Integer programming for multi-mode resource-constrained project scheduling
针对多模式资源受限项目调度问题，提出了几种离散时间和一种连续时间混合整数线性规划模型，实验表明连续时间模型在大规模实例上优于现有模型。
Abstract Project scheduling is a vital management task in many organizations across various industries. A project typically consists of activities that require time and scarce resources for execution. In many projects, there are trade-offs between the resource requirements and the duration of activities. These trade-offs can be represented via multiple execution modes of activities, which are considered in the multi-mode resource-constrained project scheduling problem (MRCPSP). The MRCPSP comprises determining the activities’ start times and execution modes to minimize the project completion time while respecting precedence relations and availabilities of renewable and nonrenewable resources. In this paper, we propose several discrete-time (DT) and one continuous-time (CT) mixed-integer linear programming (MILP) model for the MRCPSP based on models for the single-mode resource-constrained project scheduling problem (RCPSP). We first analyze the models’ LP relaxations and show an equivalence between DT models. Then, we compare the computational performance of the models on benchmark instances. Our results indicate that the proposed CT model outperforms the state-of-the-art models on large problem instances and problem instances with relatively long activity durations, while it is competitive on smaller problem instances. A possible explanation for this outperformance is that the LP relaxations of the proposed CT model can be solved considerably faster than the LP relaxations of the state-of-the-art models.