A multiobjective evolutionary approach for linearly constrained project selection under uncertainty

In the project selection problem a decision maker is required to allocate limited resources among an available set of competing projects. These projects could arise, although not exclusively, in an R&D, information technology or capital budgeting context. We propose an evolutionary method for project selection problems with partially funded projects, multiple (stochastic) objectives, project interdependencies (in the objectives), and a linear structure for resource constraints. The method is based on posterior articulation of preferences and is able to approximate the efficient frontier composed of stochastically nondominated solutions. We compared the method with the stochastic parameter space investigation method (PSI) and illustrate it by means of an R&D portfolio problem under uncertainty based on Monte Carlo simulation.     

Discrete Multiattribute Utility Approach to Project Selection

The purpose of this paper is to review various structures of the project-selection problem with discrete multiattribute utility. The approach of maximizing the utility for project selection is discussed where the utility function cannot be measured on a continuous scale. The review includes reference to models of uncertainty versus certainty, and to models assuming the existence of dependence and complementary relations among projects versus independent projects. Project selection in hierarchical organizations with a large number of projects and group decisions is also referred to. The various types of models are formulated and analysed, including applications in the areas of water resources, R&D and nuclear plant location. Finally, directions for future research are suggested.     

Sustainable workforce scheduling in construction program management

The multimode resource-constrained project scheduling problem (MRCPSP) deals with the scheduling of a set of projects with alternative requirements of renewable and non-renewable resources. Solutions to the MRCPSP usually consider objectives in terms of cost and time. However, social objectives related with the workforce may impact the performance of projects and affect program sustainability goals. To account for this new social input, this paper extends the MRCPSP and proposes a new multiobjective mixed-integer programming model. The proposed solution method uses an a priori lexicographic ordering of the objectives, followed by an ?-constraints approach. The model is illustrated with a case study of a construction program.     

Scenario-based portfolio selection of investment projects with incomplete probability and utility information

In the selection of investment projects, it is important to account for exogenous uncertainties (such as macroeconomic developments) which may impact the performance of projects. These uncertainties can be addressed by examining how the projects perform across several scenarios; but it may be difficult to assign well-founded probabilities to such scenarios, or to characterize the decision makers’ risk preferences through a uniquely defined utility function. Motivated by these considerations, we develop a portfolio selection framework which (i) uses set inclusion to capture incomplete information about scenario probabilities and utility functions, (ii) identifies all the non-dominated project portfolios in view of this information, and (iii) offers decision support for rejection and selection of projects. The proposed framework enables interactive decision support processes where the implications of additional probability and utility information or further risk constraints are shown in terms of corresponding decision recommendations.     

On-line Control Model for Cost-simulation Network Projects

This paper presents a newly developed hierarchical control model for several PERT type projects being realized simultaneously. The model has two objectives: to minimize the number of control points for an on-line control at the project level, and to maximize the probability that the slowest project can meet its due date on time (company level). On-line control is carried out separately for each project in order to minimize the number of control points subject to a chance constraint, which seeks to prevent deviation from the planned trajectory. If at the control point it is anticipated that the project will not be on target subject to the chance constraint, then an emergency is called. Under emergency conditions the company level is faced with the stochastic problem of budget reassigning among the projects enabling the faster projects to help the slower ones. A numerical example is presented.     

Optimising a nonlinear utility function in multi-objective integer programming

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.     

On-line control model for network construction projects

An activity-on-arc network project of the PERT type with random activity durations is considered. For each activity, its accomplishment is measured in percentages of the total project. When operated, each activity utilizes resources of a pregiven capacity and no resource reallocation is undertaken in the course of the project's realization. Each activity can be operated at several possible speeds that are subject to random disturbances and correspond to one and the same resource capacity; that is, these speeds depend only on the degree of intensity of the project's realization. For example, in construction projects partial accomplishments are usually measured in percentages of the total project, while different speeds correspond to different hours a day per worker. The number of possible speeds is common to all activities. For each activity, speeds are sorted in ascending order of their average values—namely speeds are indexed. It is assumed that at any moment t>0 activities, in operation at that moment, have to apply speeds of one and the same index that actually determines the project's speed. The progress of the project can be evaluated only via inspection at control points that have to be determined. The project's due date and the chance constraint to meet the deadline are pregiven. An on-line control model is suggested that, at each control point, faces a stochastic optimization problem. Two conflicting objectives are imbedded in the model:(1) to minimize the number of control points, and(2) to minimize the average index of the project's speeds which can be changed only at a control point.At each routine control point, decision-making centers on determining the next control point and the new index of the speeds (for all activities to be operated) up to that point. The model's performance is verified via simulation.The developed on-line control algorithm can be used for various PERT network projects which can be realized with different speeds, including construction projects and R&D projects.     

