European Journal of Operational Research 37 (1988) 347-354 North-Holland 347 Theory and Methodology Delphic hierarchy process (DHP) : A methodology for priority setting derived from the Delphi method and analytical hierarchy process Reza KHORRAMSHAHGOL * A T& T Bell Laboratories, 480 Red Hill Rd, Middletown, NJ 07748, USA Vassilis S. M O U S T A K I S Department of Management Systems, Technical University of Crete, Chania, Greece Abstract: Identifying of criteria and objectives is of paramount importance to a decision-making process and is the basis for a sound decision. A systematic approach, therefore, is needed so that the objectives of the organization not only can be identified but also prioritized so that the resources will be allocated to the relative importance of the objectives and how well the alternatives satisfy them. The methodology proposed here uses the Delphi method and integrates it with the analytic hierarchy process. It assists the decision maker(s) to systematically identify the organizational objectives and then to set priorities among them. The application of the proposed model is illustrated by a case study. Keywords: Objectives, priority setting, economic development projects, project evaluation 1. Introduction Decision making essentially deals with the planning aspect of the management process. It involves identifying objectives and alternatives and choosing among them. Identifying criteria and objectives is of paramount importance to a decision-making process and is the basis for a sound decision. Inappropriate objectives will lead to improper planning and open the door to chaos. * This work was performed when the author was with the School of Business, North Carolina Central University, Durham, NC 27707, USA. Received April 1987; revised January 1988 Because much subjectivity enters into multiobjective decision-making models, the decision can be error-prone even if the model works perfectly. Therefore, this research aims to develop a methodology that reduces subjectivity and allows decision makers to elicit systematically (1) the organizational objectives and (2) subjective value judgments for these objectives to be used to set priorities among them. The proposed model is an effective priority-setting technique that benefits from a strong and widely used managerial tool (i.e., the Delphi method) and integrates it with a powerful mathematical model (i.e., analytic hierarchy process). The Delphi method and analytic hierarchy process are discussed next, then the proposed 0377-2217/88/$3.50 ~'~1988, Elsevier Science Publishers B.V. (North-Holland) 348 R. Khorramshahgol,V.S.Moustakis/ Delphichierarchyprocess model is introduced and its application illustrated through a case study. 2. Delphi method The Delphi method is a systematic procedure for evoking expert opinion. According to Dalkey [3], there are three features to Delphi: (1) anonymity; (2) controlled feedback; (3) statistical group response. Anonymity, effected by the use of questionnaires or other formal communication channels, such as on-line computer communication, is a way of reducing the effect of dominant individuals. Controlled feedback--conducting the exercise in a sequence of rounds and giving participants a summary of the results at the end of each r o u n d - - i s a device to produce objectivity. Use of a statistical definition of the response is a way of reducing group pressure for conformity; at the end of the exercise there may still be a significant spread in individual opinions. Probably more important, the statistical group response is a device to assure that the opinion of every member of the group is represented in the final response. Within these three basic features, it is, of course, possible to have many variations. The rationale behind the Delphi, according to Dalkey [3], is the age-old adage: " t w o heads are better than one", (or in general: n heads are better than one). Linstone and Turoff [9] explain the process of conventional Delphi as: " A small monitor team design a questionnaire which is sent to a larger respondent group. After the questionnaire is returned the monitor team summarizes the results and, based upon the results, develops a new questionnaire for the respondent group. The respondent group is given at least an opportunity to re-evaluate its original answers based upon examination of the group response. To a degree, this form of Delphi is a