Algorithms for optimal project scheduling: a dissertation submitted in partial fulfilment of the requirements for the degree of doctor of philosophy
Kyriakidis, Thomas S.
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ABSTRACT Project scheduling plays a vital role in project management, and constitutes one of the most important directions in both research and practice in the Operational Research (OR) field. During the last decades, the Resource- Constrained Project Scheduling Problem (RCPSP) has become the most challenging standard problem of project scheduling in the OR literature. The RCPSP involves the construction of a precedence and resource feasible time schedule which identifies the starting and completion times of activities, under a specific objective. Several variations of the RCPSP exist that represent different practical problems with different objectives, resource types, more than one way (mode) to execute an activity, generalised precedence relations for activities, etc. The RCPSP and its variants belong to the class of strongly NP-hard problems and a number of solution methods, both exact and approximate have been proposed in the literature. Scheduling is also a critical issue in process operations. The process scheduling problem consists of determining the most efficient way to produce a set of products in a time horizon given a set of processing recipes and limited resources. The activities to be scheduled usually take place in multiproduct and multipurpose plants, in which a wide variety of different products can be manufactured via the same recipe or different recipes by sharing limited resources, such as equipment, material, time, and utilities. The common problem features, such as required resource types, precedence relations and initial/target inventories, suggest that exchanging solution techniques between the two research fields is both possible and useful. The process scheduling industry is driven by the substantial advances of related modelling and solution techniques, as well as the rapidly growing computational power. On the other hand, project scheduling research effort has mostly focused on developing approximate solution techniques. However, recent project scheduling research papers show a renewed interest for mathematical programming-based solution strategies. Moreover, the best lower bounds ever found on broadly-studied RCPSP test instances, were obtained by a hybrid method involving constraint propagation and a MILP formulation. Additionally, mathematical programming solvers are often the only software available to industrial practitioners. Therefore, the study of exact methods, and especially mathematical programming techniques for solving the RCPSP is of particular theoretical and practical interest. The main objective of this work is to develop new optimal project scheduling techniques inspired by the process scheduling literature. This thesis consists of a literature review and state-of-the-art, three chapters with novel mathematical programming solution methods for the RCPSP and its variants under the objective of minimising the makespan and finally some concluding remarks. The first part presents new mixed-integer linear programming models for the deterministic single- and multi-mode RCPSP with renewable and non-renewable resources. The modelling approach relies on the Resource-Task Network (RTN) representation, a network representation technique used in process scheduling problems, based on continuous time models. Next, two new binary integer programming discrete-time models and two novel precedence-based mixed integer continuous-time formulations are developed. These four novel mathematical formulations are compared with four state-of-the-art models from the open literature using a total number of 2760 well-known open-accessed benchmark problem instances. The computational comparison demonstrates that the proposed mathematical formulations feature the best overall performance. Finally, a new precedencebased continuous-time formulation is proposed for a challenging extension of the standard single-mode resource-constrained project scheduling problem that also considers minimum and maximum time lags (RCPSP/max). The new formulation is then used to conduct an extensive computational study on a total of 2,250 benchmark problems, which illustrates its efficient performance.