5 METHODOLOGY .1 Scope
5.2 Concordance as a Multiobjective Problem
We now recall some of t h e points m a d e in Section 1, and expand on t h e s e ideas using t h e concepts developed in subsequent sections. It was shown t h a t changes in p a t t e r n s of energy use have led t o a crisis in t h e supply of hydro- carbon feedstocks for t h e chemical industry. We suggest t h a t this problem could be overcome if t h e PDAs dependent on hydrocarbon feedstocks could adjust their industrial s t r u c t u r e t o follow changes in t h e availability of resources m o r e closely. Thus, we describe t h e fundamental problem as one of finding concordance between available resources and technologies (see also Gorecki and Kopytowski 1980, Gorecki e t al. 1982).
It h a s already been emphasized t h a t t h e problem of choosing the m o s t appropriate industrial s t r u c t u r e , given t h e available technologies, resources, and demand for products, c a n n o t be formulated as a single-criterion problem.
The single criterion m o s t frequently used i n this type of problem, maximiza- tion of profits, depends on financial estimates of the resources t o be invested in a given development program, a n d t h i s is clearly undesirable in view of t h e unstable economic situation and the rapidly changing prices of fossil resources. In addition, t h e increasing scarcity of these resources is encourag- ing decision m a k e r s to be less sjngle-minded in their pursuit of profits; they may wish to (simultaneously) minimize factors such a s resource consump- tion and environmental pollution while maximizing (siiy) output and profits.
Since t h e s e goals a r e a t least partially conflicting, some s o r t of multiobjec- tive procedure is required to find a n acceptable compromise solution. In t h e approach describeti here, each criterion is given in t e r m s of resources so t h a t t h e whole analysis takes place in resource space.*
Thus, we shall describe t h e s e a r c h for concordance a s a multiobjective decision problem. The e l e m e n t s involved in this process a r e :
*The book by Kendrick and Stoutjestijk (1978) on the planning of industrial investment pro- grams provides an extensive study of the methodological aspects of process-type models. Un- fortunately it is one of very few publications on the subject.
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a decision maker, who has to make a final choice from t h e alternatives"learns" from the system how changes in his preferences affect the results of t h e analysis.
In t h e particular case considered h e r e t h e idea is to help the decision maker learn how t h e estimated resources and t h e relevant s t a t e s of t h e model a r e related in criteria space. Each s t a t e of t h e model represents a par- ticular subset of available technologies together with a particular level of technology utilization. We a r e interested in those s t a t e s which belong t o the so-called Pareto-optimal s e t in criteria space. The concept of Pareto- optimality is illustrated in Figure 16. This figure shows the s e t of states (com- binations of technologies) t h a t can be attained u n d e r t h e conditions and con- feasible compromise solutions, and t h e quest for a satisfactory concordance between technologies and resources becomes an analysis of geometrical rela- tions.
Returning to our four elements of a multiobjective decision-making sys- t e m , we have t o transform t h r e e of t h e m into criteria, constraints, and objec-
The decision maker sometimes has to deal with considerable uncertainty in t h e data: examples include "apparent" availabilities of resources and estimated operating requirements for hypothetical plants based on new tech- nologies. However, the reliability of these two types of information is not t h e
Q I +max Set of Paretoaptimal states
Attainable
I \
statesof PDAv
Q p m i n
FIGURE 16 Attainable states and Pareto-optimal states of the PDA in criteria space.
was introduced and developed theoretically by Gorecki and his co-workers (Gorecki 1981, Gorecki e t a l . 1982). Without going i n t o detail, t h e method is based o n scalarization with r e s p e c t t o t h e "skeleton" of a n Admissible Demand S e t (ADS). The ADS is delimited by e s t i m a t e d ranges of t h e availabil- ity of c r i t i c a l resources, a n d t h e skeleton r e p r e s e n t s solutions which a r e equidistant from these limits. One of t h e m o r e useful features of t h e pro- cedure is t h a t it, enables t h e decision m a k e r t o evaluate t h e attainability of various e s t i m a t e s . This is discussed f u r t h e r (with reference t o Case 3 from Section 4.3) i n Section 5.6.
