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To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method on two types of planning problems under uncertainty arising in navigation of an autonomous agent and in inventory management.<\/jats:p>","DOI":"10.1142\/s0219622013400075","type":"journal-article","created":{"date-parts":[[2013,10,3]],"date-time":"2013-10-03T01:29:55Z","timestamp":1380763795000},"page":"1021-1053","source":"Crossref","is-referenced-by-count":11,"title":["A COMPROMISE PROGRAMMING APPROACH TO MULTIOBJECTIVE MARKOV DECISION PROCESSES"],"prefix":"10.1142","volume":"12","author":[{"given":"WLODZIMIERZ","family":"OGRYCZAK","sequence":"first","affiliation":[{"name":"ICCE, Warsaw University of Technology, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PATRICE","family":"PERNY","sequence":"additional","affiliation":[{"name":"LIP6, University Pierre and Marie Curie, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAUL","family":"WENG","sequence":"additional","affiliation":[{"name":"LIP6, University Pierre and Marie Curie, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,10,2]]},"reference":[{"key":"rf1","first-page":"679","volume":"6","author":"Bellman R.","year":"1957","journal-title":"Journal of Mathematics and Mechanics"},{"key":"rf2","volume-title":"Dynamic Programming and Markov Processes","author":"Howard R. 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