A zero-one model for project portfolio selection and scheduling

A zero-one integer linear programming model is proposed for selecting and scheduling an optimal project portfolio, based on the organisation's objectives and constraints such as resource limitations and interdependence among projects. The model handles some of the issues that frequently arise in real world applications but are not addressed by previously suggested models, such as situations in which the amount of available and consumed resources varies in different periods. It also allows for interactive adjustment following the optimisation process, to provide decision makers a method for controlling portfolio selection, based on criteria that may be difficult to elicit directly. It is critical for such a system to provide fast evaluation of alternatives the decision makers may want to examine, and this requirement is addressed. The proposed model not only suggests projects that should be incorporated in the optimal portfolio, but it also determines the starting period for each project. Scheduling considerations can have a major impact on the combination of projects that can be incorporated in the portfolio, and may allow the addition of certain projects to the portfolio that could not have been selected otherwise. An example problem is described and solved with the proposed model, and some areas for future research are discussed.     

Problem structuring in project management: an application of soft systems methodology (SSM)

Recent research suggests a major role for problem structuring methods (PSMs) in the field of project management, particularly at the front-end of projects, where objectives are often unclear and where different constituencies have conflicting aims. This paper presents a case example of soft systems methodology (SSM) at the front-end of a major project within Tesco Stores Ltd. A detailed account of the intervention is given, including the results achieved and a discussion of how the methodology was used for multiple purposes within the same intervention. Within the literature, there remains a lack of detailed examples from which people can learn more about the use of PSMs in project management. By providing a detailed example of SSM in action, this paper seeks to highlight the importance of problem structuring at the front-end of projects and the potential role an approach such as SSM can play at this crucial stage.     

The role of weights and scales in the application of multiobjective decision making

The application of multiobjective solution techniques requires, at some point in the analysis, the specification of the preference structure of the decision maker over the set of objectives. In practice, this step must often take the form of determining a set of weights that attempts to quantify the relative importance of the various competing objectives. This paper looks at how some of the well known techniques make use of these weights in attempting to achieve the best compromise solution. The definition of the weights (i.e., what meaning they carry into the analysis) is also explored. It is found that one must be very careful about applying weights when using these techniques. A different set of weights for the same objectives may apply when implementing two different techniques. In addition, a related factor, the specification of scales or ranges over which the objectives are to be evaluated, is explored. Again, it is found that different techniques use these scales in ways that change the manner in which they should be defined. The techniques reviewed are compromise programming, multiattribute utility theory, ELECTRE and cooperative game theory. Concepts are illustrated through the use of a water resources example problem.     

Discrete time/cost trade-offs in project scheduling with time-switch constraints

The discrete time/cost trade-off problem assumes the duration of project activities to be discrete, non-increasing functions of the amount of a single non-renewable resource. The problem has been studied under three possible objectives. The so-called deadline problem involves the scheduling of project activities in order to minimize the total cost of the project while meeting a given deadline. The budget problem aims at minimizing the project duration without exceeding a given budget. A third objective involves the generation of the complete efficient time/cost profile over the set of feasible project durations. In this paper we describe a solution procedure for the deadline problem in which three special cases of time-switch constraints are involved. These constraints impose a specified starting time on the project activities and force them to be inactive during specified time periods. We propose a branch-and-bound algorithm and a heuristic procedure which both make use of a lower bound calculation for the discrete time/cost trade-off problem (without time-switch constraints). The procedures have been coded in Visual C++, version 6.0 under Windows 2000 and have been validated on a randomly generated problem set. We also discuss an illustrative example based on a real-life situation.     

Valuation of project portfolios: An endogenously discounted method

Real options analysis (ROA) has been developed to value assets in which managerial flexibilities create significant value. The methodology is ideal for the valuation of projects in which frequent adjustments (e.g. investment deferral, project scope changes, etc) are necessary in response to the realization of market and technological uncertainties. However, ROA has no practical application when valuing portfolios of multiple concurrent projects sharing resources, as the size of the problem grows exponentially with the number of projects and the length of the time horizon. In this paper an extension of ROA suitable for the valuation of project portfolios with substantial technological uncertainty (e.g. R&D portfolios) is proposed. The method exploits the distributed decision making strategy encountered in most organizations to decompose the portfolio valuation problem into a decision-making sub-problem and a set of single project valuation sub-problems that can be sequentially solved. Discrete event simulation is used for the first sub-problem, while a tailored ROA based strategy is used for the set of valuation sub-problems. A case study from the pharmaceutical industry is used to compare the decision tree analysis (DTA) method and the proposed method.     

Iterative algorithms for the curfew planning problem

The curfew planning problem is to design an annual timetable for railway track maintenance teams. Each team is capable of handling certain types of repairs and replacement jobs. The jobs are combined into a set of projects according to their locations and types. The timetable shows which project should be worked on by each team on a weekly basis throughout an entire year. Our objective is to design a schedule with minimum network disruption due to ongoing maintenance projects that require absolute curfew. Absolute curfew projects are those that cause complete closure of the rail traffic. For tackling this problem, we develop four optimization-based iterative algorithms. We also present very promising computational results obtained within a few minutes using data provided by a major North American railroad.     

