Leadtime reduction in a (Q,r) inventory system: An agency perspective

We examine the problem of designing and implementing a continuous-review (Q,r) inventory system from an agency perspective, in which the agent's effort influences the item's replenishment leadtime. Our results are as follows: if the agent is risk-neutral, a linear or quadratic contract achieves first-best. For a risk-averse agent with an exponential utility function, assuming a normal leadtime distribution, we determine the optimal linear contract. Extensive numerical experiments suggest that ignoring the possible influence of the agent on the replenishment leadtime can be costly, but that the cost penalty of ignoring agency can be significantly reduced by a simple contract.