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Knowledge representation for problem processing in a decision support system
EngngApplic.Artif. lntell. Vol.6, No. 4, pp, 381-386,1993 Printed in Great Britain
0952-1976/93$6.00+0.00 PergamonPressLtd
Brief Paper Knowledge Representation for Problem Processing in a Decision Support System WANG MENGGUANG Northeastern University, Shenyang LIU ZHINING Northeastern University, Shenyang YANG ZIHOU Northeastern University, Shenyang
(Received February 1990; in revised form November 1992) This paper examines the position and function of a "problem processing system" (PPS) in the context of a decision support system (DSS), and proposes a relatively complete framework for such a problem processing system. Using the concept of a "problem processing mode", the paper introduces further research into the so-called "representation of procedural knowledge", and presents a generalized structure for PPSs. This structure has been used in specific problem processing in a productionplanning context. Keywords: DSS, PPS, problem-processing mode. 1. INTRODUCTION
• processing the user's requirements.
The study and development of decision support systems is a very interesting field of computer applications. The historical evolution from electronic data processing, through management information systems, to decision support systems has been described in the literature, t-3 Alter et al. 4 have pointed to the classification of decision support systems into two main groups; dataoriented and model-oriented systems. In addition, recent developments in decision support systems appear to involve the use of artificial intelligence; 6-7 these systems might well be referred to as "intelligenceoriented" or "knowledge-oriented" systems. Most systems combine the above three types. The idea of a "problem processing system" being an important component of a decision support system was first proposed by Bonczek, s who introduced the concept of a "problem processor" into the "generalized intelligent decision support system" (GIDSS), 9 as shown in Fig. 1. In the decision support system, the functions of problem processing involve:
Until now, only the preliminary idea of a problem processing system has been presented in various papers, referring to decision support systems, but specific research and practical applications are limited. This paper presents the complete framework and generalizes the structure of a problem processing system, and includes the knowledge of the problem processing mode within the design of such a system. The function of the problem processing system is described in this paper, in terms of a business management decision support system, to be developed for an application in a medium-scale iron/steel plant. The decision support system is implemented by a local network system of microcomputers. The functional Decision +
I
• recognizing the user's problem (perception), • co-ordinating the system resources (information base), and
I Problmn
Correspondence should be sent to: Wang Mengguang, Department of Automatic Control, Northeastern University, P.O. Box 135, 110006 Shenyang, P. R. China. 381
Perception
I PI'OC,I~SOr]
QUERY PROCESSOR
Fig. I. R. H. Bonczck'sGIDSS structure (simplified).
382
W A N G M E N G G U A N G eta/.: PROBLEM PROCESSING SYSTEM -tl. Plant director inquiry sub - system [
2. GENERAL CONCEPTS OF PROBLEM PROCESSING SYSTEMS
"~2o p|mnningmamagement sub - s y l t e m I
The key problem in designing a decision support system has the following two aspects:
"~3. Production manapmwat tub - system I
• understanding the decision problem (or the decision-maker's attempts at making a decision), and • the actual processing of the decision problem.
--~4. Finance manapmem sub - mystem ] --~5. Sales m a n a l B ~ t sub - system [
2.1. The decision problem Previous authors ~°have postulated that the decisionmaking problem can be summed up as the execution of the following three operations:
---J6. Bqu/pment mlmagem-.nt sub - syatem J ---[7. Goods and materials supply sub - aysmm J
• problem recognition, • making the meta-decision, and • making the specific decision.
"--[8. Quality msuapm~at sub - system J Fig. 2. New Fushun steel plant DSS.
structure of the decision support system is shown in Fig. 2. In the intelligent decision support system, based on the processing of business management information, the system gives powerful support to significant decision-making, for example, the formulation of development planning, scheduling of production, determination of the optimal mix of products, and the optimal distribution of energy and other resources, etc. Therefore the intelligent decision support system has been designed with the logical system structure shown in Fig. 3. The main functions of the problem processing system within the intelligent decision support system include: • generating the processing mode when necessitated by the problems of the user, • co-ordinating the system's various resources, and • co-ordinating the various functions which are used to operate the system as a whole. The introduction of the problem processing system enables the sub-systems to act independently of each other, and gives the decision support system the flexibility required for developing and adapting to varying conditions.
"Meta-decision" means the choice of strategy used to make the specific decision. Regarding the contents of the decision activity, Simon '1 proposed a four-stage strategy of decisionmaking: 1. 2. 3. 4.
Intelligence (information). Design. Choice (judgement). Review.
