Research On Resource-constrained Project Scheduling Problem Considering Double Maximum Constraints

The basic resource-constrained project scheduling problem refers to arranging the start time and end time of each activity under the condition of satisfying the precedence relations constraints and resource constraints between project activities,so as to achieve the goal of the shortest total project duration.Because the basic RCPSP model simplifies many assumptions,such as the requirement that no interruption is allowed during the execution of activities,there is only a minimum precedence relationship constraint with FTS equal to zero between activities,and the activities durations are simplified to fixed values/minimum values.Therefore,the application of the basic model in practice has many limitations.In the past,scholars have extended RCPSP in many ways to solve this problem.However,due to the complex and diverse actual project environment,further research is needed to expand the basic RCPSP.In this regard,the paper starts from the actual project,and on the basis of the RCPSP that considers the maximum constraints of the generalized precedence relations between activities(RCPSP/max model),further considers the maximum constraint of the activity duration due to actual process characteristics or contract constraints.That is,considering the double maximum constraints in the project scheduling process,construct the RCPSP/max/max model.At the same time,due to the multi-objective nature of the project,this paper expands the optimization objective to a dual objective optimization with the shortest total makespan and the smallest resource investment.The model is abbreviated as RCPSP/max/max-MSRI.In terms of the solution,firstly,the network plan analysis method is used to conduct scheduling analysis under the condition of sufficient resources for the project with double maximum constraints to determine the values of the activities durations under this condition that are most beneficial to the goal of minimizing the total makespan.And use this analysis as the reference basis for the selection and analysis of the duration of each activity under the condition of resource constraints.The network plan used in the network plan analysis is a modified GPRs network to adapt to the situation where this article considers double maximum constraints.Then,according to the characteristics of the problem in this paper,the RCPSP/max/max-MS-RI mathematical model is constructed,and an ant colony-hybrid particle swarm algorithm is designed to solve the model.The algorithm uses the ant colony algorithm as the external framework to generate the initial population and optimizes it generation by generation through pheromone update.Hybrid particle swarm algorithm is embedded in it to search the solution space again.The hybrid particle swarm algorithm is a hybrid algorithm that uses the crossover/mutation operation of genetic algorithm to update the individual extreme value and the group extreme value.At the same time,the sharing function in the niche technology is introduced to calculate the fitness value of the individual to select an individual from the Pareto solution set as the individual/group extremum.Individuals in the algorithm are coded using an activityresource list.The duration of each activity is selected based on the conclusions obtained from the analysis of the network plan.Decode the individual through SSGS/max,and store the results in the Pareto archive collection for generation-by-generation update.At the same time,in order to facilitate the decision makers to make technical and economic decisions,this paper uses the entropy TOPSIS method based on the multi-objective decision-making method to select a plan from the Pareto solution obtained by the ant colony-hybrid particle swarm algorithm as the final recommended implementation plan for the decision maker as reference.Finally,an actual warehouse construction project verifies the necessity of the proposed model and the effectiveness of the algorithm.