Criticality Analysis In Networks With Generalized Precedence Relations (GPRs)

In classical CPM/PERT model, it only has finish-to-start (FTS) technological precedence relation with zero minimal time lag among activities whereas it includes all types of technological precedence relations among activities such as finish-to-start (FTS), finish-to-finish (FTF), start-to-start (STS), start-to-finish (STF) and hybrid precedence relations by any two of FTS, FTF, STS, STF in networks under generalized precedence relations (GPRs) with minimal and maximal time lags. Therefore, the later is fit for real projects better than the former and has many applications in various fields. However, there are many difficult problems associated with project scheduling, project schedule optimization etc under GPRs because of the complex precedence relations, which limit its comprehensive applications and generalization in real projects. For this reason, the researchers in this field mainly focus on the algorithms of single object and multi-objects optimization whereas they ignore two important and basic problems related to networks under GPRs. On the one hand, there are many different characteristics in GPRs networks compared with the classical CPM/PERT model, in which the influence on network structure and project makespan by changes in activities durations could not be obtained by analogy with the classical CPM/PERT model. On the other hand, how can we identify critical activities and critical sequences for a project scheduling under resource constraints and GPRs? The two aspects are very important to the maturity of GPRs networks theory systems and project management in theory and practice. This paper gives comprehensive and intensive criticality analysis in non-resource constrained and resource constrained networks under GPRs, which includes:(1) Criticality and inflexibility analysis in non-resource constrained networks under GPRs. Firstly, the author discusses some important concepts such as critical path, critical activity, critical relation etc and gives their exact definitions. Secondly, the influence on project makespan of critical activities is studied. Thirdly, critical sub-graphs in networks under GPRs are systematically analyzed. Fourthly, a classification for critical activities under GPRs is proposed. At last, identification methods for inflexible and flexible activities are also given.(2) Floats analysis in non-resource constrained networks under GPRs. Firstly, the influences of a change in an activity duration on the floats of itself and other activities are analyzed. Some new concepts such as node early (later) realization time (ER, LR), node early (later) possible realization time (EP, LP) are proposed. The formulas of ER, LR, EP, LP, total float (TF) and free float (FF) are given. The preconditions which determine the change of an activity's float are classified. Meantime, guaranteeing network time feasibility and keeping activities durations fixed, the computing methods for extreme compressible value (ECV) and extreme prolongable value (EPV) are studied. The laws of the influence of a change in an activities'duration on the floats of itself and other activities are probed into based on the classification of the relations among activities. Secondly, the influence of the change in two critical activities'durations on project makespan is analyzed. The maximal variable intervals of activities durations are discussed on condition that the network time feasibility is guaranteed when the durations of two activities are changed. And then, identifying methods for the influence of the change in two critical activities on project makespan are presented on the basis of the new proposed concept the maximal variable value of activity k's arcs.(3) Critical analysis in resource constrained projects. Firstly, the intuitive meanings of minimal feasible sets (MFS) are explained in detail and its strict definition is given. And then, the properties of MFS are discussed on the basis of a proposed scientific classification for the resource dependency relations among activities. Thirdly, the identifying methods for the optimal MFS and the establishing methods for the optimal resource links are researched into thoroughly. Fourthly, the applications of MFS are generalized to the precondition of MFS unsatisfied. Critical activities and critical sequences can be correctly identified in resource constrained projects according to the resource links established by MFS.(4) Evaluation of criticality analysis measurements in resource-constrained projects. The author classifies the problems related to resource links, analyzes seven methods proposed by the former researchers related to the identification of critical activities and critical sequences and compares them with MFS respectively. And then, evaluating criteria for identifying methods of critical activities and critical sequences are brought forward. Computational results manifest that MFS does not perform inferior to other methods at least and excels them in most situations in establishing resource links, computing floats, the sum of critical activities.