s2008.prelim4 - PRELIM 4 ORIE 321/521 Closed book exam...

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Unformatted text preview: PRELIM 4 ORIE 321/521 April 29, 2008 Closed book exam. Justify all work. 1. Suppose jobs j = 1 , 2 , . . . , n are available for processing at time 0. Job j requires t j units of processing time and each job may be assigned to any one of m identical machines, all of which are continuously available. Each machine can process only one job at a time, and once a job is assigned to a machine, it must be processed to completion on that machine (i.e., job pre-emption is not allowed). (a) (25 points) Give an integer programming model for determining a processing schedule which will complete all work as early as possible; i.e., an assignment of jobs to machines is sought which will minimize the latest job completion time. (Hint: To minimize the maximum value attained by a family of linear functions f i ( x ) , 1 ≤ i ≤ m , one can solve the LP min { μ : μ ≥ f i ( x ) , 1 ≤ i ≤ m } ). (b) (25 points) Assume now that only one machine is available for processing all n jobs and further assume that for each pair of jobs (...
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