combination of a polling procedure and a conference procedure which attempts to shift a significant portion of the effort needed for individuals to communicate from the larger respondent group to the smaller monitor team." Through the Delphi inquiry, the views of the decision makers as well as others in the organization can be obtained and used to generate new ideas, unique suggestions, and distinct alterna- tives. Delphi also enables the monitor team to bring together the opinion of individuals located in different geographical areas whose views are crucial for decision analysis, and whose joint meeting is impossible or costly. Dalkey [3], however, warns against the fact that there might also be at least as much misinformation in n heads as there is in one. Therefore, selection of the panel members and questionnaire formulation are of utmost importance. An excellent and readable book by Stanley L. Payne [13] can be of great assistance in designing the questionnaire. This book explains the art of asking the right questions in the right way, and it deals with human behavior and the principles of wording. 3. Analytic hierarchy process (AHP) AHP, introduced by Saaty [15], is based on the idea that a complex issue can be effectively examined if it is hierarchically decomposed into its parts. A H P implementation entails a hierarchy whose top level reflects the overall objective: the flows. Criteria on which the focus is dependent are listed at intermediate levels, while the lowest level includes the alternatives. An element at a higher level is said to be a governing element for those elements at the lower level• Elements at a certain level are compared to each other with reference to their effect on the governing element. Let us consider the elements C 1, C2. . . . . Cn of some level in a hierarchy and let us denote their normalized, unknown, priority weights by w 1, w 2 . . . . . wn, respectively. The value of w i reflects the degree of importance of C, with respect to C/s governing element. The first step in the calculation of W, 's is to derive pair-wise comparisons between the n elements. These pairwise comparisons are structured into a n-by-n reciprocal matrix a = [a(i, j)], called the judgment matrix: G C1 ]Va(1, 1) An = C2 [a(2, 1) C, [~(n', 1) c~ .-. co a(1, 2) a(2, 2) ... -.. a(2, n) a(n, .-- a(n, n 2) a(1, n1 R. Khorramshahgol, V.S. Moustakis /Delphic hierarchy process Elements of matrix A are derived using the following scale: a(i, j ) = 1 when i = j , diagonal elements, a(i, j ) = 1 if C, and ~ are equally important, = 3 if C, is weakly more important than 349 number of areas ranging from energy management to political decision making [14,15] and software package evaluation [11,12]. Zahedi [20] gives a good survey of A H P and its applications and Harker [6] assesses A H P and its critics. cj, = 5 if C~ is strongly more important than 4. Outline of the proposed model = 7 if C, is very strongly more important than ~ , = 9 if C, is absolutely more important than = 2, 4, 6, 8: used to compromise between two judgments. Also a(i, j ) = 1 / a ( j , i) for all i, j = 1, 2 . . . . . n. If element C~ dominates over element C 2, then the whole integer is entered in row 1, column 2 and the reciprocal (fraction) is entered in row 2, column 1. If element C'2 dominates element C~ then the reverse occurs. If the elements being compared are equal, then one is assigned to both positions. There are n ( n - 1 ) / 2 judgments required to develop a n-by-n judgment matrix, since reciprocals are automatically assigned in each pair-wise comparison. Second, the unknown weights are calculated from the judgment matrix A through the following equation n (A - I ) W = O; Y'. wj = 1 j=l where I and O are the unitary and zero matrices, respectively, and W the normalized vector of weights W 1 ... IV,. In addition, Saaty [14,15] has developed an inconsistency index to capture any bias when relative comparisons are made. The reciprocity of the judgment matrix requires that a(i, k ) = a ( i , j ) * a ( j , k), but this is often violated. The inconsistency ratio (IR) is defined as: X-n IR=-- n--1 where X is the largest eigenvalue. A zero value would indicate perfect consistency whereas larger values indicating increasing levels of inconsistency. Saaty has indicated that the I R should be about 10% or less to be acceptable. If the I R exceeds the 10% level, value judgment may need to be revised. A