Abstract

Abstract
The uncertainty of project networks has been mainly considered as the randomness of duration of the activities. However, another major problem for project managers is the uncertainty due to the randomness of the amount of resources required by each activity which can be expressed by the randomness of its cost. Such randomness can seriously affect the discounted cost of the project and it may be strongly correlated with the duration of the activity. In this paper, a model considering the randomness of both the cost and the duration of each activity is introduced and the problem of project scheduling is studied in terms of the project's discounted cost and of the risk of not meeting its completion time. The adoption of the earliest (latest) starting time for each activity decreases (increases) the risk of delays but increases (decreases) the discounted cost of the project. Therefore, an optimal compromise has to be achieved. This problem of optimization is studied in terms of the probability of the duration and of the discounted cost of the project falling outside the acceptable domain (Risk function) using the concept of float factor as major decision variable. This last concept is proposed to help the manager to synthetize the large number of the decision variables representing each schedule for the studied project. Numerical results are also presented for a specific project network.

Abstract
The risk of the duration of a project exceeding a certain limit has been studied since the early papers proposing the PERT method but no results are available relating the statistical distribution of the total duration with the morphological features of the network. In this paper, a set of indicators is proposed to describe the morphology of the project network and an experimental research is carried out to relate the distribution of the total duration with such indicators. A random generator of project networks is used as well as a model to produce graphical representations of the network. Major results are presented showing how sensitive are the parameters of the distribution of the total duration to the morphology of the network, allowing the project manager to estimate the risk of delay in terms of the proposed indicators. Thus, these results can be used as a decision aid to select alternative designs for the project network taking into account the correspondent risk of delay.

Abstract
The performance of methods to manage projects depends heavily on the features of their project networks. This is particularly true for methods devoted to project scheduling, risk analysis and resources allocation. Therefore, a long line of research has been developed to generate benchmark sets of project networks and several sets have been proposed in the literature. Unfortunately, no comparative analyses of their features were published and hence serious doubts about the comparability of results using different benchmark sets can be raised. In this paper, a multi-dimensional taxonomy for the morphology of project networks is used and four benchmark sets are evaluated: Patterson collection of problems (Patterson JH. A comparison of exact approaches for solving the multiple constrained resource, project scheduling problem. Management Science 1984;30:854-867) and the sets produced by the generators due to Agrawal et al. Agrawal MK, Elmaghraby SE, Herroelen WS. DAGEN a generator of testsets for project activity nets. European Journal of Operational Research 1996;90:376-382. Kolisch R, Sprecher A, Drexl A. Characterization and generation of a general class of resource - constrained project scheduling problems. Management Science 1995;41:1693-1703. Tavares Tavares LV. Advanced models in project management. Kluwer, 1999 and Tavares et al. Tavares LV, Antunes Ferreira JA. Coelho JS. The risk of delay of a project in terms of the morphology of its network. European Journal of Operational Research 1999;119:510-537. Original results about the lack of representativeness of these sets are obtained showing that misleading conclusions can be deduced. The last set is, by far, that one covering most extensively the morphologic space of instances which could be foreseen because the generation of networks is carried out in terms of an wider range of parameters. This conclusion is quite useful for project managers willing to assess alternative methods to solve their problems based on project networks.

Abstract
This paper reports on a new solution approach for the well-known multi-mode resource-constrained project scheduling problem (MRCPSP). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and non-renewable) resource feasible project schedule with a minimal makespan. The problem type is known to be NP-hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean non-renewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.

Abstract
This paper evaluates and compares different network generators to generate project scheduling problem instances based on indicators measuring the topological network structure. We review six topological network indicators in order to describe the detailed structure of a project network. These indicators were originally developed by [L.V. Tavares, J.A. Ferreira and J.S. Coelho, The risk of delay of a project in terms of the morphology of its network, European Journal of Operational Research 119 (1999), 510-537] and have been modified, or sometimes completely replaced, by alternative indicators to describe the network topology. The contribution of this paper is twofold. Firstly, we generate a large amount of different networks with four project network generators. Our general conclusions are that none of the network generators are able to capture the complete feasible domain of all networks. Additionally, each network generator covers its own network-specific domain and, consequently, contributes to the generation of data sets. Secondly, we perform computational results on the well-known resource-constrained project scheduling problem to prove that our indicators are reliable and have significant, predictive power to serve as complexity indicators.