) (16.47) (5.86) (9.04)

Diesel klitres 579** 100 100 133 (31.39) (5.03) ( 5.07) (6.70)

Petrol klitres 205 293 281 279 (11.47) (15.17) (14.70) (14.50)

Furnace oil klitres 145 0 0 145 (7.60) (7.06)

Fuel oil klitres 3 0 0 3 (0.15) (0.14)

Electricity MWh 3986 10324 9772 10313 (16.83) (41.32) (39.39) (41.37)

Total Gcal 19921 21502 21352 21453 (100.00) (100.00) (100.00) (100.00)

*Figures outside parentheses are in thousands; figures within parentheses are expressed in percent. **Including diesel consumed in freight transport.

- - According to scenario II, when pollution loading goal G 6 is assigned greater importance than energy budget goal G 0 followed by the other two goals, namely, energy import and over-utilization (denoted by G4 and G2 respec- tively), only five out of eleven fuels (actually used in Delhi during 1985- 86) are required for achieving sectoral end-use energy demand goal G, completely in the presence of capacity goal G~. Moreover, the pollutant CO is well below the safe level and SPM is just below the safe level. NOx loading has coincided with the safe level, but SO2 has just exceeded the safe load- ing level. Since pollution loading is given greater importance than energy budget, it can be seen that energy budget is affected very badly and more so in the low-income house- holds for meeting domestic and travel needs. - -Accord ing to scenario III, when energy import goal G4 is given greater importance than energy budget goal G0 followed by the other two goals, namely, air pollution loading and over-utilization of energy goal (denoted by

G~ and G2 respectively), all the eleven fuels are required for achieving sectoral end-use energy demand goal G1 completely in the pres- ence of capacity goal G 3. Here, an excess of electricity is spent for some of the domestic end-uses than the desired level along with excess utilization of petrol/diesel in the trans- port sector. This has a negative impact on both G 0 and G~. - - Annual loading of CO in Delhi during 1985-86 in all the three scenarios (represent- ing a different type of decision environment) has not crossed the safe annual loading level of 255 x 103 tonnes.

The LGP model therefore determines the best mix of fuels required for meeting sec- toral end-use energy demands by minimizing the goal deviations from a number of goals, some of which are conflicting in nature. Fur- thermore, the model yields a different fuels mix each time depending upon the order in which these goals are assigned relative im- portance.

ACKNOWLEDGEMENTS

The authors express their deep gratitude to Dr. R. K. Pachauri, Director, Tata Energy Research Institute (TERI), New Delhi, for his encouragement and support during various discussions and to Ms. Sharmila Sengupta for editorial comments.

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