5.3 Methodological Implications of the General Model
A g e n e r a l model of a Production/Distribution Area was presented in Sec- tion 3 . 2 . We now analyze t h e methodological i m p l ~ c a t i o n s of t h i s model, tak- ing as a s t a r t i n g point t h e philosophy behind t h e m u l t i c r i t e r i a decision prob- l e m considered.
A decision m a k e r h a s t o have illformation o n t h e properties of t h e PDA network. The m a i n c h a r a c t e r i s t i c of t h e network is t h a t i t contains a finite r e p e r t o i r e of possibilities described in t e r m s of existing and possible (known) technologies, a n d this m e a n s t h a t t h e in:iormation available for e a c h model is r e s t r i c t e d by t h e supply of technological d a t a . I t is clear t h a t t h e accuracy of t h i s informatjon depends on t h e reliability of t h e information source. Given t h e availability of r e s o u r c e s a n d his goals or preferences, t h e decision m a k e r c a n e x p e r i m e n t with various combinations of technologies within this finite repertojre of possibilities. The decision m a k e r ' s range of options is limited f u r t h e r by consider.ation of critical r e s o u r c e s , technological constraints, and compleinentary o r auxiliary c o n s t r a i n t s .
These t h r e e categories are n o t specified formally i n t h e model b u t a r e defined by t h e decision m a k e r during t h e formulation of t h e decision
problem. Critical resources a r e those which a r e seen by t h e decision maker a s being particularly scarce or difficult to obtain; examples m a y be crude oil, manpower, energy, or capital. In practice t h e s e t of critical resources is also t h e s e t of criteria, since we try to find an optimal solution with respect t o all critical resources. Technological constraints a r e quite easily identifled and a r e related to factors such as production capacities and operating conditions.
All t h e other constraints in the model, such a s t h e demand for a particular product, t h e availability of (noncritical) raw materials, or prices, fall into t h e category of complementary or auxiliary constraints. t h e analysis should enable t h e decision maker to evaluate "initial conditions"
in t e r m s of critical resources. The o t h e r a r e a of t h e analysis should yield all kinds of m a r k e t information, supply forecasts and t h e like, a specific example being t h e coordination variables describing t h e coordinated sale and pur- chase of chemicals between various PDAs. This kind of information is included i n t h e form of auxiliary constraints i n t h e general model described i n the pre- vious sections. The technological analysis furnishes forecasts concerning t h e n a t u r e of t h e processes expected t o be developed, t h e date when they are strictly connected with its formal properties. It has strong implications for t h e solution of t h e problem and hence influences the methodology.
All t h e limitations (including constraints on critical resources) are taken t o be constraints in t h e linear programming problem. Thus, monotonic results can be obtained for each constraint separately (within its range of activity), assuming all other constraints to be inoperative. To show how this f e a t u r e may be incorporated in our methodology, we first consider two partic- nologies. The consequence of such a n "ideal" unrestricted availability of criti- cal resources is t h a t we may in fact optimize t h e PDA model with respect t o a single criterion such as economic efficiency or earnings. (It does not make sense t o optimize with respect t o something which is completely uncon- strained.) These two solutions therefore represent t h e best possible outcomes
for t h e smallest and largest repertoires o f technologies t h a t we shall con- single- or multiobjective problem corresponds t o a particular PDA structure and t o a particular s t a t e o f flow within t h a t s t r u c t u r e . T h e r e i s n o reason why
*This procedure. based on optimization of the ratio of effects to consumed resources, is well established theoretically (see Bellman 1961).
This leads t o t h e possibility of formulating t h e decision problem as a m i n i m a x problem based on performance ratios. For t h e sake of simplicity we usually c o n c e n t r a t e o n a s e t of ratios with a common denominator or n u m e r a t o r .
We should emphasize a t t h i s point t h a t t h e preceding discussion does not l i m i t t h e generality of t h e multiobjective problem formulation in any way. We have m e r e l y drawn methodological observations from t h e properties of the model and t h e problem of concordance described above, a n d pointed out t h e various ways i n which they c o u l d be used. The use of performance ratios i n t h e multiobjective problem is only one of t h e s e options.
5.4 The Attainable Performance Area and Critical Resource Area of a PDA