Â The Analytic Hierarchy Process (AHP) is the widely known method and methodology of multiple criteria decision making, which enriches many other areas of mathematical and statistical data analysis. This work considers an extension of AHP hierarchical structuring by incorporating it into another method of prioritization known in marketing research as Best-Worst scaling (BWS). BWS is used for finding choice probabilities among the compared items, but when there are a large number of items it is rather difficult to apply this approach directly to all the items. The AHP methodology of hierarchical structuring and estimation of local priorities that are then synthesized into global preferences permits one to build BWS nested models to facilitate choice evaluations. For instance, the compared items can be divided into several subsets by the criteria of brand, size, packaging, etc. The BWS balanced designs and data eliciting procedure can be applied to each of these groups separately, with additional comparisons among the criteria. Synthesizing local choice probabilities by the priorities of the criteria yields global probabilities for the items of choice. In this paper we also apply another simple approach, the so-called â€œsecretary problemâ€ from the operations research field, for comparison. Numerical results demonstrate that these techniques can be very useful for prioritization problems in marketing research where there are a large number of items.
AHP, BWS, hierarchical structuring, Secretary Problem, choice probability
Gass, S. (2005). Model world: The great debate â€“ MAUT versus AHP. Interfaces, 35, 308-312.
Golden, B.L., Wasil, E.A., & Harker, P.T., editors (1989). The Analytic Hierarchy Process: Applications and studies. Berlin: Springer.
Ijzerman, M.J., van Til, J.A., & Bridges, J.F.P. (2012). A comparison of Analytic Hierarchy Process and Conjoint Analysis Methods in assessing treatment alternatives for stroke rehabilitation. The Patient, 5, 45-56. Doi:10.2165/11587140-000000000-00000
Lipovetsky, S. (1996). The Synthetic Hierarchy Method: An optimizing approach to obtaining priorities in the AHP. European Journal of Operational Research, 93, 550-564. Doi:10.1016/0377-2217(95)00085-2
Lipovetsky, S. (2006). Optimal hierarchy structures for multi-attribute-criteria decisions. Journal of Systems Science and Complexity, 22, 228â€“242. Doi:10.1007/s11424-009-9159-5
Lipovetsky, S. (2009). Global priority estimation in multiperson decision making. Journal of Optimization Theory and Applications, 140, 77-91. Doi:10.1007/s10957-008-9447-6
Lipovetsky S., (2010). An interpretation of the AHP eigenvector solution for the lay person, International Journal of the Analytic Hierarchy Process, 2, 158-162. Doi: http://dx.doi.org/10.13033/ijahp.v2i2.42
Lipovetsky S. (2011). An interpretation of the AHP global priority as the eigenvector solution of an ANP supermatrix. International Journal of the Analytic Hierarchy Process, 3(1), 70-78. Doi: http://dx.doi.org/10.13033/ijahp.v3i1.90
Lipovetsky S. (2011). Priority eigenvectors in Analytic Hierarchy/Network Processes with outer dependence between alternatives and criteria. International Journal of the Analytic Hierarchy Process, 3(2), 172-179. Doi: http://dx.doi.org/10.13033/ijahp.v3i2.123
Lipovetsky S. (2013). Supermatrix eigenproblem and interpretation of priority vectors in Analytic Network Process. International Journal of the Analytic Hierarchy Process, 5(1),105-113. Doi: http://dx.doi.org/10.13033/ijahp.v5i1.132
Kallas, Z., GÃ³mez-LimÃ³n, J.A. & Barreiro, J. (2007). Decomposing the value of agricultural multifunctionality: Combining contingent valuation and the analytical hierarchy process. Journal of Agricultural Economics, 58(2), 218 â€“ 241. Doi: 10.1111/j.1477-9552.2007.00085.x
Kallas, Z., Lambarraa, F., & Gil, J.M. (2011). A stated preference analysis comparing the Analytical Hierarchy Process versus Choice Experiments. Food Quality and Preferences, 22, 181-192. Doi: http://dx.doi.org/10.1016/j.foodqual.2010.09.010
MeiÃŸner, M., Scholz, S.W., & Decker, R. (2008). AHP versus ACA â€“ An empirical comparison. In Preisach, C., Burkhardt, H., Schmidt-Thieme, L., & Decker, R. (Eds.), Data analysis, machine learning, and applications (447-454). Berlin: Springer. Doi:
MeiÃŸner, M., Decker, R., & Scholz, S.W. (2010). An adaptive algorithm for pairwise comparisonâ€based preference measurement. Journal of Multi-Criteria Decision Analysis, 17, 167-177. Doi: 10.1002/mcda.461
Mulye, R. (1998). An empirical comparison of three variants of the AHP and two variants of Conjoint Analysis. Journal of Behavioral Decision Making, 11, 263-280.
