{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T13:44:14Z","timestamp":1698068654352},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,12,19]],"date-time":"2006-12-19T00:00:00Z","timestamp":1166486400000},"content-version":"vor","delay-in-days":6196,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Optim Control Appl Methods"],"published-print":{"date-parts":[[1990,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents an application of the maximum principle and the generalized maximum principle (a recent extension of that principle) to a discrete\u2010time model of consumer choice behaviour. The model includes two brands in a market and uses a non\u2010stationary first\u2010order Markov chain. The optimization is carried out by algorithms based on the above mentioned principles. These algorithms are described, and their performances are discussed and compared both with and without fulfilment of the directional convexity property.<\/jats:p>","DOI":"10.1002\/oca.4660110103","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T21:57:46Z","timestamp":1183413466000},"page":"21-37","source":"Crossref","is-referenced-by-count":0,"title":["Maximum principles applied to a model of consumer brand choice"],"prefix":"10.1002","volume":"11","author":[{"given":"Josa A. Soeiro","family":"Ferreira","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,19]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Mathematical Models in Marketing","author":"Leeflang P. S. H.","year":"1974"},{"key":"e_1_2_1_3_2","volume-title":"Stochastic Models of Buying Behavior","author":"Massy W. F.","year":"1970"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6586-4"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.11.10.B231"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/3151426"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/3151050"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.23.10.1037"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.21.10.1102"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/3315232"},{"key":"e_1_2_1_11_2","unstructured":"Nilsson O. \u2018Stochastic processes as decision models\u2019 8th Ann. Meeting European Academy for Advanced Research in Marketing Groningen 1979."},{"key":"e_1_2_1_12_2","unstructured":"Nilsson O. \u2018A dynamic decision model of consumer brand choice\u2019 Ph.D. Thesis Institute of Theoretical Statistics Copenhagen School of Economics and Business Administration 1983(in Danish)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.2307\/3150745"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.2307\/3149706"},{"key":"e_1_2_1_15_2","volume-title":"Introduction to Stochastic Processes","author":"Hoel P. G.","year":"1972"},{"key":"e_1_2_1_16_2","volume-title":"Theory of Optimal Control and Mathematical Programming","author":"Canon M.","year":"1970"},{"key":"e_1_2_1_17_2","unstructured":"Ferreira J. A. S. \u2018Optimal control of discrete\u2010time systems with applications\u2019 Ph.D. Thesis IMSOR Technical University of Denmark 1984."},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207178408933292"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1021\/i160004a001"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1966.1098235"},{"key":"e_1_2_1_21_2","volume-title":"Lectures Notes in Control and Information Sciences","author":"Nahorski Z.","year":"1983"},{"key":"e_1_2_1_22_2","unstructured":"Ferreira J. S.andR. V.Vidal \u2018On the connections between mathematical programming and discrete optimal control\u2019 in Prkopa A. (ed.) 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