AGroupDecision-MakingModel of Risk Evasion in Software Project Bidding Based on VPRS

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1 AGroupDecision-MakingModel of Risk Evasion in Software Project Bidding Based on VPRS Gang Xie 1, Jinlong Zhang 1, and K.K. Lai 2 1 School of Management, Huazhong University of Science and Technology, Wuhan, China xgbill@hotmail.com, jlzhang@mail.hust.edu.cn 2 Department of Management Sciences, City University of Hong Kong, Hong Kong and College of Business Administration, Hunan University, China mskklai@cityu.edu.hk Abstract. This study develops a group decision-making model based on Variable Precision Rough Set, which can be used to adjust classification error in decision tables consisting of risk-evading level (REL) of software project bidding. In order to reflect experts ability, impartiality and carefulness roundly during the course of group decision-making, a weight is endowed with each expert. Integrated risk-evading level (IREL) of projects and risk indices are computed. Then, risk-evading measures, the rank of risk-evading strength and risk-evading methodology are discussed. 1 Introduction Risk evasion, including risk identification, risk assessment, risk analysis, risk reduction and risk monitoring, is an approach to prevent and remove the risk in software project bidding, and its purpose is to achieve the success of the bidding. Based on the experts experience, subjective judgement and sensibility, risk evasion is a complex, unstructured or semi-structured decision-making process. Risk-evading level (REL) of software project bidding is the experts evaluation on risk-evading strength project and indices needed. Because of evaluating error, practical risk-evading strength is always different from that which the projects really need: If bidders risk-evading strength is too high, they will refuse to bid for software projects with lower risk than their evaluation, or it will cost more to develop and implement the software projects. On the other hand, if their riskevading strength is too lower, bidders will erroneously accept software projects with higher risk than expected, which causes the failure of projects without precaution. In the same way, improper risk-evading measures also result in the bidding failing. In this study, successful bidding refers to not only achieving the contract but also the profitable development and implementation of software projects. As a matter of fact, risk evasion is a prerequisite of successful bidding, D. Śl ezak et al. (Eds.): RSFDGrC 2005, LNAI 3642, pp , c Springer-Verlag Berlin Heidelberg 2005

2 A Group Decision-Making Model of Risk Evasion 531 which needs proper risk-evading measures and strength. Therefore, a group decision pattern is adopted to gain comprehensive and precise decisions, since this makes the best use of experts knowledge and experience. With the development of communication, computation and decision support in information technology, related demand accelerates the study in the field of group decision support system, and facilitates expert groups with different knowledge structures and experience to work together in the process of unstructured and semi-structured decision-making problems [1,2]. Integrated risk-evading level (IREL) is the aggregation of all expert s evaluation of REL. As a rule, IREL of risk indices decides the strength of corresponding risk-evading measures. The IREL of a project decides the risk-evading strength of the project. Under a group decision pattern, experts score the REL that software projects and the indices need, based on which decision tables are established. This paper makes use of VPRS [3,4] as a data mining tool to process the data in decision tables, remove noise in the data by setting an approximate precision factor β(0.5 <β 1), and endows each expert with a weight. Then, REL of experts is aggregated into IREL. Relationship among IREL, risk-evading measures, riskevading strength and risk-evading methodology are discussed. 2 Group Decision-Making Model Suppose C, D A are the condition attribute set and the decision attribute set respectively, and A is a finite set of attributes, U is the object set. Then with Z U and P C, Z is partitioned into three regions: POS β P (Z) = Pr(Z X i) β {X i E(P )} NEG β P (Z) = Pr(Z X i) 1 β {X i E(P )} (1) BND β P (Z) = 1 β<pr(z X i)<β {X i E(P )} where E( ) denotes a set of equivalence classes, i.e. the condition classes based on P. The significance of P to D, also the quality of classification, is defined as γ β (P, D) = card(posβ P (Z)) card(u) (2) where Z E(D) andp C. Suppose there are m experts, n risk factors, which are independent with each other, in the risk index system. P i denotes the ith risk factor in the system, i =1, 2,...,n. Decision table is established based on the experts score of the REL of each software project bid (see Table 1). From formula (2), the significance of P ki to D is γ β (P ki,d)= card(posβ P ki (Z)) (3) card(u) where P ki is the score that the kth expert (k =1, 2,...,m)evaluatestheREL of P i.

