Methodology of Simulation Approach to Decision Assessment in Enterprises

Copyright © IFAC Automated Systems Based on Human Skill, Kranjska gora, Slovenia, 1997

METHODOLOGY OF SIMULATION APPROACH TO DECISION ASSESSMENT IN ENTERPRISES M. Kljajic, R Leskovar, A. Skraba, L Bernik

University o/Maribor Faculty o/Organizational Sciences. Presernova /1 . 4000 Kranj. Slovenia

Abstract: The paper describes a simulation system for decision making support in enterprises. Variants of the business scenarios are evaluated with the multicriteria linearly weighted decision function. The weight of the each criterion is determined by the experts with the brain storming method exploring group decision support methodology. Interactive methods of the evaluation of possible solutions are supported with the expert system providing for various analyses and comparisons, such as target and criterion preferences. The result of the simulation has been also analysed according to the principle of the analytical hierarchy processes AHP. Copyright © 1998 IFAC Keywords: decision support system, simulation, enterprise, management

I. INTRODUCTION

simulation methods and expert systems (Rajkovic et aI. , 1987; Hall, 1996; KIjajic et al. 1996). It is described (Kljajic and Leskovar, 1994), the modelling methodology and simulation models of business systems SlMLES as well as it's validation. The model was preliminary tested in two enterprises where it exhibited a high degree of confidence at the replication of the business dynamics and at the foreseeing of its behaviour with a known scenario. The developed model comprises soft and hard methodologies at the preparation and selection of the scenario. The evaluation criteria and business goals are gained by methods of group decision support systems GDSS with in connection with the method of analytical hierarchy process AHP (Saaty, 1990). Group decision support systems enable participants creative, independent and anonymous estimation of single decision variable. The consequence is a variation of estimations that can violate the consistency axiom of AHP method. One can obtain the consistency of the decision of the whole group by using suitable tools inside the system for the group decision making. On this way the decision makers should creatively participate in modelling of business

The organisational systems (enterprises) are sets of by its nature different subsystems created and organised into whole by man who is part of them as well. Socio-technical-ecological system is that one whose quality and functioning toward the goals are achieved by decision making. The property of the enterprises isn't only in quality and functioning in achieving the goals, but in goals itself and in means used to reach these goals. Therefore, decision making are the main stream in developing of enterprises. The system simulation is one of the ways of solving decision problems in enterprises. The system behaviour is studied on the model, which enables reasoning on consequences of the chosen strategy. Since system dynamics methodology has been introduced by (F orrester, 1961) the use of simulation models has an important role in management science. Application of simulation methodology for business assessment has been less present in small and medium enterprises specially in transition country. Presently the most intensive research efforts are spent on the combination of

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is enabled on the basis of apriori assumptions on the model and not just on the basis of empirical experiences. Loops a) and c) are the basic ones for the acquisition of knowledge and experience for learning and quality decision making and b) represents the pragmatic validation of the model.

policy, consistently define the decision criteria and rationally choose the solution. The proposed methodology deals with the behaviour of the integrated simulation system for support in business decision making in enterprise and for the pedagogical purpose. On the case, by means of the simulation system SIMLES and expert system DEX (Bitenc at all,1995), and AHP methods the developed methodology will be demonstrated

2. METHODOLOGY

simulation result

The system consists of three parts: the basic model that represents the business process, programme for the scenario formulation, programme for the analysis of the simulation results and selection of solutions, and programme for normative analysis. The simulation scenarios are made of two subset: a subset of independent input facts that anticipate the impact of the environment (exogenous scenarios) and a subset of management decisions that represent the endogenous scenarios. They give the answer to the basic paradigm of the problem solving which consists of asking question with regard to the problem situation for which the answer is being looked for. In literature it is known as the "what if, then, so what" analysis. "What if' hereby means the formulation of questions regarding the problem situation, and their individual impact on the business system. "Then" represents the possible impact on the system behaviour. The system for the support allows reasoning about of the arisen situation in the sense of the search of answers to "why" that explains individual events and provides for the selection of the important solution for the system from the set of the possible ones. It proceeds into the procedure "so what". The procedure is repeated until a satisfactory solution is found. Generation of scenarios of the simulation system that respond to the part "what if' is based on the variation of parameters of the basic scenario at the extrapolation of the past behaviour and expert evaluation of development targets with the Brainstorming method. Variants of the business scenarios are evaluated with the multi criteria lineary weighted decision function.

business result

Fig.