Of the four stages, the decision making mainly involves the first three. The four-stage strategy may be called the "Simon" mode. Generally, a typical decision problem cannot be described as a "simple" Simon mode. Logically, it should first be partioned into two stages: the meta-decision and the specific decision. The metadecision is also a decision problem; therefore, either the meta-decision or the specific decision can be described as a "Simon" mode.
2.2. Problem-processing mode In order to introduce the problem-processing mode, the concept of a "decision mode" must first be presented. The so-called "decision mode" means the practical decision strategy which is used by a decisionmaker in some specific circumstances. The decision mode involves the whole process of decision; it is the
User interface ] [Problem processor[
( I Data base management system 1
I Model base management system
Fig. 3. The logical structure of IDSS.
t
Knowledse management system . I
WANG MENGGUANG et al. : PROBLEM PROCESSING SYSTEM
383
4. An artificial-intelligence approach. ~2
I recognition Problem I
[ Meta -problem I recognition
Generating system
Meta - inference~ _ ~ engine
Meta-processing [ mode J
1
I Infe~;rnc¢ ['~-~Pr---oblemm°PdrOCeS-~si~g [
I ,o,o=:oo I Fig. 4. The general structure of the PPS. framework of the decision-making behavior. Each decision-maker always follows some modes, consciously or unconsciously, in a decision-making process. There will be a definite decision mode for a structured decision problem, but for an ill-structured or semi-structured decision problem, a fuzzy decision mode will be employed. The designer of a decision support system must consider how to map the "decision mode" into a method of problem processing. This mapping, corresponding to the results of the decision mode in the computer system, is called the "problemprocessing mode". In order to obtain this problem-processing mode, negotiation is needed between the decision maker or user, and the designer. In this way, the designer will understand the objectives of the decision maker, and will take them into account in the problem processing, and in its computer implementation. 3. GENERAL STRUCTURE OF THE PROBLEM PROCESSING SYSTEM, AND A GENERAL
PROCESSING STRATEGY Based on the concept of the problem processing mode outlined above, the general structure of a problem processing system can be constructed as shown in Fig. 4. It is made up of the problem-solving mode, intelligent coordination and inference. The structure is based on the following considerations: 1. The concept of the problem processing mode. 2. The idea of an "intelligent coordinator". 3. The possibility of computer implementation and the generality of the structure.
In this structure, the problem processing mode is the centre of the whole problem processing system. The knowledge used in the problem processing mode is a specialized case of that used in the decision mode. Problem processing is considered to be a type of decision problem, so it can also be partioned into the problems of so-called "special processing" and "metaprocessing". The "generating system" of the problem processing mode corresponds to meta-processing, and includes meta-problem recognition, the meta-inference engine and the meta-processing mode. In Fig. 4: • The information base stores domain data or domain knowledge in some form. • The active blocks are special or general function blocks, used for some model, algorithm, data input, report output, etc. • The system monitor assists the inference engine to use the "mode knowledge". A decision can be understood as a sequence of activities, where the order of activities shows the following characteristics: 1. "Branch" characteristics: the results of a preliminary activity control the choice of the next activity. 2. "Circulating" characteristics: some activities circulate in sequence in implemented order. 3. "Stochastic" characteristics: an activity which results from a previous activity is stochastic. A simple decision problem is composed of a simple combination of decision behaviors; a complex decision problem is composed of a complicated combination of the hierachical sequences. Corresponding to the sequence of decision activities, problem processing also has a sequence. This is called the "problem structure", where each simple operation is a single step. Therefore, the problem structure provides an appropriate problem processing mode. In the knowledge base of the problem processing mode, one rule corresponds to one combination of condition of implementation, and resulting state. Each operation and implementation of a single step relies on the corresponding active block. The knowledge of the problem processing mode is represented by the hierarchical frame combination. Each piece of knowledge in the frame corresponds to one state (the resulting state of some single step), and many slot-values of the frame describe the conditions for entering the state and the operations which result in the state. A problemprocessing process is realized by using the related combination of frame-slot-value, that is, a hierarchical sequence combination. The method can therefore be summed up as a procedural representation method based on state relations.
