Free disposal

• Chore division - since all chores must be done.
• Allocation of land with an old structure - since the structure may have to be destructed, and destruction is costly.
• Allocation of an old car - since the car may have to be carried away to used cars garage, and moving it may be costly.
• Allocation of shares in a firm that may have debts - since the firm cannot be disposed of without paying its debts first.

• It enables truthful cake-cutting algorithms:' The option to discard some of the cake gives the players an incentive to reveal their true valuations.
• It enables fast envy-free cake-cutting algorithms,' and more economically-efficient envy-free allocations: Discarding some of the cake helps to reduce envy.
• It enables online assignment algorithms.