1. General scheme of the simulation methodology for the decision making support in the enterprices

2.1. Decision making strategy The general simulation model of the business system have been described by the Forrester's system dynamics. System structure consists of level elements and the parameters defining the rate and the auxiliary elements connected in the flow diagram. The diagram is sufficiently abstract to allow a qualitative analysis of the system functioning through feed-back loops. As soon as someone become satisfied with the "picture" of the model, will proceed to the definition of the simulation model. Mathematical model of the simulated system is described by the non-linear differential equations of the first order: y(k + 1)

=J(y(k),x(k), u(k»; k =O,I,2, .. N

(1)

where y E Y represents n-dimensional vector of state variables such as inventory of material/products, cash, income, liabilities etc., x E X represents mdimensional vector of external input to the system (exogen scenario) and u E U represents 1dimensional control vector of the variables (endogen scenario). From the control point of view the simulation procedure could be defined as: fmd a control vector u E Ai E U (alternative) which will

Fig. 1 shows an interaction between the user, simulation model, and scenario in the phase of searching of the solution to the managerial problem for support in decision making of the business system (Kljajic and Leskovar, 1995). The following three basic feed-back loop are emphasised: a) the causal or the feed-back loop representing the business result as a consequence of former decisions making, and being a part of management experiences and history of the system, c) the anticipation or intellectual loop provides the feedforward information which is important for the formulation of the system strategy and b) the aposteriori information about the model applicability and former decisions making. Learning

y(O) to the goal state transfer the initial state y d (N), and satisfy the performance function C for

the given external scenario x enviroment).

Every

certain probability Pi 146

E

scenario E

Si

E

X (state of the

Si EX caracterise

P, relevant for decision

making evaluation. As the results, non inferior sets J of the solution could be obtained after that follows selection of the best solution. The general procedure for the multicriteria choice of the simulation scenario was performed in the following steps:

making. The results of simulation are collected in decision matrix C Table 1, which represents payoff of strategy .

Table 1 Decision payoff matrix

Sj

1. expert judgement to get the list of criteria (interview, brainstorming, voting, expert opinion) 2. pairwise comparison of criteria (AHP) 3. global matrix elicitation and adjustment (AHP) 4. scenario generation (brainstorming, expert opinion) 5. simulation with proposed scenarios (core simulation model) 6. elimination of unacceptable scenarios 7. pairwise comparison of scenarios based on simulation results (AHP) 8. evaluation of scenarios (AHP)

Strategy choice A1A2

Scenario and its probability PI

pm In Table I Cif represents values ofi-th scenario atjth strategy. Considered Ci/ as the linear weighted sum of objectives:

The expert system is one of the possible tools for enhancement of the simulation scenario evaluation. A prototype of connection between the SIMLES and the DEX expert system was presented in (Bitenc et al., 1995). The DEX gives an immediate evaluation of the simulation scenario and provide a deeper insight into the decision making process. The initial ("optimal") scenario is found faster and checked at least by the knowledge base. The DEX evaluation serves as a feedback to improve the simulation scenario either directly, automatically or indirectly through the man-machine interaction.

m

Ci/ =

Lw,J,

(2)

r=l

where w, represent weight factor of r -th objective. The individual objective function J, = q(y , U, k) reflects decision maker's preference of the business politics. It is obvious that the control which satisfy the particular objective in (2) could be in conflict with the goals and the other objectives. Therefore several solutions should be examined in the multicriteria optimization. The definition of the goals, multiple criteria, constraints and preferences is the constant task of the business managers in the market economy. The procedure is iterative and begins with a qualitative description, following by the semi-quantitative and completes with the quantitative description of the simulation elements. There are many different forms of the utility function. In particular case, a common multiple objective function has been chosen as sum of a linearly weighted ratio of simulated and target value of each objective:

Cif

=±(y~s 1.." r=1

Y,d)'"

3. RESULTS AND DISCUSION The described methodology has been preliminary tested in a real business environment. The goal was rather concerned to persuade users of the potential benefits of the new methodology in the management control. The business system is an important producer and reseller in its branch employing over 2000 workers. Variables describing the business process were obtained via historical data. However, specification of goals, multiple criteria, constraints and preferences has been defined by the experts of the firm. As the criteria variables Y , =(Net profit, Current ratio, ITWC ratio, Inventory turn own, Inventory turn-other, Cash, Inventory level) and its respective weights as normalized eigenvector of AHP matrix w,= (.362, .058, .093, .289, .289, .059, .106, .033) it was chosen. The base scenario covers time of 78 weeks. Empirical data is used for the first 25 weeks, the rest was forecasted. The main characteristic of the base scenario is a continuation of the trends from the past period. Further 12 scenarios were derived from the base scenario. The problem scenario proposes difficulties in selling on various market segments and the control scenario includes responses and actions to improve the

