An incentive contract for leadtime reduction in an (S-1,S)(S-1,S) inventory system

We consider a single-item, infinite-horizon, continuous-review (S-1,S)(S-1,S) inventory system with Poisson demand and stochastic leadtimes. In the business scenario examined, the supplier exerts a one-time effort that reduces the mean and/or variance of replenishment leadtimes, and the inventory manager of the system makes periodic payments to the supplier based on realized leadtimes. Assuming an exponential utility function for the supplier and a normal leadtime distribution, we provide the parameters of a contract, under which the supplier periodically receives a fixed amount plus the sum of linear incentive payments for the replenishment orders delivered during that period based on their leadtimes. Extensive numerical experiments suggest that the cost impact of the leadtime reduction can be large, and that the proposed fixed-amount-plus-linear-incentive contract is very effective.Statement of scope and purposeThe problem of determining optimal leadtime reduction and its impact on inventory costs has been studied by many researchers. However, most of the leadtime-reduction literature has assumed the presence of a central planner, one with full information, who bears all the costs and benefits of leadtime reduction. In this paper we examine leadtime reduction in an (S-1,S)(S-1,S) inventory system from an agency perspective, in which the supplier exerts a one-time, hidden effort that reduces the mean and/or variance of stochastic leadtimes and the inventory manager of the system periodically makes incentive payments to the supplier based on realized leadtimes.