384
WANG MENGGUANG
: PROBLEM PROCESSING SYSTEM
e t al.
x; + x;> hj
4. P R O B L E M PROCESSING FOR THE
FORMULATION OF PRODUCTION PLANNING In the practical DSS shown in Figs 2 and 3, the PPS is used to generate a problem processing mode to solve the decision problem according to the decision demands of the user, to co-ordinate the system's various resources, and to co-ordinate the various functions which are used to operate the system as a whole. The PPS, being a shared part of the system, is located in the server of the network. In the DSS, the useful functions of decision support include formulating a year's production planning and formulating monthly planning, etc. It is one of the system's functions which can provide powerful support for the formulation of production planning. The purpose of formulating a year's production planning is to determine the optimal product mix, which means determining, under the limitations of full utilization of resources, what kinds of steel product are needed, and what quantities should be made. In this decision activity, the problem processing mode of the system is also a hierarchical sequence combination. Formulating the year's production planning is based on the linear programming model, the goal programming model, and a fuzzy synthetical evaluation model. In these, the host model is linear programming (LP), with the following mathematical formulae: max
c) /2 cjxj+ 2,;] it
(1)
aqx;+
aqxT<~bi
(2)
t
t
f
subject to
j=l
j=l
i = 1,2, 3,4,5
~ a6jx;<~b6
(3)
j=l
~ aTjx~'~b7
(8)
j=l ..... n
x;+x;' gj
(9)
j=l ..... n x;~ > 0, x;~ 0
(10)
j = l . . . . ,n where n is the number of possible product varieties, x;, x~'express the jth kind of product which is produced by the steel of the electrical furnace and of the converter (unit:ton). For expression (1), the objective function is profit, where c;, and c~' express the profit coefficient of each corresponding product. Expression (2) expresses the constraints of the five rolling mills' capabilities (unit:h). Expression (3) gives the capability constraints of the electric furnace (unit:h). Expression (4) gives the capability constraints of the converter (unit: h). Expression (5) gives the capability constraints of sintering and iron-smelting (unit:ton). Expression (6) gives the constraints of the energy resources (electricity, coal, oil, coke) and raw materials (scrap steel, concentrate powder) (unit: ton; kwh). Expression (7) shows total output constraints. Expression (8) gives the lower boundaries of quantities of various products. Expression (9) gives the upper boundaries of quantities of various products. In the application in the New Fushun Steel Plant, the scale of the model can include 400 variables and 416 constraints; it is therefore very large. In order to simplify the above model, 2 was defined as the proportion of products produced by the electric furnace ingot, and (1 - 2 ) as the proportion of products produced by the converter ingot. There, the quantity of each kind of product is a variable, so (2) is also a variable.
(4)
max
j=l
CO)x
(11)
subject to
~abx'j+~ai;x;'~bi j=~
(5)
j=l
i=8,9 (6) j=l
j=l
(7) j=l
(12)
g~x<<.h
(13)
0~<2~<1
(14)
C(2) = c' + (1 - 2)c" a(2) =2,4' + (1-2)A".
i = 10 . . . . . 15
j=l
A(2)x ~
After the simplification, the scale of the model was greatly reduced, and now has only 16 constraints and 201 variables. However, model equations (11)-(14) become the nonlinear model, because 2 is also a vari-
WANG MENGGUANG
et al. : PROBLEM
PROCESSING SYSTEM
385
maxf(~)
subject to o
~ (7.) ~ 1
I Determining approach of solving the problem [
I D'spIa': 1: single-step;
muC(~)x
2: string
I
aubjectt o
A(~.)x~b 8~x~h
Fig. 5. The two-level hierarchical algorithm.
Operating
I able. It can still be solved as an LP problem if the decomposition-co-ordination approach shown in Fig. 5 (the two-level hierarchical algorithm) is used. In the lower level, the LP problem whose ft is given in some values is solved by adopting the simplex algorithm for bounded variables. In the upper level, the problem is one-dimensional. The purpose is to find the optimal value of ft. Theoretically, this is an LP problem under the conditions where a solution will always exist. In practice, however, when a practical model is built, a solution of the LP model does not exist because some constraints may be contradictory. Therefore, in this system, when the solution of the LP model does not exist, the model will be translated into goal programming because the solution of goal programming always exists, and is used to correct the right side of each constraint. The fuzzy synthetical evaluation model is used to evaluate various optimal schemes which can help the decision-maker in making the right choice. The basic decision support procedure for formulating a year's planning is shown in Fig. 6. This basic procedure can be partitioned into three stages: generating the problem, determining a solution approach and solving the problem. These are carried out under PPS. The approach to a solution includes two types: singlestep operation and string operation. Under single-step operation, the system displays the functions of the various steps to the user, and then despatches the corresponding modules after the user has made choices. In order to prevent a situation where, when one step is not carried out, the following step is chosen, the system sets the functions of break-point processing and of state protection. Under string operation, the system first finds the knowledge needed, and then strings the problem-solving steps in order. Then the corresponding functional modules are called to run in an orderly way by the PPS. The above three stages can be further partitioned into seven steps: 1. 2. 3. 4. 5.
