DecisionAiding Analysisofheuristicsolutionstothebestchoiceproblem WilliamE.Stein a, * ,DarrylA.Seale b ,AmnonRapoport c a Department of Information and Operations Management, Mays Business School, Texas A&M University, College Station, TX 77843-4217, USA b Department of Management, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-6009, USA c Department of Management and Policy, University of Arizona, Tucson, AZ 85721-0108, USA Received23May2001;accepted3June2002 Abstract Inthesequentialdecisionmakingtaskknownasthebestchoiceproblem, n itemsarepresentedinarandomorder oneatatime.Aftereachitem,thedecisionmaker(DM)candetermineonlytheirrelativeranks.TheDMÕsgoalisto selectthebestofall n itemswithoutthepossibilityofrecallingpreviouslyobserveditems.Thepurposeofthispaperisto compare the optimal policy to three classes of heuristic decision rules that were identified and studied in previous research.Wealsoinvestigatethelimitingcaseas n !1. Ó 2002ElsevierB.V.Allrightsreserved. Keywords: Decisionanalysis;Secretaryproblem;Optimalstopping;Appliedprobability;Heuristics 1. Introduction Many important business decisions such as choosing a venture partner, adopting techno- logical innovation, or hiring an employee can be modeled using a sequential decision framework. The best choice problem (BCP)isthenamefora class of sequential decision problems where the goalistoselectthebestoneof n items.Thedeci- sioneithertostopthesearchwiththecurrentitem ortocontinuedependsonlyontherelativeranks of the items that have been observed so far. The BCPisaspecialcaseofthewell-knownsecretary problem. Therein a decision maker (DM) is pre- sentedwithasequenceofaknownnumber(n)of applicants for employment in random order of desirability.Aftereachapplicantispresented,the DMisassumedtobeabletorankorderallofthe applicants observed so far without ties. The DM mustthenmakeadecisionto stop,therebytermi- nating the search process with the most recent applicant, or continue the search. The DMÕs ob- jective is to maximize the probability of selecting theapplicantwiththebestrankofall n applicants. Itisgenerallyagreedthatthefirststatementof whathasbecomeknownasthesecretaryproblem appearedina1960columnof Scientific American, written by Martin Gardner (Ferguson, 1989). Lindley(1961)seemstobethefirsttohavesolved * Correspondingauthor.Tel.:+1-979-845-4339;fax:+1-979- 845-5653. E-mail addresses: wstein@tamu.edu (W.E. Stein), dseale@ unlv.edu(D.A.Seale),amnon@u.arizona.edu(A.Rapoport). 0377-2217/$-seefrontmatter Ó 2002ElsevierB.V.Allrightsreserved. doi:10.1016/S0377-2217(02)00601-X EuropeanJournalofOperationalResearch151(2003)140–152 www.elsevier.com/locate/dsw