Investment project valuation based on a fuzzy binomial approach

The typical approaches to project valuation are based on discounted cash flows (DCF) analysis which provides measures like net present value (NPV) and internal rate of return (IRR). DCF-based approaches exhibit two major pitfalls. One is that DCF parameters such as cash flows cannot be estimated precisely in an uncertain decision making environment. The other one is that the values of managerial flexibilities in investment projects cannot be exactly revealed through DCF analysis. Both of them would have significant influence on strategic investment projects valuation. This paper proposes a fuzzy binomial approach that can be used in project valuation under uncertainty. The proposed approach also reveals the value of flexibilities embedded in the project. Furthermore, this paper provides a method to compute the mean value of a project’s fuzzy NPV. The project’s fuzzy NPV is characterized with right-skewed possibilistic distribution because these flexibilities retain the upside potential of profit but limit the downside risk of loss. Finally, this paper discusses the value of multiple options in a project.     

A fuzzy real option approach for investment project valuation

The main purpose of this paper is to propose a fuzzy approach for investment project valuation in uncertain environments from the aspect of real options. The traditional approaches to project valuation are based on discounted cash flows (DCF) analysis which provides measures like net present value (NPV) and internal rate of return (IRR). However, DCF-based approaches exhibit two major pitfalls. One is that DCF parameters such as cash flows cannot be estimated precisely in the uncertain decision making environments. The other one is that the values of managerial flexibilities in investment projects cannot be exactly revealed through DCF analysis. Both of them would entail improper results on strategic investment projects valuation. Therefore, this paper proposes a fuzzy binomial approach that can be used in project valuation under uncertainty. The proposed approach also reveals the value of flexibilities embedded in the project. Furthermore, this paper provides a method to compute the mean value of a project’s fuzzy expanded NPV that represents the entire value of project. Finally, we use the approach to practically evaluate a project.     

A parameter-tuned genetic algorithm for the resource investment problem with discounted cash flows and generalized precedence relations

A resource investment problem with discounted cash flows (RIPDCF) is a project-scheduling problem in which (a) the availability levels of the resources are considered decision variables and (b) the goal is to find a schedule such that the net present value of the project cash flows optimizes. In this paper, the RIPDCF in which the activities are subject to generalized precedence relations is first modeled. Then, a genetic algorithm (GA) is proposed to solve this model. In addition, design of experiments and response surface methodology are employed to both tune the GA parameters and to evaluate the performance of the proposed method in 240 test problems. The results of the performance analysis show that the efficiency of the proposed GA method is relatively well.     

Discrete–continuous project scheduling with discounted cash flows—A tabu search approach

In this paper discrete–continuous project scheduling problems with discounted cash flows are considered. In discrete–continuous project scheduling activities require for their processing discrete and continuous resources. The processing rate of an activity depends on the amount of the continuous resource allotted to this activity at a time. A positive cash flow is associated with each activity. Two common payment models—lump-sum payment and payments at activities’ completion times—are considered. The objective is the maximization of the net present value of all cash flows of the project. Some properties of optimal schedules are discussed, and the formulation of a mathematical programming problem for an optimal continuous resource allocation is presented. Applications of a local search metaheuristic—tabu search, as well as simple search methods—multi-start iterative improvement and random sampling are described. The algorithms are compared on the basis of a computational experiment, the results are analyzed and discussed. Some conclusions as well as directions for further research are given.     

RCPSP中现金流优化问题的HGA方法

针对网络进度计划中财务方面对项目管理的影响 ,研究资源受限项目调度问题 (RCPSP)中网络现金流的优化问题。提出以网络净现值最大作为网络现金流优化的目标 ,建立了带有贴现率的非线性整数规划模型 ,采用遗传算法与模拟退火算法相结合的混合式遗传算法进行求解。仿真实例表明了方法的合理性和有效性。     

运用遗传算法实现项目调度中的现金流优化

多模式的资源受限项目调度问题(MRCPSP)是生产实践中的一类常见的重要问题,它具有NP-完全性质,难以在多项式时间内准确求解.现金流是项目财务管理及风险评估的重要指标,实现现金流优化对项目管理具有重要的意义.考虑了现金流优化与项目调度相结合的带折现流的多模式资源受限项目调度模型(MRCPSPDCF),首先对该模型建模,然后给出运用遗传算法求解的具体方案,考虑了里程碑事件和相等时间间隔两种支付方式,在仿真实验中比较了这两种支付方式的实验结果,并证明了遗传算法的有效性.     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.     

