3.1 Toward a Formal Representation of the Problem Area
Our aim is t o c o n s t r u c t a model describing t h e production s t r u c t u r e of t h e chemical industry which could t h e n be used t o g e n e r a t e various develop- m e n t alternatives. In o r d e r t o do t h i s we have t o look a t t h e i n d u s t r y as a whole and identify t h e crucial featu.res t h a t m u s t be included in t h e model.
There h a s been m u c h r e s e a r c h on this topic. Our own r e s e a r c h goes back several years (see Borek e t al. 1978, 1979) a n d is still in progress (Dobrowolski e t al. 1982). Another approach t h a t leads t o very interesting r e s u l t s is described by S t a d t h e r r and Rudd (1976) a n d Sophos e t al. (1980). The book by Kendrick a n d Stoutjestijk (1978) also proposes an interesting alternative process-type model.
Chemical production c a n b e viewed basically a s a sequence of processes t h a t change certain s t a r t i n g m a t e r i a l s into end products t h a t a r e quantita- tively a n d qualitatively (physico-chemically) very different f r o m t h e i n p u t material. The flow of m a t e r i a l t h r o u g h t h e production process c a n be con- sidered continuous, even in t h e case of period.ic reactions. There a r e usually a n u m b e r of ways of producing a given compound, nlost of which involve n o t one reaction but. a whole chain of t h e m . The s a m e compound may be used in a n u m b e r of reactions i n any gjven production chain and may also be used in other chains; t h e s e chains therefore form a network. Compounds going into o r produced by reactions i n t h e middle of chains a r e called semiproducts or i n t e r m e d i a t e s , and t h e r e is a very large m a r k e t for t h e s e m a t e r i a l s within t h e chemical industry itself. However, i t m u s t be said t h a t t h i s m a r k e t depends greatly on t h e s t r e n g t h of t h e d e m a n d for final products.
Thus t h e industry, by its very n a t u r e , is composed of a g r e a t n u m b e r of e l e m e n t s t h a t a r e very strongly interdependent, both technologically and economically.
Consider Figure 6, which shows how t h e r e s o u r c e vector X may be mapped o n t o th.e d e m a n d vector Y in a given economic environment. The d e m a n d vector m a y e i t h e r be based on observed d a t a or modeled according t o some scenario. Using t h i s demand vector a n d assumiilg t h a t i t excludes
Processinq of boundaries, although t h e relative density of technological connection is perhaps one of t h e most important factors to be considered h e r e . Others include organizational factors a ~ d ~ n a r k e t , labor, maintenance, transport, and supply conditions.
In f a c t , PDAs often corresponti roughly t o t h e a r e a s of production covered by t h e individual large chemical companies; it makes sense for each company t o deal with a particular closely related group of chemicals because they c a n t h e n coordinate t h e flow of intermediates, feedstocks, etc. through a
most efficient production s t r u c t u r e for a given economic/social/political environment; b u t , since t h i s environment is constantly changing, the produc- tion s t r u c t u r e m u s t evolve t o keep pace with it. The companies t r y t o adapt t o t h e new conditions by selling old plant, investing in new plant, and reallocat- ing resources, b u t generally t h e change in production s t r u c t u r e lags behind t h e changes in operating conditions, leading t o a loss of efficiency and hence of profits. The scale of the problem is illustrated very clearly by t h e quotes from t h e press given in Section 2. One very i m p o r t a n t application of our PDA model could therefore be t o help in determining t h e best production s t r u c - t u r e for a n individual company under various operating conditions. In addi- tion, by adjusting the boundaries of t h e PDA i t is possible to determine how individual companies could broaden t h e i r range of activities m o s t effectively.
Of course, the s a m e s o r t of results c a n also be obtained for PDAs t h a t cross these company boundaries and involve activities intersecting with those of several established production groups.
It should be emphasized t h a t t h e simplified model of the PDA described in t h e n e x t section includes only t h e easily quantifiable physical elements of t h e system; i t does n o t a t t e m p t t o take into account t h e sometimes very i m p o r t a n t but unquantifiable social and political factors t h a t will affect any development decision. The relative importance of t h e s e factors c a n only be assessed by t h e decision m a k e r ; this is why i t is i m p o r t a n t to use a n i n t e r a c -
t i v e decision support system (see Section 5 ) in conjunction with this model.