(3)

where w, is a weight of the specific objective, Yrd is the target value of the r-th variable and y~ simulation value of the r-th variable in i-th scenario for j-alternative. In case, when (2) is a function of one variables (cost or profit) the problem could be solved by classical decision theory (maximin, maximax or minimax). The simulation method "per se" represents an experimental technique and the final choice of the acceptable solution will be done by the decision maker. The main effort has been devoted to the experiment planning and the decision 147

The developed software solution includes three levels of the problem solving: the intuition, the manmachine interaction and the automatic procedures. A preliminary test in the business environment was satisfactory. Despite some good initial results, there are still many obstacles to transfer it in praxis, having its roots in the undeveloped market economy rather than in the complexity of the simulation task.

problem situation. Scenarios numbered by 0, 10,11 and 12 had been eliminated for further analyses as inferior. The results of the evaluation of the rest scenario are presented in the Table 2. The first column gives the number of the scenario sorted in the descending order from the best to the worst, the second the overall criteria function obtained by the simulation, the rest are particular evaluation criteria of first four most relevant objectives (85% of total weights). It is obvious that the rank of the scenario is strictly correlated with the value of net profit due to dominancy of its weighting factor. There is only minor difference between SC3 and SC2. Final decision or strategy take care of the external uncertainty, the criteria ambiguity and the feasibility of certain scenario are based on the basis of subjective probability. For that purpose DEX expert system is used. It provides definition in fuzzy logic management preference and risk of each scenarios with the objectives obtained through simulation.

Acknowledgement This research was supported by Ministry of Science and Technology of the Republic of Slovenia, Project number: J5-6218-0586-96.

REFERENCES Bitenc I., R. Leskovar, V, Rajkovic, and M. KIjajic (1995). Evaluation of simulation results with an expert system. Proceedings of the international

conference: Production and logistics forum (Z. Kaltnekar and T. Ljubic, Ed.), Vol 1-2, pp. 417426, Bled. Forrester, J.W.(l961). Industrial Dynamics. MIT Press, Cambridge, Mass. HallO. P. (1996). A DSS based simulation model for teaching business strategy and tactics. Proceedings of the lASTED International conference on Modelling, Simulation and Optimization (M.H. Harnza, Ed.), Gold Coast, Australia. KIjajic M. and R. Leskovar (1994). Multicriteria Assessment of Simulation Scenario for Business Decision Support. lASTED, Applied Simulation & Modelling, (M.H. Harnza, Ed.). Acta Press, Anaheim-Calgary-Zurich. KIjajic M. and R. Leskovar (1995). A Simulation System for Decision Making Support in Business Systems, Production economics and logistics forum, Vol. 1-2, pp. 463-472. Aedermansdorf Scitec Publication. KIjajiC M., R. Leskovar, A Skraba, V. Rajkovic and I. Bitenc (1996). Multicriteria evaluation of a simulation scenario for business decision support. Proceedings of the lASTED International conference on Modelling, Simulation and Optimization (M.H. Hamza, Ed.), Gold Coast, Australia. Rajkovic v., J. Efstathiou and M. Bohanec (1987). A Concept of Rule-Based Decision Support Systems. Optimization Models Using Fuzzy Sets and Possibility Theory (J. Kacprzyk, J. Orlovski and D. Reidel, Ed.). AS., Publishing Company, Dordrecht. Saaty T.L. (1990). How to make a decision: The Analytic Hierarchy Process. European Journal of Operational Research, 48, pp. 9-26.

Table 2 Summ!!!y of scenario evaluation

SC7 SC3 SC2 SCl SC4 SC8 SC5 SC9 SC6

overall net invent. score Erofit trn.own 0.36 0.13 0.17 0.17 0.27 0.22 0.17 0.23 0.18 0.14 0.16 0.29 0.16 0.10 0.12 0.09 0.14 0.11 0.07 0.09 0.05 0.06 0.07 0.07 0.04 0.06 0.04

cash ITWC ratio 0.07 0.07 0.08 0.06 0.11 0.09 0.05 0.04 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.01

4. CONCLUSION The article describes the multiple criteria methods of the simulation scenario choice for the decision support in the business system. The weights of the each criterion are determined by experts with the brain storming method exploring group decision support methodology. Interactive methods of the evaluation of possible solutions are supported with the expert system providing for various analysis and comparisons, such as target and criterion preferences. The result of the simulation has been also analysed according to the principle of the analytical hierarchy processes AHP. The underlying research interrelated a simulation with an artificial intelligence. The possibility and the urge of such an integration is emphasized. The proposed concept include the "hard" and the "soft" methods of the scenario creation and selection of the solution. The interdisciplinary approach enables a systematic, an independent and an interactive evaluation of the business strategy or an individual business decision. 148