&&& t McMASTER UNIVERSITY 1280 Main Street West Hamilton, Ontario, Canada LBS 4M4 Telephone (416) 525-9140 k& iffi FACULTY OF BUSINESS RESEARCH AND WORKING PAPER SERIES "� ------��==��-��-- '"-.,,�. ""� ... l:.:;"'*\;;,.-_ &W* W 0 - WW ;; M&WWW& M ·�1 \ EXPIM: A Knowledge-Based Expert System for Prcduction I Inventory Mo:lelling by Mahmut Parlar Faculty of Business MctA.aster University Hamilton, Ontario, L8S 4M4 · Canada Working Paper #283 August 1987 I" EXPIM: A Knowledge-B ased Expert System for Production / Inventory Mode l l ing M ahmut Parlar Faculty of Bu s ines s McMaster Univer s ity Hami lton, Ontar io, L8S 4M4 Canad a August 1 987 ( EXPERT SYSTEMS ; MODELLING; PRODUCTION/INVENTORY) I . Abstract This paper discu s s e s the development of a knowledge based expert system (EXPIM ) which can identify and recommend up to 30 p roduction - inventory model s . The user (m�nager) i s asked a s equence o f questions regarding the problem situation. The system uses backward-chaining to identify what i s the correct model t o u s e given the situation des cribed b y the user. The paper a l s o discusses the general methodology for building expert systems in m an agement science for th� purpose of identifying mode l s in other areas , such·as queueing theory and location theory. 1 1. Introduction Management s cientists and industrial engineers have, in the p ast forty years, produced hundreds of production-inventory models ranging from the simple extensions of clas sical EOQ ( Hadley and Whitin, 196 3 ) to c omplex multi-level control systems (S�hwarz, 1981). Two decades ago, Eilon and Lampkin ( 1968) summarized more than 500 p apers in inventory control developed and/or published between 1953 and 1965 . Thi s proliferation o f production-inventory (PI) models have prompted many researcher s to publish surveys of "current" status of thes e models in p articular and inventory theory in general at a rate of approximately two per per dec ade (Veinott 1966; Iglehart 1967; Aggarwal 1974; Nahmias 1978; Wagner 1980; Silver 1981. ) With every new review p aper, the readers were informed ab out recent developments in inventory modelling and p o s sible extensions of the current models along with a "wi sh list" of future research activities . Clearly, all these review articles written by the experts in their field h ave helped the research c ommunity get an excellent overview of inventory m odelling and theory, although they prob ably have not helped the actual users of inventory model s very much In recent years, s ome researchers have started inve stigating the p o s s ibility of clas sifying the inventory systems. In p articular, Hollier and Vrat ( 1978) have used a structure similar to that proposed by Kendall ( 1952) f o r queueing models. · They have attempted to des cribe any given inventory system using four aspects , i.e. stru cture , environmental p arameters, operating policies and c o sts . For example an inventory system with Erlang demand , exponential replenishment time, general shelf-life distribution and complete b acklogging was symbolized as E1/M/G/�. Given the 2 ,. apparent duality between queueing and inventory processes ( Prabhu 1 965) this classification seemed to be a natural one t o adopt for inventory systems . But, it appears that this method has not caught on and no other published papers �eem to refer to it. Recently Menipaz ( 1 982) has prop osed another class ification of inventory models based on a systematic use of twelve basic assumptions. W ith all the assumptions holding , one obtains the classical EOQ , but as the assumptions are relaxed a better approximation to the problem is obtained. In ·� maj or research effort started in 1976 and supported by the Hungarian Academy of Sciences ( Barancsi et al. 1 980; Chikan et al. 1 982 ; and Barancs i et al . 1983) another a ttempt is made to classify inventory models. These researchers' obj ect ive was to make the many of the currently ava ilable inventory models more useful for the practi t ioners. By compar ing a c ode system with 4 5 have classified codes each having between two to ten p ossible values they all these models with the purpose of providing a manager with a m o del that would be most suitable for his problem. G iven the fact that maj ority of inventory ( and management science/operations research) models are never used in implemantat ion of the ir results , the correct choice of these models becomes very important . A manager may have several inventory models available to him, but if he is not sure which is the r ight one for the given situat i on obviously he will not be able to solve his pr oblem with the wrong model. The use of classical EOQ in many inventory situati ons although it is the wrong model is an often repeated example. The importance of selecting the r ight ( inventory) model and an anecdote related to that issue is given in Ravindran et al. ( 1 987 , pp . 3 6 9 -370) . 3 It i s a n expert then he clear that when a manager is faced with a PI problem and he has available for choo s ing the r ight model ( and perhaps solving it) can be conf ident that the efforts put into analy s i s will not be wasted. But , as in m any d i s c ipline , experts in inventory modelling are also s c arce and expens ive . In recent years , the emergence of the field of expert systems hope for (ES) as a branch of artifi c i al intell igence ( AI) has provided some increas ing the ava ilab ility of expert knowledge , albeit in a computerized �orm . The premise of thi s p aper is the following. Although the attempts to create systems for class ify ing inventory models as d i s cussed in the p aragraphs ab ove m ay have provided useful information for dec i s ion makers who want to use them , these systems do not have expertise. They all seem to l ack an ab il ity to provide explanations of the ir l ine of reasoning , i . e. how d id they decide to recommend the use of , say , the newsboy model . Except possibly for the Hungari an system, they lack flexib ility , i . e . integration of new knowledge incrementally into its existing store of knowledge. We attempt to go one step farther , and build a knowledge b ased expert computer system which can accurately choo se a PI model after consult ing the user ( m anager) by asking h im a m