Using bi-level programming to analyze the royalty for private--public partnership projects: the operational quantity-based model

<title>Abstract</title> This paper develops a royalty negotiation model based on the operating quantity of Build, Operate, and Transfer (BOT) projects for both government and the private sector using a bi-level programming (BLP) approach. The royalty negotiation is one of many critical negotiation items of a concession contract. This study develops a royalty negotiation model to simulate the negotiation behavior of two parties, and derives the heuristic algorithm for the BLP problem. A number of factors are incorporated into this algorithm including the concession rate, the time value discount rate, the learning rate, and the number of negotiations. The paper includes a case study of the Taipei Port Container Logistic BOT Project. The results show that the two parties involved completed royalty negotiation at the sixth negotiation stage. The findings show that the government can receive a royalty from the concessionaire, calculated at 0.00386% of the operating quantity of this BOT project. Therefore, the royalty negotiation model developed here could be employed to explain negotiation behavior.