Abstract: Programs are the basic form of achieving multi-level strategic goals and also the basic unit for implementing major projects. In the process of program implementation, program delay management plays an important role in the overall implementation of the program. Compared with a single project, contracted project delays under multiple stakeholders bring two more significant adverse effects to the program: firstly, there are more factors that affect the on-time completion rate of contracted projects in the program, and the chain reaction is more significant, which brings adverse effects to other contracted projects, making the control of other contracted projects more complex and difficult; secondly, according to the current rules of delay compensation and claim contract terms, most of the risks brought by contracted project delays to the program are borne by the employer. This means that the adverse effects of contracted project delays on other contracted projects and peak shaving are not only nonlinear, but also have a chain and amplification effect in a multi stakeholder environment. Therefore, starting from the perspective of stakeholders, how to balance the needs of the employers while reducing the impact of contracted project delays on the entire program, thereby reducing the risks and responsibilities of the employers, is a problem that needs to be addressed.
This article, in accordance with the current rules on compensation and claims for delay damages (such as FIDIC), reveals the mechanism of cost increase and changes caused by contracted project delays to employers, and introduces the critical chain method to construct a nonlinear optimization model for program delay costs based on the critical chain. This enriches the theory of program cost optimization, and by effectively monitoring the buffer of the critical chain program, the balance of NCRPE, start rate of contracted projects, and on-time completion rate of milestone schedules and program schedules can be improved, to reduce the negative impact of NCRPE imbalance and contracted project delays on the program from the source, so that employers can assess their own risks. At the same time, employers can achieve a balance among program duration, program delay cost, NCRPE demand intensity balance coefficient, and maximum NCRPE demand intensity through key chain buffer settings based on their employer management preferences.
The first part elaborates on the non-linear relationship between the cost increase caused by contracted project delay and time in three aspects: firstly, there is a non-linear relationship between the losses caused by contracted project delay to the contracted project itself and other contracted projects and time; secondly, there is also a non-linear relationship between the additional costs and time caused by the delay of other contracted projects in the program and the requirement to compress their construction period; the third is the nonlinear relationship between the NCRPE supply imbalance coefficient and cost, and the nonlinear optimization principle of program delay cost based on critical chain is proposed.
The second part starts from the two stages before and during the implementation of the program, and constructs a nonlinear optimization model for program delay cost based on the critical chain. Considering the different joint delay effects caused by contracted project delay caused by distance on subsequent contracted projects, PERT is used to calculate the delay probability of contracted projects, and the joint delay effects caused by contracted project delay are derived, integrating this nonlinear impact into critical chain buffer monitoring, reducing the adverse effects of contracted project delays by identifying critical chains, allocating buffers, conducting buffer monitoring, and taking corresponding corrective measures.
The third part starts from two aspects: the general preference and extreme preference of the employer for the construction period. Through example analysis, the feasibility and effectiveness of the constructed model are verified. Before the implementation of the program, the peak shaving method is used for NCRPE equilibrium optimization. During the implementation of the program, the constructed model is applied to optimize the construction period, delay costs, etc. Finally, management insights for practical reference are proposed for both the employer and contractor.
Through simulation and calculation, the results show that the program’s duration, increased delay cost, maximum imbalance coefficient, and maximum demand intensity are related to the employer’s preference for duration. Compared to the initial state of the program, to some extent, this model can reduce the program’s duration, increased delay cost due to contracted project delays, maximum imbalance coefficient, and maximum demand intensity. However, compared to the optimization state before the implementation of the program, due to considerations of schedule and cost, a certain maximum demand intensity may be sacrificed.
There are two directions for further research: firstly, from the perspective of contractors, with the goal of maximizing their own interests, we can adjust the contracted project plan under constraints. The second is to conduct research on the nonlinear impact of uncertain events under various constraints on the program and its components.

Key words: program, non-commercial resources provided by employer (NCRPE), nonlinear optimization, model, key chain, preference

摘要： 合同项目延误将有可能给项目群中其它合同项目和NCRPE削峰所带来不利影响,它不但是一种非线性关系,而且在多利益主体环境下它具有连锁和放大效应。为了降低这种不利影响程度,针对现有延误和索赔规则只适用单项目的不足,如何通过有效监控关键链项目群的缓冲,提升合同项目和项目群的按时完工率是降低业主风险的关键。首先,分析合同项目延误给项目群带来的不利影响,剖析延误费用非线性优化原理。其次,引入关键链,研究并构建延误费用非线性优化模型。最后,开展项目群Q的案例分析。研究表明,本文构建的模型能够在提高资源均衡程度的同时,实现工期和费用的双优化,有助于管理者根据工期偏好程度,在费用、工期、资源均衡及最大需求强度之间作出权衡。

关键词: 项目群, 甲供非商品化资源, 非线性优化, 模型, 关键链, 偏好