inimum number of quest ions pert inent to the problem s ituat ion. Our system, named EXPIM (for EXpert Product ion/Inventory Modeller) has the ab ility to explain WHY it is asking a particular question and also HOW it reached a conclus ion and recommended a particular model . By incorporating uncertainties of both the human expert in h i s reason ing, and the manager in his responses , EXPIM can also recommend models with reduced confidence factors and can warn the manager of this fact . It also has the ab ility to automat i c ally run a program once a model choice is made and solve the problem numeri cally. It permits sens itivity analy s i s by letting the 4 i' manager change one or more of his responses to system's queries and come with (pos sibly) different model recoiilrnendations . So far, EXPIM can identify approximately 30 models ranging from the simplest EOQ to more complex coordinated replenishment models. EXPIM runs on the widely available IBM-PC microcomputer (or compatibles) with 512K memory. An expert system , s uch as EXPIM , is a computer program whose behaviour duplicates , in s ome sense, the abilities of a human expert in his area of expertise. Expert systems have been succes sfully developed in field3 such a s medical diagnosis (Shortliffe 1976) , mineral exploration (Duda et al. 1979) and chemical data interpretation (Lindsay et al. 1980) . Excellent reviews of expert systems and their principles have been provided elsewhere (Buchanan and Duda 1983; Stefik et al. 1982; Hayes-Roth et al. 1983; Waterman 1986) and the reader is referred to these sources for detailed description s. In recent years, we have also witnes sed an interest in the MS/OR community towards AI/ES and this is exemplified in the large number of papers presented on these topics in TIMS/ORSA Joint National Meeting s. A few papers have also been published reviewing AI/ES concepts for the management science community and providing pos sible research topic s for interfacing expert systems and management s cience (Kastner and Hong 1984; A s sad and Golden 1986). Other applications of ES in traditional MS/OR are reported in the areas of design optimization (Azarm and Pecht 1985), univer sity admi s sion decisions (vanBreda 1986), simulation modelling (Khoshnevi s and Chan 1986 ; Douk.idis and Paul 1985) and operations analysts (Biswas et al. 1987) . In A s sad and Golden (1986 ) the authors present some possible directions for using ES in management s cience. These includ� i) choice of models which _\ l 5 is what EXPIM does and ii) model generation where systems queries prompt the user to add c onstraints and formulate the objective function in an optimization p roblem. Binbasioglu and Jarke ( 1986) provide a discussion of such a model generation in linear programming using an AI language called Pro log. In an important arti c le , Hahn ( 1985 ) discusses the interface between statistical methods and expert systems. As the statistical computer programs are becoming increasingly available to people who are not statistical experts, he proposes that expert statistical systems be constructed which would embed expert guidance in statistical programs. Some programs that run on IBM-PCs which �o just that are already available for expert forecasting (Wisard 1986). To summarize, we see that problems which could previously be solved by human experts only, are now being attacked by using the expertise embedded in expert computer systems. Provided that these·systems are constructed properly and are thoroughly tested and validated, they will be useful in many areas of man�gement science as the above examples illustrated. As the development of these systems frequently require the use of a specialized AI language or an expert system shell, in the next section we will describe the shell we used in our resear ch. In Section 3 , the methodology we used in the development of EXPIM will be discussed , where we will try to explain the steps that should be followed in developing systems such as EXPIM . Since there are many other areas in management s cience (location theory, queueing theo ry) which may benefit from expert system technology , our discussion may be useful for the developers of such systems. 6 S ection 4 contains a discussion o f the experience gained whi l e structuring and bu ilding this expert system. Last Se ction provides a summary , suggestions for refinements of the mod e l and some possibl e avenues for further research in this new area. 2. The Expert System Shell Expert systems c an b e deve loped in almost any computer language , including FORTRA.i.� (Weiss and Kulikowski 1984) and any of the popular AI l anguages LISP and Prolog . When a computer language is used the developer (known in the AI c ircles as the "knowledge engineer " ) has more control over the flow o f log i c , search mechani sm etc. , but the development time may be very long. On the other hand , using a r e adily avai lable expert system shell r�duc e s the deve lopment time , but the knowledge eng ineer l im its hims e l f to work within the previously determ ined confines of the shell someone e l s e has written. Sinc e our ob j e c t iv e in th i s res e arch was to produc e an expert system which should be easily availab l e , we chose Texas Instruments Personal Consultant E asy as our deve lopment env ironment which runs on IBM-PC. After exam ining a few other shells we d e c ided to use PC Easy b e c ause of its IBM compat i b i lity, fac i lity of deve lopment , sensitiv ity analys i s feature , explanat ion facility in Engl ish language and in corporation of c erta inty factors . PC Easy is a production rule based she l l where the knowledge base cons ists o f IF- THEN type ru les which are chained to each other. S inc e the s e production systems were first proposed by Post (1943) as a general computational mechanism they have been applied to wide variety of problems 7 ( D avis and King 197 7) including the expert systems. A rule in PC E asy specifies a deduction that can be made in a p arti cu l ar situation, and the premise ( I F ) and action (THEN) parts can be composed of compound statements connected with and and or. For example; RULEOl l I f 1) number o f products consi�ered is multiple, and 2) supplier is the same for a l l the items