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Exam 2 Review

Exam 2 Review. Machine Scheduling Problem Critical Paths & ECT PLs & List Processing Algorithm Optimal Schedules & OCT DTA & CTA & Independent Tasks Bin Packing, Conflict Scheduling Mixture & Transportation Problems. Machine Scheduling Problem.

emerson-vinson
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Exam 2 Review

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  1. Exam 2 Review Machine Scheduling Problem Critical Paths & ECT PLs & List Processing Algorithm Optimal Schedules & OCT DTA & CTA & Independent Tasks Bin Packing, Conflict Scheduling Mixture & Transportation Problems Mathematics in Management Science

  2. Machine Scheduling Problem To schedule tasks on processors to get project done efficiently. Two variations: • fixed # procs each with unlimited capacity (Goal: minimize CT) • unlimited # of procs each with fixed capacity (Goal: minimize # procs)

  3. Critical Paths & Earliest Cpltn Time • Earliest completion time is the smallest possible time it takes to complete overall project; cannot do better than this. It is just the length of a critical path: ECT=length of critical path • A critical path is a path one with the longest processing time.

  4. List Processing Algorithm GivenPL & order requirement digraph LPA Schedule next ready task on next available processor. next task is highest priority one, next available proc is first idle one Tasks are in one of 4 states: ineligible, ready, executing, done.

  5. Optimal Schedules & OCT Schedule for an order requirement digraph is optimal if no other schedule has shorter completion time. • OCT is best possible CT for given job using fixed number of processors. • Always have lower bounds for OCT • OCT≥ ECT (ECT=earliest comp time) • OCT≥ TTT/m (m = # of procs) • Not saying can get either of these.

  6. Decreasing Time Algorithm “common sense”--do longer tasks first & leave shorter tasks for last DTA Create PL by sorting task times in decreasing order. Must still use LPA to get schedule.

  7. Critical Times Algorithm Want “critical tasks” first in PL. CPA • Find CP on current digraph. • Place first task from CP next on PL; remove to get new digraph. • Repeat until all tasks on PL.

  8. Independent Tasks This true when have no order requirements. Can check that in this setting, DTA = CTA; this bcuz the CPs are just the tasks with longest task time.

  9. Bin Packing Problem • Pack wts w1, w2, …,wninto bins. • Each bin has fixed capacity. • Use as few bins as possible. • A scheduling problem in disguise! unlimited # of procs each with fixed capacity (Goal: minimize # procs)

  10. Heuristic Algorithms NF – Next Fit FF – First Fit WF – Worst Fit BF – Best Fit In last 3, bins stay open until they are completely full. Decreasing Versions NFD – Next Fit D FFD – First Fit D WFD – Worst Fit D BFD – Best Fit D With these first sort wts into decreasing order, then pack. Bin Packing Algorithms

  11. Next Fit Packing Algortihm • Pack item in current bin. • If item will not fit in current bin: close this bin & open a new bin. • Continue until all items packed.

  12. First Fit & Worst Fit Packing • Keep all bins open until full. Then close. • To pack an item, look at open bins. • FF: Place item in first bin in which it fits. • WF: Place item in bin with the most space (and in which item fits) . • Only open new bin if item will not fit in any of the already open bins.

  13. Vertex Coloring Color all vertices of graph so that any two vertices joined by an edge have different colors. The minimum number of colors needed is the chromatic number of the graph.

  14. Chromatic Number minimum number of colors need chromatic number of a cplt graph is CN = # of vtxs chromatic number of a circuit is CN = 2 if even length CN = 3 if odd length all other graphs have CN at most the maximum vertex valence .

  15. Conflict Scheduling Have events and (potential) conflicts between these events. To show via conflict table: columns and rows with event labels X means ‘conflict’ between two events Translate to conflict graph.

  16. Conflict Graph events correspond to vertices edges join conflicted vertices look for vertex coloring any two vertices joined by an edge have different colors colors are different event times (or places or whatever)

  17. Mixture Problems Limited resources are combined into products so that the profit from selling those products is a maximum. Focus on case where there are two limited resources and two possible products that can be created using these resources.

  18. Mixture Problem Algorithm Display all info in mixture chart. Write down resource constraints (RC), minimum constraints (MC), profit formula (PF). Draw feasible region & mark corner pts. Evaluate PF at each corner point. State OPP.

  19. Transportation Problems Have suppliers, users, shipping costs. Tableau: displays info with rim conditions. Each cell has two entries: costs and amount to ship. Shipping solution: obeys all constraints. NorthWest Corner Rule: an algorthim for obtaining a shipping solution. Indicator Values: Stepping Stone Algorithm.

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