H P has had wide success in a AHP, described in the previous section, provides a framework to structure individual and group subjective judgments. In this paper we suggest that the Delphi method be conducted prior to A H P so that not only can the objectives to be considered in analysis be determined, but the opinions of all decision makers can also be incorporated in problem formulation. We refer to the merger of A H P and Delphi as Delphic Hierarchy Process (DHP). This section outlines the steps of DHP, and the next section, by means of experimentation, illustrates how D H P can be used to elicit objectives from decision makers, obtain their weighting of those objectives, and then derive priorities among them. The steps of D H P are as follows: I. Select a monitor team to conduct the Delphi inquiries. The team should consist of experts familiar with the problem area--e.g., managers a n d / o r staff or anyone who will be involved in decision making for the problem. II. Choose the participants of the Delphi inquiries. The monitor team then chooses the individuals who will participate in the inquiries--e.g., the decision maker(s) and experts as well as anyone who can provide some input. III. Use the Delphi method to determine objectives and their weights. The monitor team should design a questionnaire in which the participants are asked to specify the objectives the organization should pursue in the long or short run. Obviously these objectives may be diversified (and often conflicting). Since the purpose is to prioritize them, all objectives can be included for further analysis. If any screening is necessary, it can be done after priorization. Alternatively, the monitor team can use the weights obtained in the Delphi inquiry to eliminate the unimportant objectives before proceeding to the next step. IV. Perform another Delphi to set up a pairwise comparison matrix for objectives. Here, the objec- R. Khorramshahgol, V.S. Moustakis / Delphichierarchyprocess 350 Delphi inquiries I Delphi inquiry I Information eficiting Ranking of objectives Objectives and their weights Prepare a list of important objectives Delphi inquiry II Pairwise comparison matrix Priorities for objectives Figure 1. An overviewof the proposed model rives specified in step III should be presented to the participants in order to obtain their subjective value judgments for pairwise comparison matrix. If consensus is not reached regarding any individual element of this matrix, the arithmetic mean of the value judgments of all participants will be considered for that element. V. Obtain eigenvalues of the pairwise comparison matrix. The eigenvalues of this matrix represent the priority among objectives. This set of objectives then can be an input to any multi-criteria resource allocation model (see Khorramshahgol [7,81). 5. Why use Delphi? Many other techniques for forecasting and preference analysis exist. To name some: (1) Bernolli's Utility Theory [1], (2) Samuelson's Revealed Preference [16], (3) Econometric Models [10], and (4) Socio-Psychological Scaling Techniques [4]--e.g., Paired Comparison," The Method of Equal-appearing Intervals," The Method of Successive Intervals," Summed Rating Method, etc. For the purpose of our problem--namely, determining the objectives and their weights--the Delphi method is the most suitable because other forecasting and preference analysis models all lack the Delphi capability to elicit expert opinion iteratively. Some others such as Samuelson's Revealed Preference also need an astronomical amount of data to build a model. Other advantages of the Delphi that cannot be provided by other methods are the following: (1) All managers and decision makers will be deeply involved in the planning process because the Delphi allows them to suggest what objectives should be considered in the analysis. Therefore, Delphi will ensure not only a more agreeable solution (i.e., agreement on objectives selected) but also an effective implementation of alternative(s) chosen to achieve the objectives. (2) Because of anonymity, Delphi allows the participants to express their opinions freely and to assign numerical values to what is essentially an opinion, though an educated one. The participants will be given the opportunity to express their subjective value judgments for each objective and can be assured that their judgments will be taken into account. On the other hand, for this very reason, the subjectivity in assigning weights to objectives will be minimized and the weights will be more objective. Similarly, the subjectivity inherent in the construction of pairwise comparison matrices will be minimized. 