purchased, and 3) mode o f transportation is same Then It is definite that c oordination of replenishments is possible. is a rule which tests whether c o o rdination is possible in an inventory situation. PG E asy uses a combination of backward-chaining and forward-chaining contro l strategies. The former, also known as the g o al-directed control ( B arr and Feigenbaum 1981) reduces the number o f questions the user h as to answer and eliminates quickly many of the irrelevant choices. Forward chaining , or d at a-driven c ontrol can be used to trigger acti ons based on spe�ial conditions. strategies. ) (Appendix discusses an example of these two control When the system reaches a conc lusion regarding the. mode l to choose , the user can ask HOW this conclusion was reached. The explanation facility provides the response by referring to the rule it has used to reach the conc lusion, and prints the English trans l ation o f that rule. Sensitivity analysis is also easily done using the REVIEW feature , where the user is given the option to change one or more o f his responses 8 which h e provided during the consultation . This m ay be an important factor in problems where conditions may change from time to time. PC E asy supports certainty factors ( C F ) which are numerical values indic ating a m e asure o f confidence in the value of a parameter. These factors let a knowledge base deal with the r e ality that facts and opinions are sometimes known with l ess than abso lute c ertainty . Certainty factors c an be incorporated into PC Easy during deve lopment and during consultation when th-e user m ay feel a doubt in responding to a prompt. With this bri e f introdu ction to PC Easy ' s features , we now describe in some detail the m ethodology used in develop ing EXPIM . 1, nevelopm�nt of EXPIM An expert system such as EXPIM consists of three e l em ents: the knowledge base, the inference engine and the user interface (Feigenbaum and McCorduck 1983). The knowledge base contains the knowledge extracted from the expert .by the "knowledge engineer " who is usually a computer s cientist trained in artificial intelligenc e or someone who is we l l informed about the expert systems techno logy and the particular tool he is using. Inference engine part o f the system decides which portions of the knowledge base apply to a given problem and what additional data must be supp lied by the user . The inference engine also provid es explanations of the system's behaviour, such as r esponding to the WHY and HOW questions asked by the user. Final ly , the user interface consists of tools that c an translate the questions asked or conclusions r e ached into plain English. Currently, there are several methods available for constructing expert systems, e. g. rule-based dedu ction, statistical patterns c l assifi c ation , 9 10 etc. (Assad and Golden 1986). As discussed in Reggia and Ahuj a ( 1986), rule-based underlying type o f knowl edge , M any books deductive expert systems should be employed when i ) the knowledge is already organized as (I F-THEN ) rules and ii ) the classification i.e . inventory on inventory is predominantly categoric al. The domain of modelling does s atisfy these two r e quirements: managem ent ( Silver and Peterson 1985) give long lists o f assumptions leading to the p articular model und er discussion. For example , the assumptions le ading to the basic EOQ model are listed as i ) the d em and rate is constant and deterministic, ii) the unit v ariabl e cost does not dep end on repl enishment quantity, etc . which can e asily be put in an IF­ THEN rul e . Also, the cl assi fication of the inventory models is c ategorical in the s ense that every inventory model c an be placed in a particular model group a fter the user responding to a series of questions with two or at most thr e e alternative answers. For these re asons, we decided to use a rule- based system and adopted PC Easy as our expert system shell The rules in PC E asy are constructed using parameters which are structures that identify or contain a piece of information that the system uses to arrive at a conclusion . For exampl e, the parameter QUANTITY- DISCOUNT contains information about the applic ability of quantity discounts . W e have identified twenty three parameters with which all the rules in the knowl edge base are constructed . These parameters , in their abbreviated form are : COORDINATION, DEMAND-LEVEL, DEMAND-PROCES S, DI SCOUN T - TYPE, EOQ­ MODEL , FIXED -COS T , GENERAL - TYPE , INFLATION , LEAD-TIME , L I FE, MODEL , MON I TORING , NUMBER-OR-PRODUCT S , QUANTITY-DISCOUNT, REFERENCE - LI S T-ARTICLES , REFERENCE - LI S T-BOOKS, REPLEN I SHMENT , SHORTAGES, SPACE, SUBSTITUTE , SUPPLIERS , TRANSPORT and UNIT-VARIABLE-COST. For example , the parameter DEMAND-LEVEL has the following properties as used by PC Easy. DEMAND-LEVEL (PARAMETER) TRANSLATION : the level of the future demand PROMPT: What is the level of the future forecasted demand? HELP: :tab 2 " I f the forecasted future level o f demand is b asic ally constant (uniform over time) , choose CONSTA..�T-OVER-TIME. " : line 1 : tab 2 "If the forecast indicates lumpy demand where demand varies from time to time, choose VARIABLE - OVER-TIME. " : line 1 : tab 2 " Refer to (SIL-PET] , pp . 237-239, Section 6.6.4 . for an expl anation of a numer i c al technique which can distinguish between these two cases. " : line 2 COMMENTS : ASKED TYPE : SINGLEVALUED EXPECT: CONSTANT-OVER-TIME VARIABLE-OVER-TIME USED - BY: RULE 0 03 When PG E asy translates rules into Engl ish it uses the TRANSLATION property wh i ch construct ion. I f o f DEMAND-LEVEL, the system developer supp l ies dur ing expert system at a part i cular stage, the system needs to know the type it uses the PROMPT "What is the level of the future forec asted demand?", and prompts the user tc choose between CONSTANT-OVER­ TIME and VARIABLE-OVER-TIME. If the user is not exactly sure what the question is asking, he may obtain further HELP by pressing a function key and get an expl anat ion as displayed in Figure 1 . 