A bi-objective hierarchical program scheduling problem and its solution based on NSGA-III

In enterprise project management systems, a program at the tactical level coordinates and manages multiple projects at the operational level. There are close relationships between multiple projects in a program, which are typically manifested as shared resources and precedence relationships. Most research efforts have concentrated on the resource sharing by projects, while the precedence relationships between projects have yet to be comprehensively investigated. In this paper, a bi-objective hierarchical resource-constrained program scheduling problem proposed, where both resource sharing and precedence relationships between projects are considered in a distributed environment. The problem contains two different sub-problems at the operational level and the tactical level, and they are modeled in the same way as two bi-objective multi-mode scheduling problems. Shared resources are allocated from the tactical level to the operational level, and once they are allocated to a project, they can only be re-allocated to other projects once the current project is finished. Subsequently, a two-phase algorithm based on NSGA-III is developed. The algorithm runs at the operational level and the tactical level in turn. According to the Pareto fronts of projects that are submitted from the operational level, the bi-objective program planning at the tactical level is conducted under the constraints of precedence relationships and shared resources. The results of computational simulations demonstrate the satisfactory performance of the improved algorithm. By coordinating the local optimization of projects and the global optimization of the program in a hierarchical framework, the method proposed in this paper provides an effective integrated scheduling method for decision-makers at various levels of a program.

     

Optimal project portfolio selection with carryover constraint

In a typical capital rationing problem, a project portfolio is selected to maximize expected return on investment while adhering to the capital budget constraint. Sometimes projects may be delayed and they have to be funded beyond their planned completion time. This type of ‘unplanned carryovers’ represents a financial obligation to the company. If future years' capital budgets cannot be expanded to cover such obligations, future projects may be cancelled or postponed to fund the unplanned carryover. In this paper, we develop a methodology based on multi-attribute utility theory and chance-constrained programming to optimize portfolio selection subject to the constraints that the selected portfolio does not exceed the available budget and that the carryover of the unspent funds to the next fiscal year does not exceed predetermined limits. We use this technique to select an optimal project portfolio for Lockheed Martin Space Systems' infrastructure investments.     

Key performance indicators for successful simulation projects

There are many factors that may contribute to the successful delivery of a simulation project. To provide a structured approach to assessing the impact various factors have on project success, we propose a top-down framework whereby 15 Key Performance Indicators (KPI) are developed that represent the level of successfulness of simulation projects from various perspectives. They are linked to a set of Critical Success Factors (CSF) as reported in the simulation literature. A single measure called Project’s Success Measure (PSM), which represents the project’s total success level, is proposed. The framework is tested against 9 simulation exemplar cases in healthcare and this provides support for its reliability. The results suggest that responsiveness to the customer’s needs and expectations, when compared with other factors, holds the strongest association with the overall success of simulation projects. The findings highlight some patterns about the significance of individual CSFs, and how the KPIs are used to identify problem areas in simulation projects.     

Multi-mode resource constrained multi-project scheduling and resource portfolio problem

This paper introduces a multi-project problem environment which involves multiple projects with assigned due dates; activities that have alternative resource usage modes; a resource dedication policy that does not allow sharing of resources among projects throughout the planning horizon; and a total budget. Three issues arise when investigating this multi-project environment. First, the total budget should be distributed among different resource types to determine the general resource capacities, which correspond to the total amount for each renewable resource to be dedicated to the projects. With the general resource capacities at hand, the next issue is to determine the amounts of resources to be dedicated to the individual projects. The dedication of resources reduces the scheduling of the projects’ activities to a multi-mode resource constrained project scheduling problem (MRCPSP) for each individual project. Finally, the last issue is the efficient solution of the resulting MRCPSPs. In this paper, this multi-project environment is modeled in an integrated fashion and designated as the resource portfolio problem. A two-phase and a monolithic genetic algorithm are proposed as two solution approaches, each of which employs a new improvement move designated as the combinatorial auction for resource portfolio and the combinatorial auction for resource dedication. A computational study using test problems demonstrated the effectiveness of the solution approach proposed.     

Comparative analysis of UTA multicriteria methods

This paper reviews the main variants of the utility additive (UTA) multicriteria method, and systematically compares their predictive performance on two sets of data. It analyses both those cases where the model provides a ranking with errors and those without errors. First, it shows that the reference projects should be chosen carefully in order to elicit as much information as possible from the decision maker: a set of projects satisfying a fractional factorial plan is recommended. Second, it discusses the use of alternative post-optimality methods for solving the problem of multiple solutions and their different predictive performances. Third, it presents the results of simulations based on utility functions involving interdependence between criteria, and shows that UTA handles this problem effectively by an adjustment of its coefficients. Finally, the influence of the model's parameters on the predictive performance is also investigated.     

A combined approach for fuzzy multi-objective multiple knapsack problems for defence project selection

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.     

Resource allocation in dynamic PERT networks with finite capacity

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.