# Ss2009_ch11 - The Job Shop Problem Chapter 11 Elements of...

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The Job Shop Problem Chapter 11 Elements of Sequencing and Scheduling by Kenneth R. Baker Byung-Hyun Ha

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2 Outline Introduction Types of schedules Disjunctive programming Schedule generation Shifting bottleneck procedure
3 Introduction Job shop model Each job has operations with precedence constraint Each operation should be done by a specific machine Representation of a job ( i , j , k ) -- operation j of job i requires machine k Example 4 jobs with 3 operations and 3 machines Operation 1 2 3 Job 1 Job 2 Job 3 Job 4 4 1 3 3 3 4 2 3 2 4 3 1 Operation 1 2 3 Job 1 Job 2 Job 3 Job 4 1 2 3 2 2 1 2 3 3 3 1 1 Processing time Machine assignment

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4 Introduction Two views of a feasible schedule 4 jobs with 3 operations and 3 machines (cont’d) 212 221 322 331 111 431 412 122 313 423 233 133 Machine 1 Machine 2 Machine 3 212 221 322 331 111 431 412 122 313 423 233 133 Job 1 Job 2 Job 3 Job 4 14
5 Types of Schedule Semi-active schedules Idle time is not helpful for regular measures Local left-shift Adjusting start time of operations earlier, without altering the sequence, lest superfluous idle time exists 212 221 322 331 111 431 412 122 313 423 233 133 212 221 322 331 111 431 412 122 313 423 233 133

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6 Types of Schedule Semi-active schedules (cont’d) Dominant set w.r.t. regular measures Number of semi-active schedules -- not more than ( n !) m Network model Precedence constraints Disjunctive arcs 2 jobs and 2 machines, 3 jobs and 2 machines Operation 1 2 Job 1 Job 2 1 2 2 1 Machine assignment 1,1 1,2 2,1 2,2 111 122 212 221 311 212
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Ss2009_ch11 - The Job Shop Problem Chapter 11 Elements of...

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