6. The application of the proposed model The case of La Carreteria Bolivariana Marginal De la Selva: An international development highway To test its practicality, the proposed model (DHP) was applied to an international development highway called La Carreteria Bolivariana R. Khorramshahgol, V.S. Moustakis / Delphic hierarchy process Marginal De la Selva. This highway is to start from the frontier of Columbia and Venezuela and end at Santa Cruz in Bolivia. (For a detailed explanation, see Steiner [17,18]). President Fernando Belaunde was the prime mover of this highway and presented its socio-economic concept in his 1959 book, The Concept of Peru by Peruvians. Bolivariana appears in the highway's name because the road traverses part of the area liberated by Simon Bolivar and because the highway is a step toward Bolivar's great h o p e - - t h e unification of South America. It will be a major step since it is to link in its course all areas suitable for agriculture, cattle raising, and forest exploitation along the upper rim of the jungle, which washes against the eastern slope of the Andes in Colombia, Ecuador, Peru, and Bolivia. At present, the Peruvian Oriente, which is the country's largest region, is isolated from the rest of the country. However, there is a great potential for developing Oriente's natural resources and its agricultural product and cattle raising. " T h e technique of our engineers has been, until now, that of joining two more or less distant points by the shortest road. This criterion is not appropriate for a colonizing highway such as the Bolivar Highway, where the main interest lies in opening up the largest possible area of useful land for agriculture and cattle raising [2, p. 4]. After his election as President of Peru in 1963, Belaunde began to carry out his idea by inviting the governments of the countries concerned to consider the project. In October, 1963, the Ministers of Development and Public Works of the four countries met in Lima. They agreed to a preliminary feasibility study and subsequently more detailed studies. " I n the case of Peru, the transportation modes connecting coastal Peru with its jungle are truck, airplane, and beast of burden. All these, coming west from the jungle (the Oriente) must cross the Andes (the Sierra-Alti-plano) and come down to the coastal desert where Lima and many other cities and towns are located. But east-west roads are scarce, the terrain is formidable, and earthquakes and landslides are frequent. Thus the cheapest mode, the truck, is undependable. For producers of perishable agricultural products, dependability of transport is vital. However, the construction and improvement of these east-west links--called penetration roads--is proceeding 351 rapidly, and if all goes as scheduled, by the time the Bolivar Highway is completed, the penetration roads will have been in operation for some years. The Bolivar Highway will connect the ends of the penetration roads. As each section of it is finished the agricultural lands it crosses will be open for colonization. The Bolivar Highway will provide the missing eastern side to the grid formed by the Pan-American highway running north and south along the coast and the penetration roads running east and west over the Andes" (Steiner [17]). To set construction priorities along the route, the highway was divided into sections that formed a " T " with the penetration roads from the coast. The vertical of the " T " is the penetration road, the horizontal is the new highway. Each section of the Bolivar Highway is connected to a penetration road already in existence, planned, or in the process of construction. One of the primary objectives of the Bolivar Highway is to initiate the integration of the country's largest region, the Peruvian Oriente, with the rest of the country, as well as developing its natural resources and agricultural potential. As an international highway, the Bolivar project is expected to foster economic interchange among the four countries through which it passes, thereby, doing its share toward reaching the major goal of all South American transport projects: the tying together of a continent. Table 1 summarizes a