11 12 Insert Figure 1 here Sometimes , the values of some parameters are determined internally by the s y s tem . This may be neces sary when the user may not be able to answer questions very easily pertaining to the se parameters. For example , following rule determines in an indirect manner , whether the general model type is EOQ: RULE004 (INFERRING-RULES ) If 1) the forecast for the future demand i s DETERMINISTIC , and 2) the level of the future demand i s CONSTANT-OVER - TIME , Then it is def inite (100%) that general model type i s EOQ . IF' : DEMAND-PROCESS THEN: GENERAL-TYPE DETERMINISTIC AND DEMAND-LEVEL EOQ DESCRIPTION: General type ECQ. CONSTANT-OVER-T!ME This is achieved in an indirect way , by a s k ing the user two eas ier to answer questions regard ing the demand for the product under consideration. Three of the parameters in the above l i st, i.e. MODEL , REFERENCE-LIST­ BOOKS, REFERENCE-LIST-ARTICLES are the goals in the knowledge bas e which the PC Easy tries to prove. Us ing the backward-chaining inference mechanism des cribed in the Appendix , system tries to prove the above three goal s , one by one. When the goal MODEL is proven , the other two are al so automat i cally proven and the system reaches a conclus ion , and l is t s a l l the books and articles used in the knowledge base for the user's information . In its present vers ion , EXPIM has 68 rules with 12 rule groups constructed for ease of development. These rule groups are : i) EOQ Related Groups 1 . EOQ and Extensions 2 . "Not Clas sical EOQ" 3. EOQ Po s s ib i lities ii) 4. Determini s t ic Non-EOQ i i i) Newsboy Model Related Groups iv) 5. Newsboy 6. Newsboy Pos sibilities Stocha stic " Non-Newsboy" 7. Cont inuous Review Groups 8. Cont inuous Review Po s s ib i l ities 9. Per iodic Review 10. Periodic Review Pos s ib i l ities v) Auxil iary Rule Groups 11. Inferring 12. Conclus ions The first rule group has 14 rules each of which g iving rise to an EOQ type model ranging from the c la s s ical EOQ to production lot s ize with lost sales. As an example the fol lowing Rule #5, if sat i s f ied , recommends the cla s s ical EOQ model with a mes s age to the user warning him to check h i s a s s umption before using th i s model. The rule also provides a pub l i shed 1 3 14 reference for th i s model along with the name of the bas ic l anguage computer program ( EOQ.BAS ) the user can run after the consultation is over. ( The program s are prov ided with the knowledge base ) . RULE005 [EOQ - AND-EXTENSIONS-RULES] I f 1 ) general mode l type is EOQ , and 2 ) lead-t ime i s ZERO , and 3) number of products cons idered i s ONE , and 4 ) inventory shortage i s NOT-PERMISSIBLE , and 5 ) replenishment rate o f the order i s ALL-AT-ONCE, and 6) amount paid to the suppl ier for each unit purchased is INDEPENDENT-OF-ORDER-QUA..�TITY and 7) 1 ) future inflat ion expectations i s LOw , or 2) future inflation expectations is STABLE, and 8 ) item's l i fetime is SUFFICIENTLY-LONG, and 9) storage space availabi l ity is SUFFICIENT, and 10) coordination of replenishments is NOT-FEASIBLE , Then it i s definite ( 100% ) that the model you should use is Class ical EOQ. Th i s is the oldest inventory model available in inventory literature. Because o f its s imp l icity in computations, it has frequently been misused. It i s a good idea to re-check your assumptions be fore adopting this mode l. REFERENCE : [SIL-PET] , pp. 174-180 . EOQ . BAS Sect ion s 5.1.5.3 . COMPUTER PROG&:-'\M: IF GENERAL-TYPE EOQ AND LEAD-TIME = ZERO AND NUMBER-OF-PRODUCTS = ONE AI'ID SHORTAGES = NOT-PERMISSIBLE AND REPLENISHMENT = ALL-AT­ ONCE AND UNIT-VARIABLE-COST = INDEPENDENT-OF-ORDER-QUANTITY AND INFLATION LOW OR INFLATION = STABLE AND LIFE = SUFFICIENTLY-LONG AND SPACE SUFFICIENT AND COORDINATION = NOT-FEASIBLE THEN: MODEL TEXTVAL :LINE 2 :TAB 2 "C las s ical EOQ . " :LINE 2 :TAB 2 "This is the o ldest inventory model available in inventory l iterature. Because of its s imp l icity in computations, it has frequent ly been m i sused . It is a good idea to care fully I recons ider your as sumptions be fore adopting th i s model . " :LINE 2 :TAB 2 "REFERENCE : [SIL-PET] , pp. 174-180 . Sections 5. 1-5.3 . " :LINE 2 : TAB 2 "COMPUTER PROGRAM : EOQ . BAS" : LINE 2 DESCRIPTION : · C l as sical EOQ [ 100] It is important to note that, along with the EOQ type general model requirement nine other requirements are present in order for the model to recommend the C l as s ical EOQ mode l . These are (LEAD-TIME = Zero) , NUMBER-OF- PRODUCTS ( =One), SHORTAGES (=Not Perm i s s ible), REPLENISHMENT , (= A l l at Once), UNIT-VARIABLE-COST (= Independent of Order Quantity), INFLATION (= Low or Stable) , LIFE (=Sufficiently long), SPACE (= Suffic ient) and COORDINATION (= Not Fe a s ib le) . If any one of these is not s at i s f ied , but the others are , then the system recommends a mode l wh ich is the extens ion of the c lassical EOQ . When the general type is EOQ, and if any two of the above nine parameters are not s at i s fied in Rule #5 above, then we can no longer have a model which qua l i fies as an EOQ extens ion. The second rule group "Not Class ical EOQ" contains a total of e ight new rules e ach reach ing the conclus ion that po s s ible choice for an EOQ model is not c las s ical EOQ. Although it was pos s ible to make up a s ingle rule w ith 3 6 condit ions 15 in its I F part , we preferred to use eight different rules for facility o f d ebugging. Following Rule #44 is an example to the rules in this group . RULE004 [NOT- CLA S S I CAL-EOQ-RULES ] I f 1 ) general model type i s EOQ , and 2) 1) 1) l ead-time is not ZERO , and 2). number o f products considered is MULTIPLE , or 2) 1) lead - time is not ZERO , and 2) 1) inventory shortage is PERMISSIBLE-BACKLOGGING , or 2) inventory shortage is PERMISSIBLE-LOST-SALES , or 3) 1) lead-time is not ZERO , and 16 2) replenish..