These lecture notes are for the course ORMS 1020 �Operations Research� for fall 2009 in the University of Vaasa. The notes are a slightly modified version of the notes for the fall 2008 course ORMS 1020 in the University of Vaasa. The chapters, or sections of chapters, marked with an asterisk (*) may be omitted � or left for the students to read on their own time � if time is scarce. The author wishes to acknowledge that these lecture notes are collected from the references listed in Bibliography, and from many other sources the author has forgotten. The author claims no originality, and hopes not to be isued for plagiarizing or for violating the sacred c laws.