few of the facts about the Bolivar Highway (see TAMS report [19]). The appfication of DHP In the case of the La Carreteria Bolivariana Marginal De la Selva, the purpose of D H P was threefold: (1) to elicit the objectives to be pursued Table 1 Some facts about the Bolivar Highway Total length of the Highway Colombia Ecuador Peru Bolivia Existing portions Portions under construction Portion to be built 5 590 kms. (24%) ( 15 %) (44%) (17%) 1 320 860 2460 950 kms. kms. kms. kms. 1030 kms. 743 kms. 3 810 kms. 352 R. Khorramshahgol, V.S. Moustakis /Delphic hierarchy process Table 2 Part I of questionnaire--Round 1 Table 3 Part II of questionnaire--Round 1 Please read the case study carefully. Assume that you are an economist in the Socio-Economic Studies Division of the Department of Transportation of the Government of Peru. In the space provided, please name at leastfive objectives that you think should be pursued when allocating resources for the construction of the La Carreteria Bolivariana De la Selva. Please be very specific and consider the viewpoint of the Peruvian government only. Example: In a private company the possible objectives might be: Refer to your answer to Part I. Please rank the objectives in order of importance, from most to least important. Weight these objectives using a scale of 1 to 100. Assign 100 to the objective you consider most important, and judge all others by that objective. One almost as important might be 95; half as important would be 50. 1. To increase sales revenues 2. To maintain the level of employment 3. To decrease employee absenteeism 4. To improve the quality of products No. Objective Weight I n the next r o u n d of the Delphi, the respondents were given a list of the objectives (Table 4) o b t a i n e d from R o u n d 1. They were then asked to review the s u m m a r y a n d to weight the objectives again. The p u r p o s e for the second r o u n d of the Delphi was to p r o v i d e each p a r t i c i p a n t with some overall i n f o r m a t i o n a b o u t the objectives a n d their weights a n d to give t h e m a chance to change their responses (in the light of new i n f o r m a t i o n ) if they wished. Table 4 Questionnaire--Round 2 w h e n c o n s t r u c t i n g the Bolivar Highway, (2) to screen these objectives so that u n i m p o r t a n t ones will n o t be considered further a n d (3) to prioritize the screened objectives. The experiment was as follows ( R o m a n n u m e r als correspond to those of the p r o p o s e d m e t h o d o l ogy, page 7): I. A m o n i t o r team consisting of the authors was formed to c o n d u c t the Delphi inquiries. II. The p a r t i c i p a n t s were selected b y the m o n i tor team. The a u t h o r s at the time taught two graduate level courses in E c o n o m i c A n a l y s i s for P l a n n i n g at The George W a s h i n g t o n University. T h e students of these two classes were chosen to be the p a r t i c i p a n t s in the Delphi inquiries. The case study presented in the previous section a n d the socio-economic aspects of it were a part of the course. Therefore, the case was fully discussed in b o t h classes a n d its details explained. III. A Delphi i n q u i r y was performed, its purpose being to get the p a r t i c i p a n t s ' ideas a b o u t objectives to be p u r s u e d when allocating resources for the c o n s t r u c t i o n of the highway. Tables 2 a n d 3 are the questionnaires for the first r o u n d of the Delphi inquiry. The following is a summary of the responses to the recent questionnaire on objectives for road construction fund distribution in Peru. They were chosen based on the average weight and the number of respondents favoring each objective. A list of the weights for different objectives is also given. Please take a few minutes to review the summary, and weight the objectives on a scale of 1 to 100. Assign 100 to the objective you consider most important, and judge all others by that objective. One almost as important might be 95; half as important would be 50. No. 1 2 3 4 5 6 7 8 9 10 Objectives To increase level of employment To improve agriculture and cattle raising To provide access to natural resources To provide access to markets To serve the largest number of people To reduce transportation expenses To increase GNP To increase trade with neighboring countries To increase foreign exchange To increase tourism Weights from Round 1 39.80 