3 532 G. Xie, J. Zhang, and K.K. Lai Generally, experts weight is assumed same for convenient. In this paper, we divide experts weight into subjective weight s k and objective weight o k. s k is endowed according to the advantages of the experts, such as competence, speciality, fame, position, etc. o k is decided according to the score of experts [5]. As subjectivity and randomness exists in s k, this study mainly discusses using distance matrix theory to decide experts o k. Combining AHP [6] and VPRS, from formula (3), taking expert k as an example, we construct judgment matrix B as follow. b 11 b 12 b b 1n b 21 b 22 b b 2n B =.... b n1 b n2 b n3... b nn We can see that b ij is the element of the ith row and jth column in judgment matrix B, and it denotes the relative significance between risk indices P i and P j. b ij = γβ (P ki,d) γ β (P kj,d) = card(posβ P (Z))/card(U) ki card(pos β P kj (Z))/card(U) = card(posβ P ki (Z)) card(pos β P kj (Z)) (4) As b ij b jk = b ik, B is a matrix with complete consistency. Obviously, the judgment matrix is always complete consistency when VPRS and AHP are combined to compute the weight of attributes. We obtain a priority vector for each expert after processing the data in decision table (Table 1). A distance matrix [7,8] is constructed to reflect difference between the score of experts, and we obtain o k. According to the REL of the risk indices scored by expert k, the geometric mean is used to obtain priority vector W k. After normalization, the weight of P ki is defined as W ki = ( n b ij ) 1 n j=1 n ( n b ij ) 1 n i=1 j=1 where W ki is the weight of P i decided by expert k, so the priority vector consisting of the weight of n risk indices is (5) W k =(W k1,...,w ki,...,w kn ) T (6) Repeat formula (4)-(6), priority vector of each expert is computed. And the distance between two experts priority vectors, for example, W a and W b (a, b = 1, 2,...,m) is defined as d(w a,w b )= 1 l (W ai W bi ) 2 2 (7) i=1

4 A Group Decision-Making Model of Risk Evasion 533 where d(w a,w b ) indicates the difference between the decision-making of expert a and that of expert b. To reflect the judgment difference from one expert to the others, we construct distance matrix D as 0 d(w 1,W 2 ) d(w 1,W 3 )... d(w 1,W m ) 0 d(w 2,W 3 )... d(w 2,W m ) D = symmetry 0 Let d k = m d(w k,w j ), where d k denotes the difference in degree between W k j=1 and other priority vectors. The objective weight of expert k shows the evaluating difference of expert k from other experts, and o k decreases in d k. Based on this theory, o k is defined as o k = 1/d k m (8) (1/d k ) k=1 In particular, when d k =0,thismeansthatallexperts evaluationisexactly the same. However, this result seldom happens, but if it does, the experts should be reorganized to evaluate the REL once again, and go on the procedure. The weight of expert k is defined as γ k = cs k + do k (9) where c+d = 1.We let subjective weight of experts s k a constant in this paper.by changing the values of c and d, we can adjust the proportion of s k and o k within the weight of experts, which means that the model can be applied to different m kinds of group decision patterns. Clearly, s k =1, m o k =1, m γ k =1. k=1 k=1 k=1 According to above analysis, experts score the REL of all bidding projects (decision attributes) and their indices (condition attributes). After processing the data in decision table consisting of REL, we obtain the IREL of software projects and their indices. The IREL of index P i is defined as m U i = P ki γ k W ki (10) The IREL of project i is defined as V i = k=1 m D ki γ k (11) k=1 where D ki is the REL of the ith project that expert k scores. U i and V i integrate the evaluation of all experts. U i decides the risk-evading strength of corresponding risk-evading measures, while V i indicates the risk of the project and is used to decide whether bidders should bid for the projects or not.