Input of the original data. Enquiry and updating of the original data. Generation of the planning model. Solution of the model. Evaluation of the solution and updating the model.
G:nlrant~ the prUjblem
I
Finding the first step in the sequence
[
Operating the step
I
single -step approach
I
step I I
Fig. 6. The basic decision support procedure for formulating a year's planning. 6. Evaluation of alternatives. 7. Result reporting. Under the coordination of the PPS, each of the above items can be either one step of the whole process, or an independent service to the user. These seven steps consist of the upper-level sequence of problem processing, but some among them (such as "solving the model") can be extended to a problem processing sequence in the next level, that is: (1) Solve the model that is generated automatically. If it has a solution then go to (4); otherwise go to (2). (2) First, adjust the proportion of products produced by the electric furnace and by the converter, updating the LP model, and then go to (1). If the parameter cannot be adjusted, for example, if the capability of the equipment is limited, then go to (3). (3) Formulate the goal programming model according to the LP model; to solve the model, find a scheme for adjusting the constraints on the LP model; modify the LP model, and go to (1) (4) Based on the optimal solution, balance the capacities among the different mills in the different shops, and finally, obtain the alternative plan.
386
WANG MENGGUANG et aL : PROBLEM PROCESSING SYSTEM
The knowledge representation of the PPS adopts a frame structure : K n o w l e d g e f r a m e = Structure + Sign + Condition + Corn + F1 + F2 + Introduction + D o n e , in which: Structure involves two types of control: (1) If the solution of the optimal problem exists, quit the level of "solving the model" and go back to the u p p e r level. (2) In cyclic control, after each single step is carried out, the corresponding next single step follows. Sign is a m a r k used to label the choice between "condition" and "carry out", and includes two types:
(1) "If" shows that the single step is a conditional step; (2) "Direct" shows that the single step is a nonconditional step. Condition is the condition of "Rule". C o m is the sequence n u m b e r of the general module. F1 is the name of the operating step. F2 is the label m a r k for operating, which includes:
(1) " d o " , according to the c o m m a n d file ".prg"; (2) "run", according to the executable file ".exe"; (3) "and", according to the macro-substitution pattern. Introduction denotes a single step. D o n e marks that a single step has been carried out. U n d e r PPS, the knowledge of the problem processing m o d e is searched; the searching process is controlled by using the structure controlled slot value.
5. C O N C L U S I O N This p a p e r describes the PPS conceptually and in practice in a DSS, and presents a general structure,
which is obtained by considering the decision as an activity sequence composed of single steps. Furthermore, it provides the so-called "state-based representation of procedural knowledge". Finally, this general structure has been used in problem processing in a production-planning environment.
REFERENCES 1. Bonczek R. H. et al. The evolving role of models in DSS.
Decision Support System--A Data-based, Model Oriented Developed Discipline, pp. 343-370. PetroceUi Books, New York
(1983). 2. Sprague R. S. et al., Bit by bit: toward decision support systems. Decision Support System--A Data-based, Model-oriented User-developed Discipline pp.15-32. Petrocelli Books, New York (1983). 3. Sprague R. H. A framework for development of decision support systems. Decision Support System--A Data-base, Model-oriented User-developed Discipline, pp. 85-124. Petrocelli Books, New York (1983). 4. Alter S. et al. A taxonomy of decision support systems. Decision Support System--A Data-based, Model-oriented User-developed Discipline, pp. 33-56. Petrocelli Books, New York (1983). 5. Zhang Zhongjun and Yang Jianpo. Theory and its application of decision support system. System Engng V, (6), 1-9 (In Chinese). 6. Schneider H. J. The DSS based on the knowledge. Comput. Sci. 2, 9-15 (1988) (in Chinese). 7. Sen A. and Biswas G. Decision support systems approach. Decision Support Syst. !, 9-15 (1985). 8. Bonczek R. H. et al. The evolution from Mis to DSS, extension of data management to model management. Decision Support System-Proceedings of the NYU symposium on DSS, pp. 61-78. North Holland, Amsterdam (1982). 9. Bonczek R. H. et al. Computer-based support of organization decision making. Decision Support System--A Data-based, Model Oriented Developed Discipline, pp. 29-324. Petrocelli Books, New York (1983). 10. Liu Chuandong. The study of Production and Management Decision Support System of lntegralized Oil Refinery Plant. Doctorial thesis, Dalian University of Science and Engineering (1989). 11. Simon H. A. The New Science of Management Decision. Prentice-Hall, Englewood Cliffs, NJ. (1982). (Translation in Chinese by publishing house of social science.) 12. Fu Jingxun. Artificial Intelligence and Its Applications. Qinghau Publishing Agency, Beijing (1987).