17.00 16.00 11.75 10.00 7.25 6.75 5.00 2.50 2.50 Weights for Round 2 353 R. Khorramshahgol, V.S. Moustakis /Delphic hierarchy process Table 7 Overall pairwise comparison matrix Table 5 Objectives and their weights (1) (2) (3) (4) (5) No. Weights % of respond. Round 1 Round 2 Round 3 favoring goal i in Round 3 (6) (4) x (5) final weights l 39.80 2 17.00 3 16.00 4 11.75 5 10.00 6 7.25 7 6.75 8 5.00 9 2.50 10 2.50 78.68 61.78 79.37 68.06 42.60 36.25 60.88 44.29 30.59 18.53 90.63 66.75 75.63 77.81 68.75 53.06 64.50 48.38 29.94 21.13 78.68 64.89 79.37 71.84 61.32 43.05 64.26 52.26 36.32 22.00 100.00 94.74 100.00 94.74 69.47 84.21 94.74 84.74 84.21 84.21 T a b l e 5 gives the result of the D e l p h i inquiry. N u m b e r s in the first c o l u m n refer to the objectives listed in T a b l e 4. In Table 5, c o l u m n s 2, 3, a n d 4 give weights o b t a i n e d in r o u n d s 1, 2, a n d 3 of the D e l p h i . C o l u m n 5 gives p e r c e n t a g e o f the r e s p o n d e n t s who favored a given objective (e.g., all chose o b jectives 1 and 3 - - n a m e l y , assigned a n o n - z e r o weight to t h e m - - b u t o n l y 69.47 p e r c e n t of the p a r t i c i p a n t s t h o u g h t that the fith objective s h o u l d b e c o n s i d e r e d for further analysis). T h e final weights for objectives ( c o l u m n 6) were calculated b a s e d on two factors: (1) the average weight for an objective, a n d (2) the percentage of p a r t i c i p a n t s favoring it. T h e r e a s o n for c o n s i d e r i n g these two factors is to reduce the weight for an objective that m a y have a high weight b u t m a y not b e highly favored (consider Table 6 Summary of objectives No. 1 2 3 4 5 6 7 8 9 10 Objectives Weights from Table 5 To provide access to natural resources To increase level of employment To provide access to markets To improve agriculture and cattle raising To increase GNP To increase trade with neighboring countries To serve the largest number of people To reduce transportation expenses To increase foreign exchange To increase tourism 79.37 78.68 68.06 61.78 60.88 44.29 42.60 36.25 30.59 18.53 No. 1 2 3 4 5 1 2 3 4 5 1 3.60 1 2.30 0.90 1 3.20 2.40 3.60 1 5.00 4.00 4.70 3.50 1 the case where an objective weights 100 b u t is c h o s e n b y o n l y o n e p a r t i c i p a n t ; in other words, all p a r t i c i p a n t s b u t one t h i n k it should not be c o n s i d ered for further analysis). T h e weights in c o l u m n s 2 a n d 3 were o b t a i n e d in the same way as in c o l u m n 6. T h e final weights given in T a b l e 5 were used b y the m o n i t o r t e a m to screen the objectives. A c c o r d ingly, further analysis was c o n f i n e d o n l y to the first five objectives in T a b l e 6 b e c a u s e the last five objectives were weighted c o n s i d e r a b l y less t h a n the others. IV. The m o n i t o r t e a m c o n d u c t e d a n o t h e r Delp h i i n q u i r y to o b t a i n the pairwise c o m p a r i s o n m a t r i x for the five objectives selected. The individual value j u d g m e n t s p r o v i d e d b y the p a r t i c i p a n t s were a v e r a g e d to d e t e r m i n e the entries in the overall pairwise c o m p a r i s o n m a t r i x ( T a b l e 7). T h e n u m b e r s in the first c o l u m n of T a b l e 7 refer to the first five objectives in T a b l e 6. V. T h e eigenvalues of the m a t r i x of T a b l e 7 c o r r e s p o n d i n g to ?tm,~ were o b t a i n e d with the help o f a software p a c k a g e called " E x p e r t Choice", which has been d e v e l o p e d for i m p l e m e n t i n g A H P (see F o r m a n [5]). A c c o r d i n g to Saaty [15], these eigenvalues p r e s e n t the p r i o r i t y a m o n g the objectives. T a b l e 8 gives the objectives a n d their r a n k ing, which the p l a n n e r s of the Bolivar H i g h w a y should c o n s i d e r when allocating c o n s t r u c t i o n funds. Table 8 Objectives and their ranking No. Objectives Eigen- Rank value 1 2 3 4 5 0.423 0.185 0.236 0.106 0.050 To provide access to natural resources To increase level of employment To provide access to markets To improve agriculture and cattle raising To increase GNP 1 3 2 4 5 354 R. Khorramshahgol, V.S. Moustakis / Delphic hierarchy process 7. Advantages of DHP The advantages of D H P in general and in particular as applied to the case of Bolivar Highway are as follows: (1) It combines two well established