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Agency models in supply chain management
Abstract
In this thesis we examine several business scenarios in which the owner (principal) of an inventory system, who is risk-neutral, delegates its design and/or implementation to an agent (internal manager, external supplier, or consultant) whose hidden effort influences the duration of the item's replenishment leadtimes. In the (Q, r) agency model, we examine two scenarios: the one-time-effort scenario and the combined-effort scenario. For both scenarios we demonstrate that if the agent is risk-neutral, then a simple contract achieves first-best. In the one-time-effort scenario, if the agent has an exponential utility function and the leadtime is drawn from a normal distribution, then we provide the parameters of the optimal linear contract. In the (S-1, S) agency model with Poisson demand and stochastic replenishment leadtimes, we provide the first-best optimal payment scheme, in which the agent is completely insured against the random timing and the random size of his payoffs. For the second-best case, if the agent has an exponential utility function and the leadtimes are drawn from a normal distribution, then we provide a salary-and-linear-bonus heuristic payment scheme, in which the agent receives a fixed payment in each of his consumption periods and a history-independent and linear incentive payment for each replenishment order. In the periodic-review agency model, we consider a standard, T-period inventory system, where a replenishment order is delivered immediately or one-period later, depending probabilistically on the effort expended by the agent. We provide the form of optimal payment scheme, and suggest that a state-dependent base-stock policy is optimal. We also find that, unlike in the corresponding traditional multi-period newsvendor model, given the same initial inventory, the optimal order-up-to levels may not be monotonic across time periods. For each of the three agency models, we conduct a computational study, and observe that ignoring the possible influence of the agent on replenishment leadtime can be significant; and that the magnitude of agency loss for the principal due to the agent's hidden effort appears to be small except in the periodic-review agency model with an agent who has a high risk-aversion.
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.
We consider a single-item, infinite-horizon, continuous-review (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.
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