项目调度与多尺度资源配置的集成优化

Integrated optimization of project scheduling and multi-scale resource allocation problem

资源是项目活动执行的基础保障,是项目进度计划顺利实现的关键要素之一。项目调度与资源配置相互依赖、相互影响。考虑现实项目资源需求在时间维度上的波动性特征,研究项目调度和多时间尺度的资源配置的集成优化问题。建立以工期和资源配置成本最小化双目标优化模型,并针对问题特征设计基于粒子群算法的双层启发式算法。通过实验分析,探索项目调度与资源配置之间的关联,多尺度资源配置决策的优势,并且对算法的有效性进行对比分析。实验证明,提出的双层启发式算法能快速有效求解该问题。多尺度资源配置策略比单一尺度下的资源配置策略更具灵活性,能有效降低资源成本、提高资源效用。

Project scheduling problems are prevalent in the field of project management. Resources are essential for project execution and critical for successful completion of project schedule. Project scheduling and resource allocation are interdependent and interrelated with each other. In practice, many construction projects share characteristics that consist of numerous activities, including long period and large fluctuation of resource requirements. To improve resource utilization, the volatility of resource demand for long-term is taken into consideration. This paper investigates the integration of project scheduling and multi-scale resource allocation. Firstly, resource constrained project scheduling sub-problem and multi-scale resource allocation sub-problem are stated and formulated by mathematical models. Resource constrained project scheduling problem is to determine the start time of each activity, which is subjected to precedence relationship and available resource constraints, in order to minimize the total makespan of the project. In multi-scale resourceallocation problem, the plan horizon is divided into many stages with different scales, such as long term, medium term and short term. Resources are purchased or rented during these multi-scale stages in order to satisfy resource requirement and minimize the total resource cost. These two optimization problems are integrated into a bi-objective optimization model of project scheduling and multi-scale resource allocation to minimize makespan and resource cost. Since the problem is NP-hard, an effective two-level heuristic based on PSO is designed for solving the problem. The outer level of the heuristic is that a PSO is used to generate an optimal project scheduling plan. The inner level is a linear integer programming（LIP） of multi-scale resource allocation problem solved by CPLEX. The basic idea is that PSO in outer level searches for a lot of particles at first. Each particle represents a feasible project scheduling plan. We then calculate the amount of resource requirements in each time slot. These resource requirements are input parameters of the inner LIP model. The study solves the LIP by CPLEX, project scheduling plan, and obtains an optimal resource allocation plan. In addition, project scheduling plan and corresponding optimal resource allocation plan are developed to compute the degree of fitness according to objective function. Then new particles are generated by PSO mechanism. The above process is repeated until the termination condition is met. A group of cases with varying problem scales are illustrated and numerical experiments are conducted. The proposed approach is verified to be effective to solve the problem. Experiments also show that by comparing to single scale resource allocation strategy, the multi-scale resource allocation strategy is more flexible, and better on resource cost reduction, resource utility improvement, and reduction of resource waste. The findings of this study about the importance of integrating project scheduling and multi-scale resource allocation conform to the actual needs, and can support project managers to make decisions.