5 534 G. Xie, J. Zhang, and K.K. Lai According to above analysis, the algorithm is designed as the following 12 steps: Experts are invited to evaluate the REL and decision table is established. Choose the variable precision factor β. Compute γ β (P ki,d) for each risk index P i,ifγ β (P ki,d)=0,thenremove the indices that meet γ β (P ki,d) = 0 and define W ki =0. Compute relative significance b ij between risk indices for the same expert. Establish judgment matrixes based on b ij. Compute the significance of each risk index. Create priority vectors of all experts. Construct the distance matrix. Compute the objective weight o k of expert k: ifd k = 0, return to the first step. Establish the weight of expert k according to some proportion of s k and o k. Compute the IREL of projects and their indices. Sort the risk-evading strength adopted to corresponding risk-evading measures. Some literature discusses risk-evading measures in bidding [9]. Generally speaking, risk-evading measures of software project bidding can be summarized as follows: (i) mechanism. According to software engineering and experience, a good mechanism is established to improve efficiency of software development and implementation. (ii) offer. If the competition is serious, reduce the offer, or else, if the risk of project management is serious, enhance the offer or do not take part in the bid. (iii) service. By improving service such as by upgrades, maintenance frees and so on, bidders reinforce their competitiveness to win the bidding. (iv) contract. The contract regulates the force majeures and the obligations of each side involved in software projects. So when the force majeure comes into play, bidders do not respond with damages. What is more, the contract can prevent the risk from clients who do not fulfil their obligations. (v) outsourcing. Risk can be evaded by outsourcing some part of software projects that bidders are not accomplished in. (vi) cooperation. If the project is too large for any one company, bidders may cooperate with other IT companies to finish part or whole of a software project. Complementing each others advantage, they coordinate to pool their risk. 3 Example An IT company lists 10 software projects from those are inviting public bids as its bidding objects. Four experts are invited to evaluate the REL of the projects and their indices. The expert team analyzes the risk existing in the software project

6 A Group Decision-Making Model of Risk Evasion 535 bidding, and establishes the index system, which includes 5 main risk indices: client risk P 1, ability risk P 2,marketriskP 3, development and implementation risk P 4, technology risk P 5. The score includes four levels: 1, 2, 3, 4, where 1 denotes light, 2 denotes moderate, 3 denotes some serious, 4 denotes serious. After assessment of REL, decision table is established (see Table 1). Table 1. Decision table consisting of REL E 1 E 2 E 3 E 4 U P1 P 2 P 3 P 4 P 5 D P 1 P 2 P 3 P 4 P 5 D P 1 P 2 P 3 P 4 P 5 D P 1 P 2 P 3 P 4 P 5 D Here, m =4,n =5,letc = d =0.5,s k =0.25,β =0.8. Based on Table 1 and the algorithm, the objective weight of the four experts are: o 1 = 0.247,o 2 =0.328,o 3 =0.231,o 4 =0.194, then we get the weight of experts: γ 1 =0.2485,γ 2 =0.289,γ 3 =0.2405,γ 4 =0.222, respectively. So the IREL of software project bidding is as follows in Table 2. Table 2. IREL, risk-evading measures and strength sorting U P 1 P 2 P 3 P 4 P 5 D measures and strength (descending) (ii) (iii) (vi) (iv) (i) (v) (ii) (iii) (vi) (iv) (i) (v) (ii) (iii) (vi) (iv) (i) (v) (vi) (ii) (iii) (i) (iv) (v) (vi) (ii) (iii) (i) (iv) (v) (vi) (ii) (iii) (i) (iv) (v) (ii) (iii) (vi) (iv) (i) (v) (ii) (iii) (vi) (iv) (i) (v) (ii) (iii) (vi) (iv) (i) (v) (ii) (iii) (vi) (iv) (i) (v) 4 Discussion From above analysis, we continue our discussion about IREL, risk-evading strength, risk-evading measures and risk-evading methodology.