Saaty, T.L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill. Doi: http://dx.doi.org/10.1080/00137918308956077
Saaty, T.L. (1994). Fundamentals of decision making and priority theory with the Analytic Hierarchy Process. Pittsburgh: RWS Publications.
Saaty, T.L. (1996). Decision making with dependence and feedback: The Analytic Network Process. Pittsburgh: RWS Publications.
Saaty, T.L. (2000). Decision making for leaders. Pittsburgh: RWS Publications. Doi: 10.1109/TSMC.1985.6313384
Saaty, T.L., & Peniwati, K. (2012). Group decision making. Pittsburgh: RWS Publications.
Scholl, A., Manthey, L., Helm, R., & Steiner, M. (2005). Solving multiattribute design problems with analytic hierarchy process and conjoint analysis: An empirical comparison. European Journal of Operational Research, 164, 760â€“777. Doi: http://dx.doi.org/10.1016/j.ejor.2004.01.026
Scholz, S.W., & Decker, R. (2007). Measuring the impact of wood species on consumer preferences for wooden furniture by means of the Analytic Hierarchy Process. Forest Products Journal, 57(3), 23 - 28.
Scholz, S.W, MeiÃŸner, M., & Decker, R. (2010). Measuring consumer preferences for complex products: a compositional approach based on paired comparisons. Journal of Marketing Research, 47(4), 685â€“698. Doi: http://dx.doi.org/10.1509/jmkr.47.4.685
Vargas, L.G. (1987). Priority theory and utility theory. Mathematical Modelling, 9, 381-385. Doi:10.1016/0270-0255(87)90496-9
Winkler, R.L. (1990). Decision modeling and rational choice: AHP and utility theory. Management Science, 36, 247-248. Doi: http://dx.doi.org/10.1287/mnsc.36.3.247
ON CONJOINT, DISCRETE CHOICE, AND BEST-WORST SCALING
Ben-Akiva, M., & Lerman, S.R. (1985). Discrete Choice Analysis. Cambridge, MA: MIT Press. Doi: 10.1007/s11336-007-9029-9
Chrzan, K., & Yardley, D. (2009). Tournament-augmented choice-based conjoint. Proceedings of the Sawtooth Software Conference, 163-169, Delray Beach, Florida.
Hensher, D.A., Rose, J.M., & Greene, W.H. (2005). Applied choice analysis: A primer. Cambridge, England: Cambridge University Press.
Lipovetsky, S., & Conklin, M. (2014a). Best-Worst scaling in analytical closed-form solution. Journal of Choice Modelling, 10, 60â€“68. Doi: http://dx.doi.org/10.1016/j.jocm.2014.02.001
Lipovetsky, S., & Conklin, M. (2014b). Finding items cannibalization and synergy by BWS data. Journal of Choice Modelling, 12, Doi: 10.1016/j.jocm.2014.08.001.
Lipovetsky, S. & Conklin, M. (2015). MaxDiff priority estimations with and without HB-MNL. Advances in Adaptive Data Analysis, 7(1-2), 1-10. Doi: http://dx.doi.org/10.1142/S1793536915500028
Lipovetsky, S., Liakhovitski, D., & Conklin, M. (2015). What's the right sample size for my MaxDiff study? Sawtooth Software Conference Proceedings, 119-141.
Louviere, J.J. (1991) Best-Worst Scaling: A Model for the Largest Difference Judgments, Working Paper, University of Alberta.
Louviere, J.J. (1993). The Best-Worst or Maximum Difference Measurement model: Applications to behavioral research in marketing. The American Marketing Association's Behavioral Research Conference.