0952-1976/93$6.00+0.00 PergamonPressLtd
Brief Paper Knowledge Representation for Problem Processing in a Decision Support System WANG MENGGUANG Northeastern University, Shenyang LIU ZHINING Northeastern University, Shenyang YANG ZIHOU Northeastern University, Shenyang
(Received February 1990; in revised form November 1992) This paper examines the position and function of a "problem processing system" (PPS) in the context of a decision support system (DSS), and proposes a relatively complete framework for such a problem processing system. Using the concept of a "problem processing mode", the paper introduces further research into the so-called "representation of procedural knowledge", and presents a generalized structure for PPSs. This structure has been used in specific problem processing in a productionplanning context. Keywords: DSS, PPS, problem-processing mode. 1. INTRODUCTION
• processing the user's requirements.
The study and development of decision support systems is a very interesting field of computer applications. The historical evolution from electronic data processing, through management information systems, to decision support systems has been described in the literature, t-3 Alter et al. 4 have pointed to the classification of decision support systems into two main groups; dataoriented and model-oriented systems. In addition, recent developments in decision support systems appear to involve the use of artificial intelligence; 6-7 these systems might well be referred to as "intelligenceoriented" or "knowledge-oriented" systems. Most systems combine the above three types. The idea of a "problem processing system" being an important component of a decision support system was first proposed by Bonczek, s who introduced the concept of a "problem processor" into the "generalized intelligent decision support system" (GIDSS), 9 as shown in Fig. 1. In the decision support system, the functions of problem processing involve:
Until now, only the preliminary idea of a problem processing system has been presented in various papers, referring to decision support systems, but specific research and practical applications are limited. This paper presents the complete framework and generalizes the structure of a problem processing system, and includes the knowledge of the problem processing mode within the design of such a system. The function of the problem processing system is described in this paper, in terms of a business management decision support system, to be developed for an application in a medium-scale iron/steel plant. The decision support system is implemented by a local network system of microcomputers. The functional Decision +
I
• recognizing the user's problem (perception), • co-ordinating the system resources (information base), and
I Problmn
Correspondence should be sent to: Wang Mengguang, Department of Automatic Control, Northeastern University, P.O. Box 135, 110006 Shenyang, P. R. China. 381
Perception
I PI'OC,I~SOr]
QUERY PROCESSOR
Fig. I. R. H. Bonczck'sGIDSS structure (simplified).
382
W A N G M E N G G U A N G eta/.: PROBLEM PROCESSING SYSTEM -tl. Plant director inquiry sub - system [
2. GENERAL CONCEPTS OF PROBLEM PROCESSING SYSTEMS
"~2o p|mnningmamagement sub - s y l t e m I
The key problem in designing a decision support system has the following two aspects:
"~3. Production manapmwat tub - system I
• understanding the decision problem (or the decision-maker's attempts at making a decision), and • the actual processing of the decision problem.
--~4. Finance manapmem sub - mystem ] --~5. Sales m a n a l B ~ t sub - system [
2.1. The decision problem Previous authors ~°have postulated that the decisionmaking problem can be summed up as the execution of the following three operations:
---J6. Bqu/pment mlmagem-.nt sub - syatem J ---[7. Goods and materials supply sub - aysmm J
• problem recognition, • making the meta-decision, and • making the specific decision.
"--[8. Quality msuapm~at sub - system J Fig. 2. New Fushun steel plant DSS.
structure of the decision support system is shown in Fig. 2. In the intelligent decision support system, based on the processing of business management information, the system gives powerful support to significant decision-making, for example, the formulation of development planning, scheduling of production, determination of the optimal mix of products, and the optimal distribution of energy and other resources, etc. Therefore the intelligent decision support system has been designed with the logical system structure shown in Fig. 3. The main functions of the problem processing system within the intelligent decision support system include: • generating the processing mode when necessitated by the problems of the user, • co-ordinating the system's various resources, and • co-ordinating the various functions which are used to operate the system as a whole. The introduction of the problem processing system enables the sub-systems to act independently of each other, and gives the decision support system the flexibility required for developing and adapting to varying conditions.
"Meta-decision" means the choice of strategy used to make the specific decision. Regarding the contents of the decision activity, Simon '1 proposed a four-stage strategy of decisionmaking: 1. 2. 3. 4.
Intelligence (information). Design. Choice (judgement). Review.