3.2 General Model of a PDA
We regard t h e chemical industry as being divided into a n u m b e r of sub- sectors, e a c h dealing with a group of closely related chemicals. These subsec- t o r s a r e called Production/Distribution Areas (PDAs) because they basically comprise a network of productioil processes and distribution flows for a very specific group of chemicals. The PDAs a r e linked t o each o t h e r and t o o t h e r industrial sectors through t h e buying and selling of chemicals. Our general model of a PDA m u s t therefore take i n t o account:
-
t h e processing and flow of chemicals within t h e PUA;-
t h e flow of chemicals i n t o and o u t of o t h e r areas o r industries, representing t h e marketing or business activity of t h e PDA;-
t h e flow of investment, revenue, and o t h e r resources s u c h as energy, manpower, e t c .The model is given below in i t s basic form so t h a t i t s s t r u c t u r e may be more easily understood; however, t h e comp1.exity of t h e full computer imple- mentation should n o t be u n d e r e s t i m a t e d . We first define t h e links of t h e PDA with its environment (see Figure 7).
From Figure 7, we c a n write t h e following equation describing t h e outflow of any chemical j:
yms
+
Production1 Distribution
ymp j Area (PDA)
FIGURE: 7 The links between a Production/Distribution Area (PDA) and its environ- ment.
where
yjms
-
m a r k e t sale of chemical j yjmP - m a r k e t purchase of chemical j y? - coordinated sale of chemical j yFP - coordinated purchase of chemical jJ
-
s e t of indices representing t h e chemicals u n d e r consideration.Here we introduce t h e concept of a coordinated flow, i.e., agreed buying and selling of chemicals among PDAs. This makes i t possible to achieve some f o r m of inter-PDA coordination.
Note t h a t we cannot usually describe this coordination by t h e formal decomposition of a larger problem containing a n u m b e r of areas. This c a n be illustrated by t h e situation t h a t arises when t h e source of an intermediate is a different PDA: t h e second PDA may not be willing t o reveal t o t h e first all of t h e d a t a t h a t would be necessary for optimization over all t h e PDAs involved.
Resources other t h a n chemicals required for network activities a r e denoted in Figure 7 by q , and include inputs s u c h as energy, labor, a n d water.
The particular formulation of t h e performance functions depends on t h e strategy and policy adopted by t h e industry and does not influence our con- siderations until we are ready t o solve t h e optimization problem.
Now let u s briefly look a t t h e form of t h e production/distribution net- work within t h e PDA. The network is formed by two types of elements:
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process elements, which represent chemical processing;-
balance nodes, which r e p r e s e n t t h e total flow of a n y chemical j .We shall denote by J * t h e s e t of indices describing chemical processes taking place in t h e PDA under consideration.
I
Process Element PEk production level zk a production capacity jk. . . . .
FIGURE 8 Process element PEk and the associated variables and parameters.
The way in which the network i s c o n s t r u c t e d ensures t h a t all of t h e con- ditions concerning links to and from t h e environment are t a k e n into account, regardless of t h e number of process e l e m e n t s a n d balance nodes.
Let u s consider a process e l e m e n t P E k , k E J* (see Figure 8). The vari- ables used in Figure 8 may be defined a s follows:
zk
-
production level of PEk zk A-
production capacity of PEka j k z k - quantity of chemical j consumed by PEk b j k z k
-
quantity of chemical j produced by PEk qk ( z k )-
necessary resources.For t h e balance nodes we inay write a n equation of t h e following type:
y . =z+-2:
3 3 3 (2)
for each chemical j , where y j - total outflow of j z - total production of j zj 3-
-
total consumption of j.The network is coilstructed from process e l e m e n t s and balance nodes in a way t h a t reflects all of t h e technological corlnections p r e s e n t i n t h e system.
Of course, a process element may be connected to other process elements only through balance nodes.
Having defined t h e network, we rnay formulate t h e following equations:
Total production of chemical j :
Total consumption of chemical j
Substitution of (3) a n d (4) i n t o ( Z ) , a n d combination of t h e r e s u l t with (1) l e a d s t o
To complete this somewhat simplified description of t h e i n t e r n a l PDA net- work, we have t o add t h e c o n s t r a i n t s imposed by production capacity. The form of t h e s e constraints will depend on t h e type of c h e m i c a l process con- c e r n e d , a n d m a y , for example, include a n u m b e r of alternative technologies.
The idea of new technologies is fundamental t o t h i s approach since i t opens t h e way t o technological change in t h e s t r u c t u r e of t h e a r e a . (Data on all r e l e v a n t new technologies a r e included i n t h e p a r a m e t e r s e t discussed i n Sec- tion 2.)
Note t h a t t h e version of t h e model implemented describes all possible modes of production, including alternative r a n g e s of products made a t a given installation, recycling of semiproducts, a n d coupled production of a n u m b e r of chemicals a t o n e plant.
This model provides u s with a basis for formulating decision problems c o n c e r n e d with t h e generation of efficient development alternatives for a PDA. I t is obviously necessary to add a s e t of c r i t e r i a a n d some additional con- s t r a i n t s reflecting t h e preferences or goals of t h e decision maker a s well a s physical l i m i t s on resource availability, a n d this generally leads t o t h e formu- lation of a multiobjective optimization problem.