�ent rate of the order is GRADUALLY , or 4) 1) lead-time is not ZERO , and 2) amount paid to the supplier for each unit purchased is DEPENDENT-ON-ORDER - QUANTITY , or 5 ) 1) 2) 6) 1) lead-time is not ZERO , and future inflation expectations is HIGH , or lead-time is not ZERO , and 2) item's lifetime is LIMITED, or 7) 1) lead time is not ZERO , and 2) storage space availability is LIMITED , or 8) 1) l ead-time is not ZERO , and 2) coordination o f replenishments is POSSIBLE , Then it is d e finite ( 100%) that possible choice for an EOQ model is Not Classical EOQ . If: GENERAL - TYPE EOQ AND (LEAD - TIME != ZERO AND NUMBER - O F - PRODUCTS MULTIPLE) OR (LEAD - TIME != ZERO AND (SHORTAGES PERMI S SIBLE - BACKLOGGING OR SHORTAGES = PERMI S SIBLE-LOST - SALES)) OR (LEAD-TIME != ZERO AND REPLENISHMENT GRADUALLY) OR (LEAD-TIME != ZERO AND UNIT- VARIABLE - CO S T = DEPENDENT - ON - ORDER-QUANTITY) OR (LEAD-TIME != ZERO AND INFLATION = HIGH) OR (LEAD - TIME != ZERO AND LIFE = LIMITED) OR (LEAD- TIME != ZERO AND S PACE LIMITED) OR (LEAD-TIME != ZERO AND COORDINATION = POS SIBLE) THEN: EOQ-MODEL· = "Not Classical EOQ" Here, the symbol != means " is not". The third rule group has a collection of rules which would be act ivated when the general type i s EOQ and the pos s ible choice for an EOQ model is not the classical EOQ. When these conditions are satisfied , and if any one of .- the above nine parameters has a value wh ich would make the model approximate an EOQ extension , then these rule s would recommend that model , but with a s ubstantially reduced confidence factor . An example is Rule # 5 6 below , wh ich recommends us ing EOQ with quant ity d iscounts (conf idence factor 30) , but cautions the user to be careful. RULE056 [EOQ - PO S SIBILITIES-RULES] If 1) general model type is EOQ, and 2) possible cho ice for an EOQ model is Not Class ical EOQ, and 3) amount paid to the supplier for each unit purchased i s DEPENDENT - ON-ORDER - QUANTITY, Then there is weakly suggestive evidence (30%) that the model you should use is EOQ with quantity d i scounts . Caution must be exerc ised in u s ing this model as not all the assumpt ions lead ing to the model are satisf ied . Plea se 17 check your input values using the REVIEW command. REFERENCE pp. 62-66. COMPUTER PROGRAM EOQDISC . BA S . [HAD-WHI] , IF : GENERAL - TYPE VARIABLE-COS T EOQ AND EOQ-MODEL "Not Cla s s ical EOQ" AND UNIT- DEPENDENT-ON-ORDER-QUANTITY 18 THEN : MODEL TEXTVAL : LINE 2 : TAB 2 "EOQ with quantity discounts . " : LINE 1 : TAB 3 " Caution must be exercised in using this model a s not all the a s sumptions leading to the model are satis fied . Plea se check your input values using the REVIEW command . " : LINE 1 : TAB 3 " REFERENCE :[HAD-WHI] , pp. 62-6611 : LINE 1 : TAB 3 "COMPUTER PROGRAM : EOQDISC.BA S " C F 30 DES CRIPTION : EOQ with quantity discounts [ Unit-variable - cost 30 The fourth rule group contains rules which are related to determin istic non-EOQ type model s , such model (Wagner and Whitin recommending stochastic as the time vary ing, periodic review lot-size 1958) . Rule groups 5 to 10 contain rules models only. All of these rules start by determining the general model type and then ask other questions trying to reach the goal MODEL and make a recommendation. It should perhaps be clear by this time that our expert system clas sifies all of the inventory models into four mutually exclus ive (and collectively exhau stive) groups . This is achieved by identi fying the value of the parameter GENERAL-TYPE as one o f 1. EOQ , 2 . Deterministic Non-EOQ , 3. Newsboy , and 4 . S tochastic Non-Newsboy . At the outset , to assign a value to GENERAL - TYPE , the user is asked a question on DEMAND-PROCES S and DEMAND-LEVEL or LIFE depending on the answer given to the first question. Answering these two prompts , imme�iately places the system in one of the four groups , thereby effectively eliminating all the other irrelevant rules pertaining to the three groups. For example, i f GENERAL - TYPE is found to be NEWSBOY , the rules in EOQ and Extensions group, etc. are not considered at all since they would not be relevant to a stochastic demand model. This process is described in Figure 2. Insert Figure 2 here Now , the systems would attempt to prove whether the classical Newsboy or any one of its extensions is the applicable model , using e.g . rules such as Rule #68. RULE068 [NEWSBOY-RULES) If 1) general model type is NEWSBOY , and 2) number of products considered is MULTIPLE , and 3) substitute products exist , and 4 ) fixed order cost i s ZERO , 19 Then it is definite (100%/ that the model you should use is Classical Newsboy with Substitutable Products REFERENCES : [ PAR-GOY] , Opsearch, Vol . 21 , pp . 1-15, (1984 ) for the two item case with exact solution: [ PAR] , 20 Opsearch, Vol . 23, pp . 250-257, (1986) for the multi-item case with an heuristic . COMPUTER PROGRAM : NEWSBSUB . BAS IF: GENERAL-TYPE = NEWSBOY AND NUMBER-OF-PRODUCTS = MULTIPLE AND SUBSTITUTE AND FIXED-COST = ZERO - THEN : MODEL TEXTVAL :LINE 2 :TAB 2 "Classical Newsboy with Substitutable Products" :LINE 1 :TAB 3 " REFERENCES : [ PAR-GOY], Opsearch, Vol. 21 , pp . 1-15 , ( 1984 ) for the two item case with exact solution: [PAR] , Opsearch , Vol . 23, pp . 2 5 0-257, (1986 ) for the multi - item case with an heuristic" :LINE 2 :TAB 2 " COMPUTER PROGRAM : NEWSBSUB.BAS" DES CRIPTION : Classical Newsboy with Substitutable Products [ 100 ] Although it seems obvious, it is very important to emphasize that a structure such as above would cut down the search space of the problem and reduce the time required to f ind the correct model. For any expert system , the first few questions the user answers , should eliminate many irrelevant outcomes and make the search for the goal more efficient . Clearly , there are some cases where the user's responses are so unusual that , a relevant model does not exist for the given situation. An example consultation for such a case is provided in Figure 4 , where the system concludes that no (known) models are available. A result such as this may be useful to researchers working in inventory management by providing them with possibly new research topics not analyzed be fore . ---------------- ---- - Insert F i gure 3 Here Finally , the following f igure describes the results of a part i cular consultation session where the system recommends the Per iod i c lot size model. The reference [SIL - PET] is (S ilver and Peterson 1985). In the second part , the user can REVIEW his previous cho ices and re-run the system . Insert F igure 4 Here As we ment ioned be fore, the s�stem can identify appr ox imately 30 product ion- inventory models found in the current l iterature. Most of the models in every maj or production- inventory textb o ok , including S i lver and Peterson (1985), Hax and Candea (1984), Love (1979) , J o hnson and Montgomery ( 1974) and