Open pit mine production schedule optimization using a hybrid of maximum-flow and genetic algorithms

Production scheduling is a critical activity for the long-term production planning of open pit mining operations. It deals with the effective management of resources and maximizes cash flows to generate higher profits over the life of a mine. Production scheduling problems determine that blocks be mined and processed over a number of periods subjected to mining and processing constraints, which makes the problem more complex. The complexity is further increased due to the uncertainty in the input parameters. In this study, the maximum flow algorithm with a genetic algorithm is used to generate the long-term production schedule. The graph structure for maximum flow is created for multiple periods under uncertainty, and the flow in the arcs is controlled by a genetic algorithm to develop a production schedule. Numerical results for realistic instances are provided to indicate the efficiency of the solutions.     

Optimal multinational capital budgeting under uncertainty

This paper discusses the multinational capital budgeting problem — when there are some candidate foreign projects, which project(s) should the investor choose? In the paper, special cash flows and value sources of foreign projects are introduced. Regarding project parameters such as construction costs, annual net operating cash flows, terminal values of the projects as well as the foreign exchange rates as uncertain variables, the paper proposes one new uncertain zero-one integer model for optimal multinational project selection. To solve the problem, a hybrid intelligent algorithm integrating the 99 Methods and genetic algorithm is provided. As an illustration, an application example is also presented.     

Fuzzy R&D portfolio selection of interdependent projects

Global competition of markets has forced firms to invest in targeted R&D projects so that resources can be focused on successful outcomes. A number of options are encountered to select the most appropriate projects in an R&D project portfolio selection problem. The selection is complicated by many factors, such as uncertainty, interdependences between projects, risk and long lead time, that are difficult to measure. Our main concern is how to deal with the uncertainty and interdependences in project portfolio selection when evaluating or estimating future cash flows. This paper presents a fuzzy multi-objective programming approach to facilitate decision making in the selection of R&D projects. Here, we present a fuzzy tri-objective R&D portfolio selection problem which maximizes the outcome and minimizes the cost and risk involved in the problem under the constraints on resources, budget, interdependences, outcome, projects occurring only once, and discuss how our methodology can be used to make decision support tools for optimal R&D project selection in a corporate environment. A case study is provided to illustrate the proposed method where the solution is done by genetic algorithm (GA) as well as by multiple objective genetic algorithm (MOGA).     

Uncertain project scheduling problem with resource constraints

Project scheduling problem is to make a schedule for allocating the loans to a project such that the total cost and the completion time of the project are balanced under some constraints. This paper presents an uncertain project scheduling problem, of which both the duration times and the resources allocation times are uncertain variables. An uncertain programming model with multiple objectives is obtained, whose first objective is to minimize the total cost, and second objective is to minimize the overtime. Genetic algorithm is employed to solve the proposed uncertain project scheduling model, and its efficiency is illustrated by a numerical experiment.     

Mean-variance model for fuzzy capital budgeting

In an uncertain economic environment, it is usually difficult to predict accurately the investment outlays and annual net cash flows of a project. In addition, available investment capital sometimes cannot be accurately given either. Fuzzy variables can reflect vagueness of these parameters. In this paper, capital budgeting problem with fuzzy investment outlays, fuzzy annual net cash flows and fuzzy available investment capital is studied based on credibility measure. One new mean-variance model is proposed for optimal capital allocation. A fuzzy simulation-based genetic algorithm is provided for solving the proposed optimization problem. One numerical example and an experiment are also presented to show the optimization idea and the effectiveness of the algorithm.     

