Sequencing Games and Generalizations

Abstract

Four mathematics professors, Mrs. Hewitt, Mr. Isaacs, Mrs. Jones, and Mr. Kent have handed in work to be copied to the mathematics department’s copy room. Only one copy machine is functioning so they have to wait for their turn. Mrs. Hewitt was the first to hand in her job which is a referee report that she has completed. She needs to have copies made before she can send it to the editor. Mr. Isaacs, the second one to hand in his job, needs copies of exams that he has to give the next day in class, so he is in a hurry. Mrs. Jones, who handed in third, wants them to make copies of a proposal that she has to send out to apply for a grant. The last one to hand in his job, Mr. Kent, needs copies of a paper that he wants to submit to a journal. By talking to each other they get a notion that there must be a better order to make copies than the order in which they have handed in the work. Since they are mathematicians they decide to analyze the situation systematically. Each one of them writes down how much time his job will take and also how much each additional hour will cost her/him Mrs. Hewitt’s job will take 1 hour and her per hour cost is 1, Mr. Isaacs’ job will take 5 hours and his per hour costs are 10, Mrs. Jones’ job will take 6 hours and her per hour costs are 8, Mr. Kent’s job will take 2 hours and his per hour costs are 3.