PERT and crashing revisited: Mathematical generalizations

A robust scheduling of projects with time, cost, and quality considerations

“…-Maximizing project completion probability in a predefined deadline using limited budget [10] -Minimizing direct cost to reach a predefined threshold of mean completion time [5] -Minimizing direct cost to reach a predefined threshold of project completion probability in a deadline [23,24] -Minimizing total cost including direct and indirect [7] -Minimizing mean of project completion time and minimizing variance of completion time and cost [19] -Minimizing mean of project completion time and minimizing mean of total project cost [18] The solution approaches developed for traditional TCTP include the following:…”

“…& Exact approaches -Branch and bound [7,25] -Goal programming [13,21] -Goal attainment [20][21][22] -Fractional linear programming [6] -Dynamic programming [26] -Project network decomposition [27,28] & Heuristic approaches -Simulation [8,29] -Lagrangean relaxation [5] & Meta-heuristic approaches -Genetic algorithm [22,30] -Ant colony optimization [23,31] As mentioned above, in this problem only two criteria, i.e., time and cost and inter-relation between them have been considered so far. Traditionally, decisions on project scheduling problems have been done considering only total time and total cost.…”

“…Constraint set (4) guarantees that the precedence relations between project activities are preserved. Constraint set (5) ensures that the limits of resources allocated to the activities are not violated. Finally, constraint set (6) shows the starting time of project to be zero, non-negativity limits of t ij (r ij ) and x i , and indices used in the model.…”

“…& Stochastic or deterministic environment -CPM network in which duration of project activities are deterministic and all the present activities on network will be occurred [1-3] -PERT network in which duration of project activities are stochastic and all the present activities on network will be occurred [4,5] -GERT network in which duration of project activities are stochastic and the occurrence of activities is not known in advance (activities may be eliminated from planning phase with a pre-known probability) [6] -Linear-continuous cost function, in which the cost of resource allocation to the activities alters linearly in a continuous domain [9][10][11] -Nonlinear-convex cost function, in which the cost of resource allocation to the activities alters with a nonlinear convex pattern [5,12] -Linear-piecewise cost function, in which the cost of resource allocation to the activities alters linearly in some separate continuous domains [13] & Controllable variable in cost function -Allocated budget to activities [6,10,14]. It means that the decision maker can select a desirable amount of budget as control variable to be allocated to the activities.…”

A network flow algorithm for just-in-time project scheduling

“…In [11], we have given a general description of the problem and algorithm to be considered in more detail in the present paper. In [5], Foldes and this algorithm has pseudo-polynomial (in fact, pseudo-linear)…”