Of the four stages, the decision making mainly involves the first three. The four-stage strategy may be called the "Simon" mode. Generally, a typical decision problem cannot be described as a "simple" Simon mode. Logically, it should first be partioned into two stages: the meta-decision and the specific decision. The metadecision is also a decision problem; therefore, either the meta-decision or the specific decision can be described as a "Simon" mode.
2.2. Problem-processing mode In order to introduce the problem-processing mode, the concept of a "decision mode" must first be presented. The so-called "decision mode" means the practical decision strategy which is used by a decisionmaker in some specific circumstances. The decision mode involves the whole process of decision; it is the
User interface ] [Problem processor[
( I Data base management system 1
I Model base management system
Fig. 3. The logical structure of IDSS.
t
Knowledse management system . I
WANG MENGGUANG et al. : PROBLEM PROCESSING SYSTEM
383
4. An artificial-intelligence approach. ~2
I recognition Problem I
[ Meta -problem I recognition
Generating system
Meta - inference~ _ ~ engine
Meta-processing [ mode J
1
I Infe~;rnc¢ ['~-~Pr---oblemm°PdrOCeS-~si~g [
I ,o,o=:oo I Fig. 4. The general structure of the PPS. framework of the decision-making behavior. Each decision-maker always follows some modes, consciously or unconsciously, in a decision-making process. There will be a definite decision mode for a structured decision problem, but for an ill-structured or semi-structured decision problem, a fuzzy decision mode will be employed. The designer of a decision support system must consider how to map the "decision mode" into a method of problem processing. This mapping, corresponding to the results of the decision mode in the computer system, is called the "problemprocessing mode". In order to obtain this problem-processing mode, negotiation is needed between the decision maker or user, and the designer. In this way, the designer will understand the objectives of the decision maker, and will take them into account in the problem processing, and in its computer implementation. 3. GENERAL STRUCTURE OF THE PROBLEM PROCESSING SYSTEM, AND A GENERAL
PROCESSING STRATEGY Based on the concept of the problem processing mode outlined above, the general structure of a problem processing system can be constructed as shown in Fig. 4. It is made up of the problem-solving mode, intelligent coordination and inference. The structure is based on the following considerations: 1. The concept of the problem processing mode. 2. The idea of an "intelligent coordinator". 3. The possibility of computer implementation and the generality of the structure.
In this structure, the problem processing mode is the centre of the whole problem processing system. The knowledge used in the problem processing mode is a specialized case of that used in the decision mode. Problem processing is considered to be a type of decision problem, so it can also be partioned into the problems of so-called "special processing" and "metaprocessing". The "generating system" of the problem processing mode corresponds to meta-processing, and includes meta-problem recognition, the meta-inference engine and the meta-processing mode. In Fig. 4: • The information base stores domain data or domain knowledge in some form. • The active blocks are special or general function blocks, used for some model, algorithm, data input, report output, etc. • The system monitor assists the inference engine to use the "mode knowledge". A decision can be understood as a sequence of activities, where the order of activities shows the following characteristics: 1. "Branch" characteristics: the results of a preliminary activity control the choice of the next activity. 2. "Circulating" characteristics: some activities circulate in sequence in implemented order. 3. "Stochastic" characteristics: an activity which results from a previous activity is stochastic. A simple decision problem is composed of a simple combination of decision behaviors; a complex decision problem is composed of a complicated combination of the hierachical sequences. Corresponding to the sequence of decision activities, problem processing also has a sequence. This is called the "problem structure", where each simple operation is a single step. Therefore, the problem structure provides an appropriate problem processing mode. In the knowledge base of the problem processing mode, one rule corresponds to one combination of condition of implementation, and resulting state. Each operation and implementation of a single step relies on the corresponding active block. The knowledge of the problem processing mode is represented by the hierarchical frame combination. Each piece of knowledge in the frame corresponds to one state (the resulting state of some single step), and many slot-values of the frame describe the conditions for entering the state and the operations which result in the state. A problemprocessing process is realized by using the related combination of frame-slot-value, that is, a hierarchical sequence combination. The method can therefore be summed up as a procedural representation method based on state relations.
