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| Type | Notation | Definition |
|
| Sets | I | Set of garment makers or tasks, |
| J | Set of designers or design solutions, |
| Set of designer’s (j) completion tasks |
| Set of stable parings, |
| Parameters | | Cost of completion of task i by designer j |
| Expected payoff for the next task if designer j completes the present design task i |
| Duration of task i completed by designer j |
| Unit time cost of task i completed by designer j |
| Cost of completion of task I within the time limits by designer j |
| Anticipated payoff for the case in which a normal-goodwill garment maker will offer a low reward in the near future |
| Anticipated payoff for the case in which a normal-goodwill garment maker will offer a high reward in the near future |
| Anticipated payoff for the case in which a better-goodwill garment maker will offer a low reward in the near future |
| Anticipated payoff for the case in which a better-goodwill garment maker will offer a high reward in the near future |
| Benefit of garment maker i from designer’s (j) solution |
| Payment to the crowdsourcing platform by garment maker i |
| Estimated parameters |
| Earliest start time of designer j |
| Latest submission time required by garment maker i |
| Minimum utility obtained when garment maker i chooses designer j |
| Minimum utility obtained when designer j accomplishes task i |
| Decision variables | | if garment maker i and designer j match as a pairing, , otherwise |
| Reward for design solution i is selected by garment maker j |
| Auxiliary variables | | Total utility of designer j taking on task i |
| Total utility of garment maker i selecting the designer’s (j) solution |
| Total surpluses of designer j if he matches with garment maker i |
| Total surpluses of garment maker i if he matches with designer j |
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