Time-based procurement

This study investigates the design of a time-based procurement contract when a supplier possesses private information about intrinsic completion time and may choose to exert time reduction effort. We first derive the optimal (complex) contract for the buyer, and then evaluate the performance of a (simple) fixed-price and fixed-time (FPFT) contract. Our analysis shows that the structure of the optimal time-based contract and the performance of an FPFT contract depend largely on time reduction forms. Specifically, if time reduction follows a multiplicative model, the optimal contract induces the intrinsically slow supplier to reduce time, and offers a fixed payment to the intrinsically fast supplier. This result is opposite to what could occur when time reduction follows an additive model. We also show that, in a specific multiplicative model, the FPFT contract achieves at least eight-ninth of the available surplus for the buyer, whereas the performance of an FPFT contract deteriorates dramatically in an additive model. In response to this underperformance, we then propose an enhanced linear contract, and demonstrate that, using this contract, the buyer loses no more than one-sixteenth of the available surplus. Our results shed light on the important effect of time reduction forms on time-based contract design.