384
WANG MENGGUANG
: PROBLEM PROCESSING SYSTEM
e t al.
x; + x;> hj
4. P R O B L E M PROCESSING FOR THE
FORMULATION OF PRODUCTION PLANNING In the practical DSS shown in Figs 2 and 3, the PPS is used to generate a problem processing mode to solve the decision problem according to the decision demands of the user, to co-ordinate the system's various resources, and to co-ordinate the various functions which are used to operate the system as a whole. The PPS, being a shared part of the system, is located in the server of the network. In the DSS, the useful functions of decision support include formulating a year's production planning and formulating monthly planning, etc. It is one of the system's functions which can provide powerful support for the formulation of production planning. The purpose of formulating a year's production planning is to determine the optimal product mix, which means determining, under the limitations of full utilization of resources, what kinds of steel product are needed, and what quantities should be made. In this decision activity, the problem processing mode of the system is also a hierarchical sequence combination. Formulating the year's production planning is based on the linear programming model, the goal programming model, and a fuzzy synthetical evaluation model. In these, the host model is linear programming (LP), with the following mathematical formulae: max
c) /2 cjxj+ 2,;] it
(1)
aqx;+
aqxT<~bi
(2)
t
t
f
subject to
j=l
j=l
i = 1,2, 3,4,5
~ a6jx;<~b6
(3)
j=l
~ aTjx~'~b7
(8)
j=l ..... n
x;+x;' gj
(9)
j=l ..... n x;~ > 0, x;~ 0
(10)
j = l . . . . ,n where n is the number of possible product varieties, x;, x~'express the jth kind of product which is produced by the steel of the electrical furnace and of the converter (unit:ton). For expression (1), the objective function is profit, where c;, and c~' express the profit coefficient of each corresponding product. Expression (2) expresses the constraints of the five rolling mills' capabilities (unit:h). Expression (3) gives the capability constraints of the electric furnace (unit:h). Expression (4) gives the capability constraints of the converter (unit: h). Expression (5) gives the capability constraints of sintering and iron-smelting (unit:ton). Expression (6) gives the constraints of the energy resources (electricity, coal, oil, coke) and raw materials (scrap steel, concentrate powder) (unit: ton; kwh). Expression (7) shows total output constraints. Expression (8) gives the lower boundaries of quantities of various products. Expression (9) gives the upper boundaries of quantities of various products. In the application in the New Fushun Steel Plant, the scale of the model can include 400 variables and 416 constraints; it is therefore very large. In order to simplify the above model, 2 was defined as the proportion of products produced by the electric furnace ingot, and (1 - 2 ) as the proportion of products produced by the converter ingot. There, the quantity of each kind of product is a variable, so (2) is also a variable.
(4)
max
j=l
CO)x
(11)
subject to
~abx'j+~ai;x;'~bi j=~
(5)
j=l
i=8,9 (6) j=l
j=l
(7) j=l
(12)
g~x<<.h
(13)
0~<2~<1
(14)
C(2) = c' + (1 - 2)c" a(2) =2,4' + (1-2)A".
i = 10 . . . . . 15
j=l
A(2)x ~
After the simplification, the scale of the model was greatly reduced, and now has only 16 constraints and 201 variables. However, model equations (11)-(14) become the nonlinear model, because 2 is also a vari-
WANG MENGGUANG
et al. : PROBLEM
PROCESSING SYSTEM
385
maxf(~)
subject to o
~ (7.) ~ 1
I Determining approach of solving the problem [
I D'spIa': 1: single-step;
muC(~)x
2: string
I
aubjectt o
A(~.)x~b 8~x~h
Fig. 5. The two-level hierarchical algorithm.
Operating
I able. It can still be solved as an LP problem if the decomposition-co-ordination approach shown in Fig. 5 (the two-level hierarchical algorithm) is used. In the lower level, the LP problem whose ft is given in some values is solved by adopting the simplex algorithm for bounded variables. In the upper level, the problem is one-dimensional. The purpose is to find the optimal value of ft. Theoretically, this is an LP problem under the conditions where a solution will always exist. In practice, however, when a practical model is built, a solution of the LP model does not exist because some constraints may be contradictory. Therefore, in this system, when the solution of the LP model does not exist, the model will be translated into goal programming because the solution of goal programming always exists, and is used to correct the right side of each constraint. The fuzzy synthetical evaluation model is used to evaluate various optimal schemes which can help the decision-maker in making the right choice. The basic decision support procedure for formulating a year's planning is shown in Fig. 6. This basic procedure can be partitioned into three stages: generating the problem, determining a solution approach and solving the problem. These are carried out under PPS. The approach to a solution includes two types: singlestep operation and string operation. Under single-step operation, the system displays the functions of the various steps to the user, and then despatches the corresponding modules after the user has made choices. In order to prevent a situation where, when one step is not carried out, the following step is chosen, the system sets the functions of break-point processing and of state protection. Under string operation, the system first finds the knowledge needed, and then strings the problem-solving steps in order. Then the corresponding functional modules are called to run in an orderly way by the PPS. The above three stages can be further partitioned into seven steps: 1. 2. 3. 4. 5.
Input of the original data. Enquiry and updating of the original data. Generation of the planning model. Solution of the model. Evaluation of the solution and updating the model.
