Chap016 Part ii

Chap016 Part ii - Scheduling Approaches Forward scheduling...

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16 Part ii-1 Scheduling Approaches Forward scheduling Scheduling ahead from some point in time. Used when the question is: “How long will it take to complete this job? Backward scheduling Scheduling backwards from some due date Used when the question is: “When is the latest this job can be started and still be completed on time?”

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16 Part ii-2 Managing Work Flows Input/Output (I/O) control Managing work flow and queues at work centers Without I/O control: If demand exceeds processing capacity, a work center overload is created If work arrives more slowly than a work center can handle, work center underutilization results The goal is to strike a balance between input and output rates in order to minimize queues and maximize utilization
16 Part ii-3 I/O Chart

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16 Part ii-4 Assignment Assignment model A linear programming model for optimal assignment of tasks and resources Hungarian method Method of assigning jobs by one-for-one matching to identify the lowest cost solution
16 Part ii-5 Hungarian Method 1. Row reduction: subtract the smallest number in each row from every number in the row a. Enter the result in a new table 2. Column reduction: subtract the smallest number in each column from every number in the column a. Enter the result in a new table 3. Test whether an optimum assignment can be made a. Determine the minimum number of lines needed to cross out all zeros b. If the number of lines equals the number of rows, an optimum assignment is possible. Go to step 6 c. Else, go to step 4

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16 Part ii-6 Hungarian Method (contd.) 1. If the number of lines is less than the number of rows, modify the table: a. Subtract the smallest number from every uncovered number in the table b. Add the smallest uncovered number to the numbers at intersections of cross-out lines c. Numbers crossed out but not at intersections of cross-out lines carry over unchanged to the next table 2. Repeat steps 3 and 4 until an optimal table is obtained
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Chap016 Part ii - Scheduling Approaches Forward scheduling...

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