A genetic algorithm for the robust resource leveling problem

The resource leveling problem (RLP) involves the determination of a project baseline schedule that specifies the planned activity starting times while satisfying both the precedence constraints and the project deadline constraint under the objective of minimizing the variation in the resource utilization. However, uncertainty is inevitable during project execution. The baseline schedule generated by the deterministic RLP model tends to fail to achieve the desired objective when durations are uncertain. We study the robust resource leveling problem in which the activity durations are stochastic and the objective is to obtain a robust baseline schedule that minimizes the expected positive deviation of both resource utilizations and activity starting times. We present a genetic algorithm for the robust RLP. In order to demonstrate the effectiveness of our genetic algorithm, we conduct extensive computational experiments on a large number of randomly generated test instances and investigate the impact of different factors (the marginal cost of resource usage deviations, the marginal cost of activity starting time deviations, the activity duration variability, the due date, the order strength, the resource factor and the resource constrainedness).     

基于鲁棒优化理论的电梯群控调度策略

论文针对不确定线性优化问题,研究其不确定集的选择,初始不确定鲁棒优化模型的建立,以及基于该模型的鲁棒对等式转化问题.然后将鲁棒优化建模方法应用于电梯群控调度问题,建立其鲁棒优化模型,解决了交通流不确定性的影响,从而使调度结果更为合理.结合电梯群控虚拟仿真环境,设计了电梯群控鲁棒优化调度算法,并进行仿真验证.通过与其他调度算法的比较,证明了鲁棒优化调度算法在不同交通流F均具有优良的性能和适应能力.实验表明,鲁棒优化调度方法可以解决交通流预测误差的影响,很好地改善电梯群控调度性能.     

A flexible heuristic for a multi-mode capital constrained project scheduling problem with probabilistic cash inflows

We consider housing projects where an initial capital covers activity expenditures in the starting phase of the project and then, customers who arrive randomly over the project span provide the necessary funds for continuation. The goal is to maximize financial returns, i.e., the project Net Present Value (NPV). Here, capital is considered as a limited nonrenewable resource which is reduced by activity expenditures and augmented by the sales of flats. Activities may be carried out in different operating modes with different durations. The total cost of an activity is fixed irrespective of its operating mode. Thus, the rate of activity expenditures differ from mode to mode. As the previous scheduling decisions are the only controllable factors affecting the available capital at any period, it is important to adjust the speed of expenditures, namely, to select the correct activity modes. The contractor, never sure of the timing of the cash inflows, has to schedule the activities in modes which do not lead to financial bottlenecks and at the same time he has to deliver the project on time. The contractor may also borrow capital from an external source. We propose a flexible heuristic algorithm for solving the capital constrained mode selection problem where there exist general precedence relationships among activities and the magnitude of precedence lags depend on the specific activity mode selected. The algorithm is flexible in the sense that different mode selection criteria are utilized at different decision times depending on the cumulative progress of the project and on some parameters controlled by the contractor. The proposed algorithm may be used as a simulation tool to adjust parameters before the project starts or it may be used as a scheduler during the progress of the project given the current financial situation and cumulative project work done. We test the algorithm by using a typical housing project with real data and also by using hypothetical test problems. The results indicate that the schedules generated are satisfactory with regard to meeting the target project due date and maximizing NPV.     

A multi-objective bi-level location planning problem for stone industrial parks

This paper focuses on a stone industrial park location problem with a hierarchical structure consisting of a local government and several stone enterprises under a random environment. In contrast to previous studies, conflicts between the local authority and the stone enterprises are considered. The local government, being the leader in the hierarchy, aims to minimize both total pollution emissions and total development and operating costs. The stone enterprises, as the followers in the hierarchy, only aim to minimize total costs. In addition, unit production cost and unit transportation cost are considered random variables. This complicated multi-objective bi-level optimization problem poses several challenges, including randomness, two-level decision making, conflicting objectives, and difficulty in searching for the optimal solutions. Various approaches are employed to tackle these challenges. In order to make the model trackable, expected value operator is used to deal with the random variables in the objective functions and a chance constraint-checking method is employed to deal with such variables in the constraints. The problem is solved using a bi-level interactive method based on a satisfactory solution and Adaptive Chaotic Particle Swarm Optimization (ACPSO). Finally, a case study is conducted to demonstrate the practicality and efficiency of the proposed model and solution algorithm. The performance of the proposed bi-level model and ACPSO algorithm was highlighted by comparing to a single-level model and basic PSO and GA algorithms.     

