First, I would need to weigh the opportunity cost of performing the task myself vs outsourcing it to a service provider (laundry mat, app/service, dry cleaner). To find that opportunity cost, I would multiply the estimated amount of time that it would take to complete the task in its entirety by what I feel is the current value of my time. This "current value of my time" is an amalgamation of multiple, context specific factors (e.g. my professional hourly rate, how imminent the need for clean cloths/a specific garment is, the value & urgency of other tasks that could be accomplished). If the opportunity cost of performing the task myself is greater than the cost of outsourcing it to a service provider, then it should be outsourced.
If it is determined that the task should be performed by me, I would start by first separating the laundry into piles of like colors. Then each pile would be subjected to the following process, with each pile going through the process completely prior to the next pile beginning the process:
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Each garment within the pile would be checked for special instructions (e.g. dry-clean only), with those found to have special instructions being removed from the pile and placed into an independent "special instructions" collection to be dealt with later.
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The remaining pile of garments would then be separated into smaller groups that could fit within the washer. These groups would then each be subjected to following process, with each group going through the process completely prior to the next group beginning the process:
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Each garment within the group is examined for locations which require spot treatment. Spot treatment is applied to those locations. Finally, the garment is then placed within the washing machine.
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The washing machine is set to the appropriate setting and then started.
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Upon completion of all the washing machine's cycles, the group is then moved to the dryer.
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The dryer is set to the appropriate setting and then started.
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Upon completion of all the dryer cycles, the group is removed from the dryer and each garment in the group is then folded or hung on a hanger as appropriate, and then put away.
After each pile of like colors had been completed, the "special instructions" collection would be handled by grouping garments within this collection into groups that have similar/matching instructions. Each group would then be dealt with as directed.