Optimization problem of allocating limited project resources with separable constraints

The authors consider the mathematical model and solution method for the optimization problem of the allocation of limited resources of a project as a problem of the arrangement of rectangular objects, where objects being placed have variable metric characteristics that are subject to functional dependences. The partial quality criteria and the constraints of the feasible domain of the problem are formalize

TECHNIQUES OF GENERATING SCHEDULES FOR THE PROBLEM OF FINANCIAL OPTIMIZATION OF MULTI-STAGE PROJECT

The article presents the problem of scheduling a resource-constrained project with discounted cash flow maximization from the perspective of a contractor. The contractor's expenses (cash outflows for the contractor) are associated with the execution of activities. The client's payments (cash inflows for the contractor) are performed after fulfilling the agreed project stages. The following techniques are suggested for solving the problem: the activity right-shift procedure, the backward scheduling with the opti-mization of completion dates for the agreed project stages and the modified triple justification technique. The effect of these techniques of generating schedules is illustrated for an exemplary project. Finally, an experimental analysis of the proposed procedures is presented

A Two-Phase Algorithm for a Resource Constrained Project Scheduling Problem with Discounted Cash Flows

This paper presents a Resource-Constrained Project Scheduling Problem (RCPSP) settled by contractual milestones. The criterion analysed here is the maximisation of aggregate discounted cash flows from the contractor’s perspective, known as an RCPSP problem with Discounted Cash Flows (RCPSPDCF). The cash flows analysed here cover the contractor’s cash outflows (negative cash flows), related to the commencement of individual activities, and cash inflows (positive cash flows) after the fulfilment of individual milestones. The authors propose a two-phase algorithm for solving the problem defined. In the first phase, the simulated annealing metaheuristics is used, designed to identify a forward schedule with as high total DCF as possible. In the second phase, the best first-phase schedule is improved by right shifts of activities. To this end, the procedure which iteratively shifts tasks by one unit is applied, with a view to maximising the objective function. Activity shifts take into consideration precedence and resource constraints, and they are performed for a specified resource allocation to activities. This paper also includes an analysis of the problem for a sample project. The results of computational experiments are then analysed. The experiments were run with the use of standard test problems from the Project Scheduling Problem LIBrary (PSPLIB), with additionally defined cash flows and contractual milestones

A survey on financial applications of metaheuristics

Modern heuristics or metaheuristics are optimization algorithms that have been increasingly used during the last decades to support complex decision-making in a number of fields, such as logistics and transportation, telecommunication networks, bioinformatics, finance, and the like. The continuous increase in computing power, together with advancements in metaheuristics frameworks and parallelization strategies, are empowering these types of algorithms as one of the best alternatives to solve rich and real-life combinatorial optimization problems that arise in a number of financial and banking activities. This article reviews some of the works related to the use of metaheuristics in solving both classical and emergent problems in the finance arena. A non-exhaustive list of examples includes rich portfolio optimization, index tracking, enhanced indexation, credit risk, stock investments, financial project scheduling, option pricing, feature selection, bankruptcy and financial distress prediction, and credit risk assessment. This article also discusses some open opportunities for researchers in the field, and forecast the evolution of metaheuristics to include real-life uncertainty conditions into the optimization problems being considered.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P, TRA2015-71883-REDT), FEDER, and the Universitat Jaume I mobility program (E-2015-36)

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

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