Multiobjective model for solving resource‐leveling problem with discounted cash flows

Nowadays, executers are struggling to improve the economic and scheduling situation of projects. Construction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are inefficient and costly to implement on site. The objective of the resource‐leveling problem is to reduce resource fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, minimizing the discounted costs of resource fluctuations and minimizing the project makespan are considered in a multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the optimization problem is NP‐hard, we propose multiobjective evolutionary algorithms, namely nondominated sorting genetic algorithm‐II (NSGA‐II), strength Pareto evolutionary algorithm‐II (SPEA‐II), and multiobjective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order to study the performance of these algorithms, three criteria are proposed and compared with each other to demonstrate the strengths of each applied algorithm. To validate the results obtained for the suggested model, we compared the results of the first objective function with a well‐tuned genetic algorithm and differential algorithm, and we also compared the makespan results with one of the popular algorithms for the resource constraints project scheduling problem. Finally, we can observe that the NSGA‐II algorithm presents better solutions than the other two algorithms on average.     

Modeling project time–cost trade-off in fuzzy random environment

In real projects, the trade-off between the project cost and the project completion time, and the environmental uncertainty are aspects of considerable importance for managers. For complex environment with more than one type of uncertainty, this paper presents three types of time–cost trade-off models, in which the project environment is described via introducing the fuzzy random theory. The expected value and the chance measure of fuzzy random variable are introduced for modeling the problem under different decision-making criteria. After that, this paper is devoted to designing a searching method integrating the technique of fuzzy random simulations and genetic algorithm for searching the quasi-optimal schedules. Finally, some numerical examples are given to demonstrate the effectiveness of the designed method for solving the proposed models.     

A fuzzy random resource-constrained scheduling model with?multiple projects and its application to a working procedure in?a?large-scale water conservancy and hydropower construction project

The aim of this paper is to deal with resource-constrained multiple project scheduling problems (rc-mPSP) under a fuzzy random environment by a hybrid genetic algorithm with fuzzy logic controller (flc-hGA), to a large-scale water conservancy and hydropower construction project in the southwest region of China, whose main project is a dam embankment. The objective functions in this paper are to minimize the total project time (that is the sum of the completion time for all projects) and to minimize the total tardiness penalty of multiple projects, which is the sum of penalty costs for all the projects. After describing the problem of the working procedure in the project and presenting the mathematical formulation model of a resource-constrained project scheduling problem under a fuzzy random environment, we give some definitions and discuss some properties of fuzzy random variables. Then, a method of solving solution sets of fuzzy random multiple objective programming problems is proposed. Because traditional optimization techniques could not cope with the rc-mPSP under a fuzzy random environment effectively, we present a new approach based on the hybrid genetic algorithm (hGA). In order to improve its efficiency, the proposed method hybridized with the fuzzy logic controller (flc) concept for auto-tuning the GA parameters is presented. For the practical problems in this paper, flc-hGA is proved the most effective and most appropriate compared with other approaches. The computer generated results validate the effectiveness of the proposed model and algorithm in solving large-scale practical problems.     

Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap

This paper addresses a project scheduling problem (PSP) where the activities can be performed with several discrete modes and with four different payment patterns. Cash outflows depend on the activities’ execution modes, while cash inflows are determined by the payment pattern. Under project deadline constraints, the objective is to minimize the maximal cash flow gap, which is defined as the greatest gap between the accumulative cash inflows and outflows over the course of the project. Based on the definition of the problem, the optimization models are constructed using the activity-based method. Due to the NP-hardness of the problem, the mixed and nested versions of variable neighbourhood search (VNS), tabu search (TS), and variable neighbourhood search with tabu search (VNS-TS) are developed. Based on the characteristics of the problem, two improvement measures are proposed and embedded into the algorithms. Through a computational experiment conducted on a data set generated randomly, the performance of the developed algorithms, the contributions of the improvement measures, and the effects of the key parameters on the objective function are analysed. Based on the computational results, the following conclusions are drawn: Among the algorithms developed, the nested version of the VNS-TS is the most promising algorithm, especially for larger problems. The maximal cash flow gap decreases with the increase of the advance payment proportion, payment number, payment proportion, or project deadline. Among the four payment patterns, the expense based and progress based payment patterns may be more favourable for contractors to decrease the gap. The research in this paper has practical implications for contractors to smooth their cash flows and academic implications for project scheduling research due to the introduction of a new objective.