Naddor (1966) are included . We should note that the current system can be easily extended and ref ined as new models bec ome ava ilable. This is done by add ing new rules to the knowledge base and by poss ibly changing some o f the older rules wh ich interact with the new ones . It is obvious that as long as new inventory models are published and become ava ilable, this expert System w ill continue growing and will be r i cher in content and expert ise. 21 2 2 4 . Les s ons Learned As the use of expert systems in management sc ience applicat ions i s relat ively new , it would be worthwhile to summarize our exper iences gained dur ing the development of EXPIM. It is hoped that other researchers who are working on s imilar proj ects , e . g . queueing expert systems would f ind these hints u s eful. We recommend that the developer u s e an expert system shell instead of an AI language such as LIS P or Prolog. The selection of the shell should be based on its capability to do backward chaining with a forward cha ining option . qu ickly Us ing backward chaining , many irrelevant cho ices can be eliminated in the early stages. It is advisable to use a shell which can interface with out s i de programs and files . For example , many expert systems may have to do heavy mathemat ical computat ions dur ing or at the conclus ion of a consultation (e . g . running a program to solve the EOQ model in EXPIM). S imilarly , they may need to read data from outs ide files or from databases instead of ask ing the user to supply the se data value s . A s management sc ience application would invar iably involve some computat ions , these features become important. Many shells have the capab ility to answer WHY and HOW quest ions , and do sensit ivity analy ses. It is cruc ial that the developer choose one with these capab ilities. As for the development of the knowledge base , the developer should group the models into mutually exclus ive and collectively exhau s t ive groups so that any available model can be placed in exactly one of the groups . For example , in the case of queueing expert sy stem , one may init ially create two groups , i) s ingle server models and i i) multi-server models. In each group a rule should be written for the b e st known model e . g. classical EOQ in deterministic EOQ and M/M/1 in s ingle s erver queues. Then , extensions of this fundamental model should be c onsidered by writing slightly different variations o f the rule for the fundamental model . Finally, new rules should be created which would cho o s e the s e known models with lower confidence factors because of s om e o f the unsatisfied a s sumptions , e.g . Rule #56 discu s s ed in S ection 3. It is als o important t o have s ome idea who the u s er s might b e befcre the development starts. It would be us eful to have rul es which c o uld reach conclu sions by asking the user easy to understand questions , e . g. Rule #4 discu s s ed in S ection 3. When particular article) model in the model . the expert system reaches a conclusion by recommending a model, it should al so give the us er the reference (book or where the model can be found. This way , the u s er can analyze the more detail and perhaps s e e a few numerical example s r el evant to 5. Summary and Conclusions In this paper d evelopment of an we have di s cus s ed in detail , the conc eptualization and expert system (EXPIM) which can identify up to 30 production and inventory models. In the abs ence of a hu.�an expert , the manager who is interested in using thes e models can a c c e s s the expert system and a ft e r r e s ponding to a few questions , he can get a recommendation from the system . EXPIM is written in Texas Instruments' Pers onal Consultant Easy expert system shell and runs on IBM-PC micro computers with at least 512K memory . 23 24 As mentioned in Section 4, there is a potential for creating other expert systems in management science for classifying different collection of models. For example, queueing theory, with its plethora of models is a prime �andidate for this research. Location theory is another possibility. We hope that our points summarized in section 4 will aid other researchers who want to enter this new and interesting research field which combines management science and artificial intelligence. We note that to make these expert systems more "intelligent", they should have the ability to reach some intermediate conclusions on their own. For example, in EX.PIM, instead of asking the user about the DEMAND-LEVEL , the system should ideally be able to determine it on its own. This would require tha system to access external data files, do some computations as discussed in Silver and Peterson (1985, p.238) to obtain a measure of the variability of demand pattern and then determine the value of the parameter DEMAND-LEVEL. Current version of EXPIM does not have this capacibility, but it would be possible to include it in a later version. In the early days of expert system development, artificial intelligence researchers used to recommend that a knowledge engineer should not be his own expert (Nii 1983). This is still true to a certain extent but these days the availability of easy to use shells have made it easier for the domain experts to become proficient in the use of these tools and have assumed the role of a knowledge engineer. Perhaps the convenience and low price of microcomputers which can run AI software have played an important role in this development. To conclude, it is our belief that expert systems will be playing an important role in management science especially in classification and choice of models as we discussed in this paper and also in automatic model building (Binbasioglu and Jarke 1986). ACKNOWLEDGEMENT Financial support from the Natural Sciences and Engineering Research Council of Canada under Grant No. A5872 is gratefully acknowledged. 