G:nlrant~ the prUjblem
I
Finding the first step in the sequence
[
Operating the step
I
single -step approach
I
step I I
Fig. 6. The basic decision support procedure for formulating a year's planning. 6. Evaluation of alternatives. 7. Result reporting. Under the coordination of the PPS, each of the above items can be either one step of the whole process, or an independent service to the user. These seven steps consist of the upper-level sequence of problem processing, but some among them (such as "solving the model") can be extended to a problem processing sequence in the next level, that is: (1) Solve the model that is generated automatically. If it has a solution then go to (4); otherwise go to (2). (2) First, adjust the proportion of products produced by the electric furnace and by the converter, updating the LP model, and then go to (1). If the parameter cannot be adjusted, for example, if the capability of the equipment is limited, then go to (3). (3) Formulate the goal programming model according to the LP model; to solve the model, find a scheme for adjusting the constraints on the LP model; modify the LP model, and go to (1) (4) Based on the optimal solution, balance the capacities among the different mills in the different shops, and finally, obtain the alternative plan.
386
WANG MENGGUANG et aL : PROBLEM PROCESSING SYSTEM
The knowledge representation of the PPS adopts a frame structure : K n o w l e d g e f r a m e = Structure + Sign + Condition + Corn + F1 + F2 + Introduction + D o n e , in which: Structure involves two types of control: (1) If the solution of the optimal problem exists, quit the level of "solving the model" and go back to the u p p e r level. (2) In cyclic control, after each single step is carried out, the corresponding next single step follows. Sign is a m a r k used to label the choice between "condition" and "carry out", and includes two types:
(1) "If" shows that the single step is a conditional step; (2) "Direct" shows that the single step is a nonconditional step. Condition is the condition of "Rule". C o m is the sequence n u m b e r of the general module. F1 is the name of the operating step. F2 is the label m a r k for operating, which includes:
(1) " d o " , according to the c o m m a n d file ".prg"; (2) "run", according to the executable file ".exe"; (3) "and", according to the macro-substitution pattern. Introduction denotes a single step. D o n e marks that a single step has been carried out. U n d e r PPS, the knowledge of the problem processing m o d e is searched; the searching process is controlled by using the structure controlled slot value.
5. C O N C L U S I O N This p a p e r describes the PPS conceptually and in practice in a DSS, and presents a general structure,
which is obtained by considering the decision as an activity sequence composed of single steps. Furthermore, it provides the so-called "state-based representation of procedural knowledge". Finally, this general structure has been used in problem processing in a production-planning environment.
REFERENCES 1. Bonczek R. H. et al. The evolving role of models in DSS.
Decision Support System--A Data-based, Model Oriented Developed Discipline, pp. 343-370. PetroceUi Books, New York
(1983). 2. Sprague R. S. et al., Bit by bit: toward decision support systems. Decision Support System--A Data-based, Model-oriented User-developed Discipline pp.15-32. Petrocelli Books, New York (1983). 3. Sprague R. H. A framework for development of decision support systems. Decision Support System--A Data-base, Model-oriented User-developed Discipline, pp. 85-124. Petrocelli Books, New York (1983). 4. Alter S. et al. A taxonomy of decision support systems. Decision Support System--A Data-based, Model-oriented User-developed Discipline, pp. 33-56. Petrocelli Books, New York (1983). 5. Zhang Zhongjun and Yang Jianpo. Theory and its application of decision support system. System Engng V, (6), 1-9 (In Chinese). 6. Schneider H. J. The DSS based on the knowledge. Comput. Sci. 2, 9-15 (1988) (in Chinese). 7. Sen A. and Biswas G. Decision support systems approach. Decision Support Syst. !, 9-15 (1985). 8. Bonczek R. H. et al. The evolution from Mis to DSS, extension of data management to model management. Decision Support System-Proceedings of the NYU symposium on DSS, pp. 61-78. North Holland, Amsterdam (1982). 9. Bonczek R. H. et al. Computer-based support of organization decision making. Decision Support System--A Data-based, Model Oriented Developed Discipline, pp. 29-324. Petrocelli Books, New York (1983). 10. Liu Chuandong. The study of Production and Management Decision Support System of lntegralized Oil Refinery Plant. Doctorial thesis, Dalian University of Science and Engineering (1989). 11. Simon H. A. The New Science of Management Decision. Prentice-Hall, Englewood Cliffs, NJ. (1982). (Translation in Chinese by publishing house of social science.) 12. Fu Jingxun. Artificial Intelligence and Its Applications. Qinghau Publishing Agency, Beijing (1987).