Louviere, J.J., Hensher, D.A., & Swait, J. (2000). Stated choice methods: Analysis and applications. Cambridge, MA: Cambridge University Press.
Marley, A., & Louviere, J.J. (2005). Some probabilistic models of Best, Worst, and Best-Worst choices. Journal of Mathematical Psychology, 49, 464â€“480. Doi: http://dx.doi.org/10.1016/j.jmp.2005.05.003
McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In Zarembka, P., (Ed.), Frontiers of Econometrics (105-142). New York: Academic Press.
McFadden, D. (1981). Econometric models of probabilistic choice. In Manski, C., & McFadden, D., (Eds.), Structural Analysis of Discrete Data (198-272). Cambridge: MIT Press.
McFadden, D., & Richter, M.K. (1990). Stochastic Rationality and Revealed Stochastic Preference. In Chipman, J., McFadden, D., & Richter, M.K., (Eds.), Preferences, Uncertainty, and Optimality: Essays in Honor of Leo Hurwicz (151-186). Boulder, CO: Westview Press.
Netzer, O., & Srinivasan, V.S. (2011). Adaptive selfâ€explication of multiattribute preferences. Journal of Marketing Research, 48(1), 140â€“156. Doi: http://dx.doi.org/10.1509/jmkr.48.1.140
Orme, B.K. (2006). Adaptive maximum difference scaling. Sawtooth Software Research Paper Series. Sequim, WA: Sawtooth Software, Inc.
Orme, B.K. (2010). Getting started with Conjoint Analysis, 2nd edition. Madison, WI: Research Publishers LLC.
Sawtooth Software (2007). Technical Paper Series: The MaxDiff/Web v6.0, Sequim, WA: Sawtooth Software, Inc.
Sawtooth Software (2014). Technical Paper Series: ACBC Technical Paper. Sequim, WA: Sawtooth Software, Inc.
Train, K. (2003). Discrete choice methods with simulation. New York: Cambridge University Press.
Wen, C.H., & Koppelman, F (2001). The generalized nested logit model. Transportation Research B, 35, 627â€“641. Doi: http://dx.doi.org/10.1016/S0191-2615(00)00045-X
Wirth R. and Wolfrath A. (2012). Using MaxDiff for evaluating very large sets of items. Proceedings of the Sawtooth Software Conference, 59-78.
ON SECRETARY PROBLEM
Bearden, J.N. (2006). A new secretary problem with rank-based selection and cardinal payoffs. Journal of Mathematical Psychology, 50, 58-59. Doi: http://dx.doi.org/10.1016/j.jmp.2005.11.003
Chow, Y.S., Moriguti, S., Robbins, H., & Samuels, S.M. (1964). Optimal selection based on relative rank. Israel Journal of Mathematics, 2, 81â€“90. Doi: 10.1007/BF02759948
Ferguson, T.S. (1989). Who solved the Secretary Problem? Statistical Science, 4, 282-296. Doi:10.1214/ss/1177012498
Freeman, P.R. (1983). The secretary problem and its extensions â€“ a review. International Statistical Review, 51, 189â€“206.
Petruccelli, J.D. (1984). Best-choice problems involving recall with uncertainty of selection when the number of observations is random. Advances in Applied Probability, 16, 111-130. Doi: https://doi.org/10.1017/S0001867800022370
Presman, E.L., & Sonin, I.M. (1972). The best-choice problem for a random number of objects. Theory of Probability and Applications, 17, 657-668. Doi:10.1137/1117078
Rose, J.S. (1982). A problem of optimal choice and assignment. Operations Research, 30, 172â€“181. Doi: http://dx.doi.org/10.1287/opre.30.1.172
Samuels, S.M. (1985). A best-choice problem with linear travel cost. Journal of the American Statistical Association, 80, 461-464.
Stein, W.E., Seale, D.A., & Rapoport, A. (2003). Analysis of heuristic solutions to the best choice problem. European Journal of Operational Research, 151, 140â€“152. Doi: http://dx.doi.org/10.1016/S0377-2217(02)00601-X
Vanderbei, R.J. (1980). The optimal choice of a subset of a population. Mathematics of Operations Research, 5, 481â€“486. Doi: http://dx.doi.org/10.1287/moor.5.4.481
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