7 536 G. Xie, J. Zhang, and K.K. Lai 4.1 IREL REL is the evaluation on the risk-evading strength of projects and their indices by each expert. In order to enhance the precision of software project bidding risk evasion, group decision-making pattern is used, under which knowledge of multi-expert is integrated, to form IREL. 4.2 Risk-Evading Strength Risk-evading strength of measures is implemented according to IREL to reduce the risk. According to the experts experience, the software projects are divided into 3 types and 3 corresponding IREL intervals respectively. In Type I, IREL (1,1.5], the projects have low risk. Type II, IREL (1.5,3.5], are middle risk. Type III, IREL (3.5,4.0], are high risk. The intervals can also be adjusted according to the detail situation. From Table 2, we see that for projects of type I, for example, projects 2 and 4, the IREL is on the low side. Hence, they need the least risk-evading strength, and the cost of risk evasion can be reduced on this type of project. The IREL of type III projects is very high (for example, projects 8 and 10) and therefore they need the highest risk-evading strength. It is difficult to accomplish the type III projects, and to work out which will most probably have the largest budget deficits. We should reject these types of projects, i.e. not bid for them. A majority ofprojectshavenormalirel,suchasprojects1,3,5,6,7and9,andtheseare type II projects. The IREL of some indices is low (such as P 4 and P 5 )which indicates that the indices are less important in the system, i.e. the impact of these indices on the risk-evading strength is low. On the other hand, some of the indices have the greater IREL (for example P 3 ) which indicates that this index is the most important in the system and it influences the risk-evading measures and their strength most. 4.3 Risk-Evading Measures Each risk index corresponds to some kind of risk-evading measures. The riskevading measures are mainly implemented to the projects of type I and II. The study shows: Client risk (P 1 ) is caused by the tenderee, such as by lack of management support, improper demand orientation, financial crisis and uncoordinated personnel, and the risk-evading measure can be (iv). Capability risk (P 2 )includes bidders assets, relative experience and understanding of clients demand, and (vi) is a good measure. When there are many bidders, market risk (P 3 )is serious, and risk-evading measures (ii) and (iii) are appropriate, i.e. adjusting the offer and improving service. Development risk (P 4 ) always occurs because of a lack of a good mechanism, and risk-evading measure (i) is needed to improve the situation. If technology risk (P 5 )appears,itmaycosttoomuchtime to continue the project through learning or cooperation, so (v) is a proper riskevading measure. For a software project, there may be many other risk-evading measures. While, the measures are not always used separately, if all of them

8 A Group Decision-Making Model of Risk Evasion 537 are used, their strength should be different. Thus, the risk-evading strength of the measures is sorted, which will help managers know the significance of the measures in practice (see Table 2). 4.4 Risk-Evading Methodology Patterson and Neailey [10] consider that the project risk management is a circular procedure. The risk management system consists of various tools, techniques and methods underlying the process. They construct the risk register database system within risk reduction stage, and this risk register can be updated as an ongoing and dynamic process. Based on the methodology, the intellectualized riskevading system (IRES) can be established using expert group decision-making pattern. The IRES can monitor the whole circular process of risk evasion, and process correlative information continuously. As a part of the system, experts make their decisions on the five stages online. Data is updated according to experts decision-making in each stage within a new circulation, and new knowledge is mined in databases, which means that the decision-making is always the optimal within the context of the current knowledge background. The methodology is a mechanism that system owns the ability of self-study and intellectualised information process. 5 Conclusion VPRS is a good tool to remove the data noise in the information system, which improves the precision of decision-making. Under the pattern of expert group decision-making, experts are endowed with a weight, which can reduce the negative effect caused by differences in experts subjectivity and ability difference. The risk-evading strength of the measures increases in IREL of corresponding risk indices, while the risk-evading strength of a project increases in IREL of the bidding project. Sometimes, software projects have too high risk-evading strength to bid for since the IREL is too high and no surplus is expected. Generally, if proper risk-evading measures and strength are implemented for software projects with corresponding IREL, the efficiency of risk evasion will be improved greatly. Acknowledgement This project is supported by National Natural Science Foundation of China ( ) and Ministry of Education ( ) and the grant from the NNSF of China and RGC of Hong Kong Joint Research Scheme (Project No. N CityU103/02). We thank Hubei Bidding Company for providing us with the data used in our experiments.

9 538 G. Xie, J. Zhang, and K.K. Lai References 1. Gerardine, D., Brent, G.R.: A foundation for the study of group decision support systems. Management Science, 33(5) (1987) Bidgoli, H.: Group decision support system. Journal of System Management, 14(1) (1996) Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences, 46(1) (1993) Beynon, M.: The Elucidation of an Iterative Procedure to eâ-reduct Selection in the Variable Precision Rough Sets Model. LNAI, Springer-Verlag Berlin Heidelberg, 3066 (2004) Ramanathan, R., Ganesh, L.S.: Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members weightages. European Journal of Operational Research, 79 (1994) Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York, (1980) 7. Hayden, T.L., Tarazaga, P.: Distance matrices and regular figures, Linear Algebra Appl., 195 (1993) Trosset, M.W.: Distance Matrix Completion by Numerical Optimization, Computational Optimization and Applications, 17 (2000) Wu, Q.L.: Risk analysis before tender, Chinese Cost Management of Railway Engineering, 1 (2000) Patterson, F.D., Neailey, K.: A risk register database system to aid the management of project risk, International Journal of Project Management, 20 (2002)