25 List of Figures Page Figure 1. The HELP Facility 12 Figure 2 . Initial Classification of Models 19 Figure 3. The case of No Conclusions 21 Figure 4 . The " Conclusions" and " Review" Screens 21 Backward Chaining Append ix Backward and Forward Cha ining in PC Easy (From PC Easy Reference Guide , pp. 3-19/ 3 - 30) Al ·Backward cha ining is the primary means by which PC Easy arrives at a solution to a problem- - the knowledge base goal . The driving force behind a PC Easy consultation is the attempt to set a value for each of the one or more parameters l isted in the knowledge base GOALS property. PC Easy begins the attempt to set the value of a goal parameter by looking for a rule whose THEN sta tement ass igns a value to the parameter. When it finds a rule , it tests it , or determ ines whether the condit ions expressed in the rule's IF statement are true. To determine whether the condit ions expressed in the rule's IF statement are true , PC Easy may need to f ind the value of one or more parameters included in the IF statement. Lhis search may lead to another rule that sets the value of one or more of these parameters. If the conditions in the IF statement are true , the rule passes. If the cond itions in the IF statement are not true , the rule fails. If a rule passes , PC E asy f ires the rule--car r ies out the action specified in its THEN statement. PC Easy fires a rule only once dur ing a consultation . A2 Example In this example , PC Easy find s the value of the goal parameter GIFT by backward chaining. GIFT-TYPE and RECEIVER are parameters in the knowledge base. 1. The consultation begins. 2 . P C Easy find a rule that a s signs a value to GIFT: IF statement: GIFT-TYPE = PERSONAL THEN statement: GIFT = FLOWERS To determine whether to apply the action of this rule and set the value of GIFT TO FLOWERS, PC Easy must search for the value of GIFT-TYPE. 3. PC Easy finds a rule that assigns a value to GIFT-TYPE: IF statement : RECEIVER = SPOUSE THEN statement : GIFT-TYPE = PERSONAL To test this rule, PC Easy must find the value of RECEIVER. 4. Because no rule assigns a value to RECEIVER and RECEIVER has a PROMPT property , PC Easy prompts the client: Is the receiver o f the gift your spouse? A3 5 . I f the cl ient answers yes, P C Easy.a s s igns RECEIVER the value S POUSE. Because the condition stated in the IF statement of the rule i s true, PC Easy carries out the action of the THEN statement and a s s igns GIFT-TYPE the value PERSONAL. 6 . Because GIFT-TYPE has the value PERSONAL , the condition stated in the I F statement of the original rule i s true , and P C Easy determines that the value of GIFT i s FLOWER S. Forward Cha ining In forward cha ining , PC Easy tries an antecedent rule when it has a s s igned a value to one of the parameters in the antecedent rule's IF s tatement. In EXPIM an antecedent rule is used to invoke a rule whose THEN s tatement does not conclude values for any parameter. For example , when the model type i s determ ined to be STOCHASTIC-NON-NEWSBOY and if the user selects NON-PERMIS SIBLE for inventory shortage paramete r , then he gets a me s sage indicat ing the unava ilability of any models for the current s ituation. The follow ing antecedent Rule #74 des cr ibes an example to forward chaining in P C Easy . RULE074 [ PERIODIC-REVIEW-RULE S/antecedent] If 1) general model type is STOCHASTIC-NON - NEWSBOY , and 2) inventory shortage is NON-PERMI S SIBLE , A4 Then it is definite (100%) that the model you should use is There is no available model . Please note that you- chose PERMI S S IBLE when the computer asked you about the SHORTAGES . P r io r to that you had spec i f ied that DEMAND was S TOCHASTIC , and LIFETIME was SUFFICIENTLY-LONG. Under these conditions it is impossible to require that - inventory should always be posit ive. Please REVIEW your responses and change them accord ingly. IF: GENERAL-TYPE = STOCHASTIC-NON-NEWSBOY AND SHORTAGES = NOT .. P ERMI S SIBLE THEN: MODEL = TF.XTVAL :LINE 1 : TAJ3 3 " There is no ava ilable model. Please note that you chose PERMI S SIBLE when the computer asked you about the SHORTAGES . Prior to that you had specified that DEMAND was STOCHASTIC, and LIFETIME was SUFFICIENTLY�LONG. 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WISARD So ftware Co . , Wisard Forecaster for IBM-PC , Green Bay , WI , 1986. EXP I M Expert P r o duct i on - I nv e nt o ry Mode l l er r--�---�������--�����-�����--�-��-����-���-� ) What is the l ev e l o f the f uture f o r e c a s t e d demand? \ l CONSTAN T -OVER - T I ME l H e lp : ���������������������-. I VARIABLE-OVER - T IME J I I f the f o r e c a s t e d f ut u r e l ev e l of demand i s b a s i c a l l y c o n s t ant ( un i f o rm over t im e ) , c ho o s e CONSTANT - OVER - T I ME . I f the f or e c a s t i nd i c at e s lumpy demand where demand var i e s f r om t im e to t im e , cho o s e VAR I ABLE - OVER- T IME : R e f e r t o [ S I L -PET ] , p p . 2 3 7 - 2 3 9 , S e c t i on 6 . 6 . 4 . f o r an exp l anat i o n o f a numer i c a l t e c hn i qu e whi ch can d i st in gu i sh b etween t h e s e two c a s e s . ** End - RETURN /ENTER to cont inue 1 U s e the a r r ow k e y s or f i r s t l et t e r o f i t em t o p o s i t i on the c ur s o r . I _ ___ :_: Pr e s s RETURN/ENTER t o _c_o_n_t_i_n_u __ e_. ____________________ _ , F :i;g.u;r e .J. I _} DEMAND - PROCE S S : D e t e rm i n i s t i c � DEMAND- LEVEL C o n s t ant V a r i ab l e L I FE I 'f EOQ D e t e rmini s t i c n o n -EOQ Figure 2 S t o cha s t i c I L im i t e d + N e w s b o y L o n g + Sto cha s t i c n o n - N e w s b o y ( " C o n s u l t at i on r e c o rd f o r : EXP I M : Expert Product i on - I nventory Mode l l er " " th e f o re c a s t f or the f u t u r e demand . . S TOCHAS T I C " " i t em ' s l i f et ime SUFF I C I E N T LY - L ONG " " pe r i o di c mon i t o r i n g of the invent o ry . . . YE S " " l e a d - t i m e STOCHAS T I C " " f ix e d o rd e r < o r s e t - u p > c o st . . POS I T I VE " " i nventory s h o r t a g e PERM I S S I BLE - LOS T - SALES " " nuI:lb e r o f p r od u c t s c o n s i de r e d MULT I PLE " " s u b s t i tu t e p r o d u c t s exi st YES " ) CONCLU S I ON S : I was un ab l e to make any c o nc l u s i on s r e g a r d i n g the m o d e l y o u s h o u l d u s e L i s t o f b o o k s u s e d i n thi s know l e dg e b a s e i s a s f o l l ows : N o t ava i l ab l e s i n c e t h e r e are no known ( o r e a s i l y imp l ementab l e ) mo d e l s f o r s o lv i ng the inventory p r ob l em d e s c r i b e d by the u s e r in thi s c o n s u l t at i on s e s s i on . P o t e n t i a l r e s e a rch t o p i c s may b e o b t a i n e d f rom t h i