Heuristic algorithms for payment models in project scheduling

Imagine that the city council of Ghent has approved the construction of a new bridge across the Leie. The bridge will serve as a means to reduce traffic congestion in the city center, and the city council imposes a deadline to ensure the bridge is completed in time. Based on the specifications, a contractor subsequently determines the required resources (e.g. manpower, machines) and constructs a project schedule. This schedule holds the start and finish times of each activity (e.g. pouring concrete for the bridge foundations), and respects the imposed resource restrictions and the order in which the activities have to be executed (e.g. excavate the river banks before pouring concrete for the foundations). Whereas the objective of the client (i.e. the city council) is clear, they want the bridge to be constructed within the specified deadline, the objective for the contractor is less obvious. Is the goal to minimize the project duration, minimize total costs, maximize net present value (NPV), etc.? Assume that the contractor can construct two schedules. The first schedule minimizes the project duration, obtains a duration of 6 weeks less than the deadline and has a NPV of € 1 mio. The second schedule, on the contrary, maximizes the project NPV, which results in a duration equal to the deadline and a NPV of € 1.2 mio. The latter schedule is obtained by delaying certain activities within the imposed restrictions, starting from the first schedule. If we assume that sufficient margins are included in the proposed schedules to compensate for any delays, the contractor would obviously prefer the second schedule, since the financial return is larger. The crucial question here is, however, how the second schedule can be obtained in an effective and efficient manner starting from the first schedule. This dissertation aims to develop algorithms, which optimize the project NPV under different restrictions, by means of five studies. The first paper chapter focuses on NPV optimization subject to precedence and resource restrictions. It is furthermore assumed that both cash inflows (payments received from the client) and cash outflows (payments to subcontractors) occur at the end of each activity. This way, the size of payments is set in advance by the client and corresponds with each activity’s cash flows, whereas the timing depends on the project schedule by means of the selected activity finish times, and is controlled by the contractor. The second and third studies consider other payment models, in which the client determines the payment times in advance, rather than the size of payments. As an example, the client may stipulate that the contractor is paid every month, whereas the size of the payments depends on the work performed by the contractor in each month. Both studies furthermore include several alternatives or modes for each activity. These modes constitute different duration-resource combinations for an activity, out of which one has to be selected by the contractor, and allow for a greater degree of flexibility. The fourth paper chapter introduces capital management on the side of the contractor, by imposing that the total funds available should not become negative during the project. The total funds or cash balance consider the initial capital available and respectively add or subtract cash in- and outflows. A general model is constructed which affects the capital availability throughout the project. The fifth and final study integrates the resource availability in the scheduling process, and as such optimizes the NPV of the project including the resource usage cost, rather than decide on the amount of a resource made available first and schedule the activities second

Distributed optimisation techniques for wireless networks

Alongside the ever increasing traffic demand, the fifth generation (5G) cellular network architecture is being proposed to provide better quality of service, increased data rate, decreased latency, and increased capacity. Without any doubt, the 5G cellular network will comprise of ultra-dense networks and multiple input multiple output technologies. This will make the current centralised solutions impractical due to increased complexity. Moreover, the amount of coordination information that needs to be transported over the backhaul links will be increased. Distributed or decentralised solutions are promising to provide better alternatives. This thesis proposes new distributed algorithms for wireless networks which aim to reduce the amount of system overheads in the backhaul links and the system complexity. The analysis of conflicts amongst transmitters, and resource allocation are conducted via the use of game theory, convex optimisation, and auction theory. Firstly, game-theoretic model is used to analyse a mixed quality of service (QoS) strategic non-cooperative game (SNG), for a two-user multiple-input single-output (MISO) interference channel. The players are considered to have different objectives. Following this, the mixed QoS SNG is extended to a multicell multiuser network in terms of signal-to-interference-and-noise ratio (SINR) requirement. In the multicell multiuser setting, each transmitter is assumed to be serving real time users (RTUs) and non-real time users (NRTUs), simultaneously. A novel mixed QoS SNG algorithm is proposed, with its operating point identified as the Nash equilibrium-mixed QoS (NE-mixed QoS). Nash, Kalai-Smorodinsky, and Egalitarian bargain solutions are then proposed to improve the performance of the NE-mixed QoS. The performance of the bargain solutions are observed to be comparable to the centralised solutions. Secondly, user offloading and user association problems are addressed for small cells using auction theory. The main base station wishes to offload some of its users to privately owned small cell access points. A novel bid-wait-auction (BWA) algorithm, which allows single-item bidding at each auction round, is designed to decompose the combinatorial mathematical nature of the problem. An analysis on the existence and uniqueness of the dominant strategy equilibrium is conducted. The BWA is then used to form the forward BWA (FBWA) and the backward BWA (BBWA). It is observed that the BBWA allows more users to be admitted as compared to the FBWA. Finally, simultaneous multiple-round ascending auction (SMRA), altered SMRA (ASMRA), sequential combinatorial auction with item bidding (SCAIB), and repetitive combinatorial auction with item bidding (RCAIB) algorithms are proposed to perform user offloading and user association for small cells. These algorithms are able to allow bundle bidding. It is then proven that, truthful bidding is individually rational and leads to Walrasian equilibrium. The performance of the proposed auction based algorithms is evaluated. It is observed that the proposed algorithms match the performance of the centralised solutions when the guest users have low target rates. The SCAIB algorithm is shown to be the most preferred as it provides high admission rate and competitive revenue to the bidders

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Stochastic programming for hydro-thermal unit commitment

In recent years the deregulation of energy markets and expansion of volatile renewable energy supplies has triggered an increased interest in stochastic optimization models for thermal and hydro-thermal scheduling. Several studies have modelled this as stochastic linear or mixed-integer optimization problems. Although a variety of efficient solution techniques have been developed for these models, little is published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intraday unit commitment under wind uncertainty, we compare two-stage and multi-stage stochastic models to deterministic ones and quantify their added value. We show that stochastic optimization models achieve minimal operational cost without having to tune reserve margins in advance, and that their superiority over deterministic models grows with the amount of uncertainty in the relevant wind forecasts. We present a modification of the WILMAR scenario generation technique designed to match the properties of the errors in our wind forcasts, and show that this is needed to make the stochastic approach worthwhile. Our evaluation is done in a rolling horizon fashion over the course of two years, using a 2020 central scheduling model of the British National Grid with transmission constraints and a detailed model of pump storage operation and system-wide reserve and response provision. Solving stochastic problems directly is computationally intractable for large instances, and alternative approaches are required. In this study we use a Dantzig-Wolfe reformulation to decompose the problem by scenarios. We derive and implement a column generation method with dual stabilisation and novel primal and dual initialisation techniques. A fast, novel schedule combination heuristic is used to construct an optimal primal solution, and numerical results show that knowing this solution from the start also improves the convergence of the lower bound in the column generation method significantly. We test this method on instances of our British model and illustrate that convergence to within 0.1% of optimality can be achieved quickly

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development