关键词: 多项目调度, 净现值最大化, 优化模型, 禁忌搜索算法, 双重资源约束

Abstract:

In reality， the implementation of multiple projects often involves two types of resources， namely， renewable and non-renewable resources. Renewable resources include labor， machinery， and facilities that are not depleted and can be reused during project execution. Therefore， these resources have a defined availability on a per-unit time. On the other hand， non-renewable resources typically consist of raw materials， components， and funding， which are consumed once they are invested in a single-project and cannot be reused for other projects. Hence， the availability of non-reusable resources is defined for the entire duration of the project. In a multi-project environment， if a renewable resource for a specific project is idle during a certain period， it can be shared with other projects， making it a global resource. Conversely， for non-renewable resources， temporary surpluses in a single project are generally not shared with others， treating them as local resources.It is noteworthy that during the project implementation process， activities generally have multiple execution modes based on the type and quantity of resources invested， leading to different durations and costs. Overall， the choice of activity modes is constrained by the project budget. Project budgets fall under the category of non-renewable resources， with availability defined over the entire project cycle， once invested in the project， they cannot be reused. Therefore， in terms of non-renewable resources， managers need to allocate them reasonably to individual projects to ensure the smooth completion of projects and the ultimate achievement of expected goals.This research delves into the multi-project resource-constraint scheduling problem， specifically tackling the challenge of optimizing net present value （NPV） under dual resource constraints-renewable and non-renewable resources. The objective revolves around allocating non-renewable resources to individual projects， determining activity modes based on the availability of these resources， and subsequently scheduling activity starting times within the confines of shared renewable resource availability. Therefore， managers are tasked with manipulating three sets of decision variables-non-renewable allocation for individual projects， activity modes， and starting times of activities for a single project-to maximize the NPV of multiple projects.In the subsequent sections， a literature review is conducted to demonstrate the theoretical significance of this research. Next， an optimization model for maximizing net present value in multi-project scheduling under dual resource constraints is constructed， and the basic properties of the model are analyzed. Subsequently， a three-tier nested tabu search heuristic algorithm for solving the model is designed， and improvement measures for the algorithm are proposed based on proposed properties. Finally， extensive computational experiments are conducted to validate the model and the algorithm. Results have shown that the three-tier nested tabu search algorithm with improvement measures proves to be the most effective algorithm for solving the problem of maximizing net present value in multi-project scheduling under dual resource constraints. Additionally， sensitivity analysis reveals： the renewable resource factor （RF） has a negative impact on NPV， while RS positively affects NPV. As project deadlines， the number of milestones， intermediate payment ratios， and advance payment ratios increase， project net present value also increases. However， the discount rate negatively influences net present value. An increase in non-renewable resources contributes to the improvement of NPV in multi-projects.

Key words: multi-project scheduling, Max-NPV, optimization model, tabu search algorithm, dual resource constraint