s c o n s u l t a t i on ' s r e s u l t s b y r e f e r r i n g t o t h e c o m b i nat i o n o f i nput s p r o v i d e d b y t h e u s e r . P l e a s e u s e the REVIEW f ea t u r e to r e c a l l your input s , i . e . the paramet e r s you s upp l i e d d u r i n g t h e c o ns u l t at i on L i s t of art i c l e s u s ed in thi s kno w l e d g e b a s e i s as f o l l ows : Agai n , n o t ava i l ab l e f o r the r e a s o n s g i v e n above 'F:i:gu:re . .3 EXP IM Expert P roduct i on - I nvent o ry M od e l l e r r C on c l us i o n s :�����������������������������������-. The mo d e l you s h o u l d u s e i s . a s f o l l ow s : P e r i o d i c r e v i ew l ot - s i z e I Thi s m o d e l c o u l d be s o lved u s i n g the Wagn e r - Wh i t i n exact a l go r i thm or b y ! u s i n g S i l v e r - M e a l heur i s t i c o r by u s i n g a f ew o t h e r heur i s t i c s reported i n the l i t e r ature . l P.EFERENCE : [ S I L -PET ) , pp . 2 2 7 - 24 3 , S e c t i o n s 6 . 5 - 6 . 7 L i s t o f b o oks r e f e r e n c e d i n thi s knowledge . b a s e i s a s f o l l ow s : BOOKS : [ BAN - FAB J : J . Banks and W . J . Fab rycky , ' Procurement and I nvent o ry S y s t em s ! An a l y s i s ' , Prent i c e - H a l l , 1 9 8 7 . [ BE R J : D . P . B e rt s eka s , ' Dynam i c P r ogramming and S t ocha s t i c C o n t r o l ' , A c a d e m i c P r e s s , 1 9 7 6 . [ E L S - BOU ) : E . A . E l s ay e d and T . O . Boucher , ' An a l y s i s and C o n t ro l o f \ Produc t i o n S y s t e m s ' , Prent i c e - H a l l , 1 9 8 5 . I [ HAD-WH I J : G . H a d l ey and T . M . Whi t i n , ' An a l y s i s of I nvent o ry S y s tems ' , ! Pr e nt i c e - Ha l l , 1 9 6 3 . I ** M o r e - RETURN/ENTER to c o n t i n u e EXP I M : Expert Product i on - I nv e nt o ry M o de l l e r -Conc l u s i ons : \ Management and Production P l ann i n g ' , 2�d E d i t i on , John W i l ey , 1 9 8 5 . I ( L i .-Rev i e w : - J C o 1 9 S u 1 - Ye s ,_,,____,,����-.,,..��::----::--�����...,....����-=====�:-:==-=::-.::-� CEJ · l the f o re c a s t f o r the future demand DETERM I N I S T I C I � the l eve l of the f uture demand VAR I ABLE - OVE . . . � • p e r i o d i c mon i t o r i n g of the inven t o ry . . . YES r l e ad - t ime ZERO r • numb e r -of p r o d u c t s c on s i d e r e d ONE � • inventory shortage NOT - PERM I S S IBLE � • r e p l e n i shment rate o f the o r d e r < o r A L L - AT -ONCE wi r · supp l i er ' s quan t i t y d i s c ount . . NOT -AVAI LABLE 2 5 i I- • future i n f l at i on e xp e c t a t i o n s . : : LOW 1 . U s e arrow keys or f i r s t l et t e r of i t em t o p o s i t i o n c u r s o r . I 2 . S e l e c t a l l app l i c ab l e r e s p o ns e s . 1 l s h ...__3_. �A_f_t_e_r ...,- m_a_k_i_· n�g�s_e_l_e_c_t_i_o_n_s...,-, �p-r_e_s_s�RE�T-U_Ri_N_ !E�N-1_T_E_R�t-o�c-o_n_ t�i -n_u_e_.�...,-����-' Figure 4 Faculty of Busine s s McMaster University WORKING PAPERS - RECENT RELEASES 257 . Joseph B . Ro s e , " S tatutory Expedited Grievance Arbitration : The Case of Ontario" , July, 1986. 258 . 259 . 260 . 261. 262. 263 . 264 . 265 . 266. 267 . 268 . 269. 270. 271. John W . Medco f , " The Effects o f Event Valence and Degree of Attribution Upon Action Recommendations " , September 1986. Paul D . Dowling and Robert F. Love , " One - D imensional Floor Layout Solutions Us ing S quared Distances" , September , 1986. Harish C . Jain , "Affirmative Action/Employment E quity in Canada : Findings of a S urvey" , September , 1986 . Min Bas adur , "Catalyzing Interfunctional Efforts to Find and Creat ively Solve Important Bu s ines s Problems", Sep tember, 1986. Roy J . A dams and Isik Zeyt inoglu, " Labour-Management D i spute Resolution in Cana dian Heavy Industry : The H ilton Works Case " , September, 1986. ' R ick D. Hackett, " New Directions in The Study of Employee Absenteeism : A Research Example", October 1986. Ali-Reza Montazemi, "An Analy s i s o f Information Technology A s s e s sment and Adoption in Small Bus iness Environment s", October , 1986. I sik U. Zeytinoglu, " Part - t ime Worker s : Unionization and Collect ive Bargaining in Canada", November , 1986 . Norman P. Archer and M . W . Luke Chan, " The Architecture of Chines e - English Microcomputer Systems " , December , 1986. Norman P . Archer, " Structuring Problems for Analy s i s with Electronic Spreadsheets " , January, 1987 . Norman P . Archer , "A Life Cycle Approach to the Implementation of Integrated Information Technology " , January, 1987. Joseph B . Rose, "An Overview of the Canadian and Australian Industrial Relations Systems " , February, 1987. Joseph B . Ros e , "A North American Perspective on Multi - Employer Cohesion in Australian Construction", February, 1987 . Christopher K. Bart , "Budgeting Gamesmanship : S urvival Tactics in a .Hostile Environment", February, 198 7 . 2 7 2 . 273 . 274 . 275 . 276. 277 . 278. 279. 280. 281. 282. - 2 - Thomas E . Muller , "Model ing the Touri st ' s Urban Experience : A New Approach to Irtternat ional Touri sm Product Development Based On Urban Quality of Life , February , 1987. A. William R i chard s on , "Cost-Vo lume - Profit Analy s i s and the Value of Informat ion : An Evaluation for the Normal and Lognormal D i stribut ions" , 1'.'ebruary , 19.87 . Roy J . Adams , "Industrial - Relations Systems : An Internat ional Comp ar i s on" , March , 1987 . John W. Medco f , "An Integration of S ome Attribution Theor ies", March , 1987. Y . L . Chan and A . R. Montazemi, "An Experimental Study of the Informat ion Cho i ces of Security Analysts" , March , 1987. I s ik Zeyt inoglu , "Part-t ime Workers and Collect ive Bargaining in Internal Labour Markets" , .May , 1987. Abraham Mehrez , "A Mult i-Obj e c t ive Approach to a M ixed Integer Non-Line ar Cover ing Prob lem", July , 1 987. Abraham Mehrez , Yufei Yuan , Arniram Gafni , "S table S o l ut i ons Vs . Multipl i c ative Util ity S olut ions For the A s s ignment Prob lem" , July , 1987. H ar i s h C. J a i n , R i ck D . Hackett , "Empl oyment Equ ity Programs In Canada : Publ i c Po l i cy And A Survey", July , 1987. Norm P. Arche r , "MBA Information Systems Curricu lum Needs : A Bus ine s s S urvey", August , 1987 . Chr i s K. Bart , "New Venture Units : Organiz ing for New Products" , September, 1987 . DSB283