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Scheduling Optimization on Resource Planning

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11. Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are:

Day M T W Th F S Su
Requirements 6 3 5 3 7 2 3

( I have solved this one already, but you will need this info to solve as per below, so I left the information)

4. Return to Problem 11(above) and the workforce schedule for part-time loading dock workers. Suppose that each part time worker can work only 3 days, but the days must be consecutive. Formulate and solve this workforce schedule problem as a Linear Program and solve it using POM for Windows. Your objective is to minimize total slack capacity. What is the minimum number of loaders needed now and what are their schedules?

Please note, this appears to be 2 problems, but the first one is referred to in the second so I left the information...

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The Satellite Mission Scheduling problem with Dynamic Tasking (SMS-DT) involves scheduling tasks for a satellite, where new task requests can arrive at any time, non-deterministically, and must be scheduled in real-time. The schedule is a time ordered sequence of activities (scheduled tasks) to be performed by the payload of a satellite. Each activity has a start time and duration. The duration of an activity is a function of its start time: it can be calculated based on such factors as target size, task type, and geometry (between target and satellite, or due to lighting conditions). The transition time between activities is instantaneous, provided the targets lie within the field of view of the payload.
In addition, the Satellite Mission Scheduling problem is priority based: a lower priority task should not adversely impact a higher priority task. A lower priority activity could cause a higher priority activity move to a new location on the schedule, but cannot bump the higher priority activity off of the schedule. However, a higher priority activity could bump a lower priority activity off of the schedule in order for it to get on the schedule. A priority of 0 (zero) is highest and a priority of 999 is lowest. Given a choice, it is preferable to complete a task as early as possible.
Question
I have researched on monotonic algorithm and genetic algorithm. I would like to know what other algorithms are used in the past for this problem. And what are the pros and cons of them? Why do we still need to find or develop new or hybrid algorithm for this problem? Thank you.

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