Expert judgments in the cost-effectiveness analysis of resource allocations: a case study in military planning
Tóm tắt
We consider resource allocation problems in which agents are assigned to tasks with the aim of (1) minimizing the costs of assigning the agents and (2) maximizing the overall value resulting from the completion of tasks. Often, such assignment problems are challenging, because it may not be known to what extent the agents can complete tasks or what the value of either full or partial task completion is. Furthermore, it may be difficult to determine how important the tasks are relative to each other. In this paper, we therefore develop an optimization framework that helps determine for a range of levels of resource expenditure (1) which combinations of agents are cost-effective and (2) to which tasks these agents should be assigned. The parameters for the optimization problem can be derived, for instance, by eliciting evaluation judgments from experts. We also provide tools for analyzing which combinations of agents outperform others in view of the judgments of all experts, and which ones are cost-ineffective based on the judgments of some or all experts. A computational algorithm is presented, and the framework is illustrated by reporting a real application in military planning.
Tài liệu tham khảo
Ahuja R, Kumar A, Jha K, Orlin J (2007) Exact and heuristic algorithms for the weapon-target assignment problem. Oper Res 55(6):1136–1146
Bufardi A (2008) On the efficiency of feasible solutions of a multicriteria assignment problem. Open Oper Res J 2(1):25–28
Burkard R, Dell’Amico M, Martello S (2009) Assignment problems. Society for Industrial and Applied Mathematics, Philadelphia
Carrizosa E, Conde E, Fernandez F, Puerto J (1995) Multi-criteria analysis with partial information about the weighting coefficients. Eur J Oper Res 81(2):291–301
Chu P, Beasley J (1997) A genetic algorithm for the generalized assignment problem. Comput Oper Res 24(1):17–23
Dyer J, Sarin R (1979) Measurable multiattribute value functions. Oper Res 27(4):810–822
Ehrgott M, Gandibleux X (2000) A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectr 22(4):425–460
Ewing P Jr, Tarantino W, Parnell G (2006) Use of decision analysis in the army base realignment and closure (BRAC) 2005 military value analysis. Decis Anal 3(1):33–49
French S (2011) Aggregating expert judgement. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas 105(1):181–206
Gärdenfors P (1973) Assignment problem based on ordinal preferences. Manag Sci 20(3):331–340
Geis J II, Parnell G, Newton H, Bresnick T (2011) Blue horizons study assesses future capabilities and technologies for the United States Air Force. Interfaces 41(4):338–353
Genest C, Zide k J (1986) Combining probability distributions: a critique and an annotated bibliography. Stat Sci 1(1):114–135
Kangaspunta J, Liesiö J, Salo A (2012) Cost-efficiency analysis of weapon system portfolios. Eur J Oper Res 223(1):264–275
Keeler E, Cretin S (1987) Uses of cost–benefit analysis. J Health Econ 3(6):275–278
Keeney R, von Winterfeldt D (1989) On the uses of expert judgment on complex technical problems. IEEE Trans Eng Manag 36(2):83–86
Keeney R, von Winterfeldt D (1991) Eliciting probabilities from experts in complex technical problems. IEEE Trans Eng Manag 38(3):191–201
Kleinmuntz D (2007) Resource allocation decisions. In: Edwards W, Miles R, von Winterfeldt D (eds) Advances in Decision Analysis. Cambridge University Press, Cambridge, pp 400–418
Kuhn H (1955) The Hungarian method for the assignment problem. Naval Res Logist Q 2(1–2):83–97
Leonard H (1983) Elicitation of honest preferences for the assignment of individuals to positions. J Polit Econ 91(3):461–479
Levy H (1992) Stochastic dominance and expected utility: survey and analysis. Manag Sci 38(4):555–593
Liesiö J, Mild P, Salo A (2007) Preference programming for robust portfolio modeling and project selection. Eur J Oper Res 181(3):1488–1505
Manne A (1958) A target-assignment problem. Oper Res 6(3):346–351
McBride M, Burgman M (2012) What is expert knowledge, how is such knowledge gathered, and how do we use it to address questions in landscape ecology? In: Perera A, Drew C, Johnson C (eds) Expert knowledge and its applications in landscape ecology. Springer Science+Business Media, LLC, pp 11–38
Montibeller G, Gummer H, Tumidei D (2006) Combining scenario planning and multi-criteria decision analysis in practice. J Multi Criteria Decis Anal 14(1–3):5–20
Morris P (1974) Decision analysis expert use. Manag Sci 20(9):1233–1241
Murray C, Evans D, Acharya A, Baltussen R (2000) Development of WHO guidelines on generalized cost-effectiveness analysis. Health Econ 9(3):235–251
Park K, Kim S (1997) Tools for interactive multiattribute decisionmaking with incompletely identified information. Eur J Oper Res 98(1):111–123
Paté-Cornell M, Dillon R (2006) The respective roles of risk and decision analyses in decision support. Decis Anal 3(4):220–232
Pentico D (2007) Assignment problems: a golden anniversary survey. Eur J Oper Res 176:774–793
Roux J, van Vuuren J (2007) Threat evaluation and weapon assignment decision support: a review of the state of the art. J Oper Res Soc South Africa 23(2):151–187
Salo A, Punkka A (2005) Rank inclusion in criteria hierarchies. Eur J Oper Res 163(2):338–356
Salo A, Keisler J, Morton A (2011) Portfolio decision analysis: improved methods for resource allocation. Springer, New York
Scarelli A, Narula S (2002) A multicriteria assignment problem. J Multi Criteria Decis Anal 11(2):65–74
Schoemaker P (1995) Scenario planning: a tool for strategic thinking. Sloan Manag Rev 36(2):25–40
Spetzler C, Holstein CASV (1975) Probability encoding in decision analysis. Manag Sci 22(3):340–358
Stewart T (1996) Robustness of additive value function methods in MCDM. J Multi Criteria Decis Anal 5(4):301–309
Stinnett A, Paltiel A (1996) Mathematical programming for the efficient allocation of health care resources. J Health Econ 15(5):641–653
Stummer C, Heidenberger K (2003) Interactive R &D portfolio analysis with project interdependencies and time profiles of multiple objectives. IEEE Trans Eng Manag 50(2):175–183
Taha H (2003) Operations research: an introduction. Pearson Education, Inc., New Jersey
Zitzler E (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195