decision making tools - namely, the Delphi and AHP. (2) The iterative process of the Delphi permits the participants to reconsider their responses if they wish. (3) It takes into account the opinions of several experts; therefore, it is less subjective and arrives at a more agreeable solution. (4) If there are too many objectives, the D H P allows them to be screened based on their weights. This screening enables the monitor team to disregard some unimportant objectives, thereby reducing the size of the pairwise comparison matrix and avoiding unnecessary comparisons. (5) Since Delphi enables different decision makers to actively participate in the entire decisionmaking process, the selected project(s) will have their full support during implementation and their patronage upon completion. However, a disadvantage of D H P is the lengthy and time-consuming process of the two Delphi inquiries. 8. Summary and conclusions The identification of criteria and determination of objectives is of paramount importance to a decision making process and it is the basis for a sound decision. In this paper, through an experiment, the Delphic Hierarchy Process (DHP) proposed here is used to determine the objectives, and to derive priorities among them. Primary results indicate that D H P can effectively be used to determine the objectives of an organization and then to prioritize them. D H P allows for the participation of all experts as well as individuals who can provide input, thereby ensuring the acceptance and effective implementation of the solution. References [1] Arrow, K.J., "Alternative approaches to the theory of choice in risk-taking situations", Econometrica 19 (1951) 404-437. [2] Belaunde, F., "The Concept of Peru by Peruvians", Peru, Ministerio de Fomentoy Obras Publicas, Carreteria Bolivariana Marginal de la Selva, 1959. [3] Dalkey, N.C., "The Delphi method: An experimental study of group opinion", The RAND Corporation, Research Paper, RM-5888-PR, June, 1969. [4] Edwards, A.L., Techniques of Attitude Scale Construction, Appleton-Century-Crofts, 1957. [5] Forman, E., and Saaty, T.L., "Expert choice, decision support software", A Software Package for Implementing the Analytic Hierarchy Process (available from DSS Inc., McClean, VA, USA). [6] Harker, P.T., and Vargas, L.G., "The theory of ratio scale estimation: Saaty's analytic hierarchy process", Management Science 33 (1987) 1383-1403. [7] Khorramshahgol, R., and Ignizio, J.P., "Single and multiple decision making in a multiple objective environment", Advances in Management Studies 3 (1984) 181-192. [8] Khorramshahgol, R., and Gousty, Y., "Delphic goal programming (DGP): A multi-objective cost benefit approach to R&D portfolio analysis", 1EEE Transactions on Engineering Management 33 (1986) 172-175. [9] Linstone, H.A., and Turoff, M., The Delphi Method." Techniques and Applications, Addison-Wesley, MA 1975, p. 5. [10] Maddala, G.S., Econometrics, McGraw-Hill, New York, 1977. [11] Moustakis, V.S., "The system cost analogy technique", DSc. dissertation, The George Washington University, May 1984. [12] Moustakis, V.S., "A model for decision support software evaluation", Research Paper, Institute for Artificial Intelligence, Department of Engineering Administration, George Washington University, Washington, DC 20051, August 1984 (photographic copy available). [13] Payne, S.L., The Art of Asking Questions, Princeton University Press, NJ, 1973. [14] Saaty, T.L., "A scaling method for priorities in hierarchical structures", Journal of Mathematical Psychology 15 (1977) 234-281. [15] Saaty, T.L., The Analytic Hierarchy Process, McGraw-Hill, New York, 1980. [16] Samuelson, P.A., "Consumption theory in terms of revealed preference", Economica 15 (1948) 243-253. [17] Steiner, H.M., and Seminario, A., "Economic aspects of the Bolivaro Highway in Peru", Engineering Economist 14 (1970) 101-107. [18] Steiner, H.M., Public and Private Investment: A Socioeconomic Analysis, Wiley, New York, 1980. [19] Tippetts-Abbett-McCarthy-Stratton, Engineers and Architects, La Carreteria Marginal de la Seloa, un informe presentado a la Comisi6n Conjunta de Ministros de Fomento y Obras Pfiblicas de Bolivia, Colombia, Ecuador y Peril, Lima: Tippetts-Abbett-McCarthy-Stratton, 1965. [20] Zahedi, F., "The analytic hierarchy process: A survey of the method and its applications", Interfaces 16 (1986) 96-108.
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