Research On Multi Resources Constrained Project Scheduling Problem Under Fuzzy Time-resources Conditions

Resource constrained project scheduling problem required to meet project timing constraints and resource constraints,arranges start time and completion time of all activities,in order to achieve an optimal goal.Classical resource constrained project scheduling problem assumes that project in a certain environment,in reality,due to factors such as weather conditions,site conditions and technical level,the project is often in uncertain environment.Therefore,aiming at shortest total project duration,this paper expands the classical resource constrained project scheduling problem to multi resources constrained project scheduling problem under fuzzy time and fuzzy resources conditions to research.Firstly,based on ?-cut level set and an interval numbers distance measure which brings in the maximum and minimum ideal point as intermediary for comparisons,this paper calculates possible degree of each path in fuzzy network,by defining a possible degree measure index and its calculation steps of project path.And on this basis,this paper identifies the possible critical path(activity),the inevitable critical path(activity)and the inevitable non-critical path(activity)in fuzzy network,which provides the basis for activity scheduling and resource allocation of fuzzy resource constrained project scheduling problem.Secondly,this paper brings in a fuzzy maximum operator which takes the maximum and minimum ideal point as intermediary for comparisons to compare the fuzzy activity time and fuzzy resource of a project.By redefining the minimal ideal point,this paper avoids inconsistent comparison results to use different ideal point(the maximum ideal point or minimum ideal point)between two fuzzy numbers.And on this basis,it calculates all possible critical paths which may change in fuzzy network.The proposed method overcomes the shortage of existing works for fuzzy resource constrained project scheduling problem which did not consider the facts that the critical path may change in case of fuzzy activity times and the shortest fuzzy completion time of a project and the fuzzy scheduling time of each activity may also change owing to the changed critical path accordingly.Finally,aimed at the established model and its assumptions of this paper,a hybrid particle swarm optimization algorithm based on chaos and differential evolution(CDEHPSO)is introduced to deal with fuzzy resource constrained project scheduling problem.The initial population of this algorithm is generated by the chaos technique,and in order to maintain the diversity of the population,the differential mutation,crossover and selection operations are involved into processing premature particles based on a premature judgment mechanism.With the purpose of further improving the global search ability of CDEHPSO,a nonlinear adaptive update method is applied to adjust the inertia weight dynamically.Based on the characteristic of fuzzy resource constrained project scheduling problem,considering parallel method may miss the optimum solution,priority-based coding method and serial schedule generation mechanism are applied,and a chaotic differential evolution based particle swarm optimization algorithm is presented accordingly to solve the proposed problem of this paper.At last,an example is illustrated to prove the effectiveness and superiority of the proposed model and method of this paper.