Alain Haït

Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance.

On electrical load tracking scheduling for a steel plant

Nolde and Morari (2010) study a steel manufacturing scheduling problem where the tasks must be scheduled such that electricity consumption matches to a pre-specified periodic energy chart. They propose a continuous time integer linear programming formulation to solve the problem. In this note, we present an alternative continuous time formulation, focused on the relative positions of tasks and time periods, that improves significantly the computation time.

The extended resource task network: a framework for the combined scheduling of batch processes and CHP plants

The issue of energy has emerged as one of the greatest challenges facing mankind. In an industrial perspective, the development of site utility systems (generally combined heat and power (CHP) systems) for the generation and management of utilities provides a great potential source for energy savings. However, in most industrial sites, a master–slave relationship usually governs this kind of system and limits the potential operating capacity of CHP. To improve the decision-making process, Agha et al. (2010. Integrated production and utility system approach for optimising industrial unit operation. Energy, 35, 611–627) have proposed an integrated approach that carries out simultaneous and consistent scheduling of batch production plants and site utility systems. The modelling of the problem relies on a mixed integer linear programming (MILP) formulation. Nevertheless, although it is a powerful mathematical tool, it still remains difficult to use for non-expert engineers. In this framework, a graphical formalism based on existing representations (STN, RTN) has been developed: the extended resource task network (ERTN). Combined with an efficient and generic MILP formulation, it permits various kinds of industrial problems, including production and consumption of utility flows to be modelled homogenously. This paper focuses on the semantic elements of the ERTN formalism and illustrates their use through representative examples.

A GA-based fuzzy resource leveling optimization for helicopter maintenance activity

Genetic algorithm is one of the main heuristics that have been applied to scheduling problems in the last few decades. This paper presents a generalization of the genetic algorithm for solving project scheduling problem under time uncertainties within resource leveling technique. The generalization consists of handling fuzzy time parameter and fuzzy resource distribution instead of crisp ones. The provided fuzzy genetic algorithm is justified and applied to a real multi-project and multi-resources problem from the helicopter maintenance activity.

A rough-cut capacity planning model with overlapping

In the early phases of projects, capacity planning is performed to assess the feasibility of the project in terms of delivery date, resource usage and cost. This tactical approach relies on an aggregated representation of tasks in work packages. At this level, aggressive project duration objectives are achieved by adopting work package overlapping policies that affect both workload and resource usage. In this article, we propose a mixed-time MILP model for project capacity planning with different possibilities for overlapping levels between work packages. In the model, the planning time horizon is divided into time buckets used to evaluate resource usage, while starting and ending times for work packages are continuous. The model was tested on a benchmark of 5 sets of 450 theoretical instances each. More than half of the tested instances were solved to optimality within 500 s. Results also show that, while overlapping is more beneficial for accelerating project delivery times, it can still have a positive impact on project cost by allowing a better distribution of workload. Finally, overlapping options seem to have less influence on the performance of the model than project slack or number of work packages.

Scheduling Parallel Production Lines With Energy Costs

This paper deals with integration of energy-related constraints into scheduling for a foundry. Accounting for energy and human resource constraints leads to better solutions in terms of cost and overall energy consumption. Following some previous work (Hait et al. (2007)), we propose a hybrid heuristic based on a two-step constraint/mathematical programming approach to solve the problem.

Fuzzy uncertainty modelling for project planning: application to helicopter maintenance

Maintenance is an activity of growing interest, especially for critical systems. In particular, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance centre is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans in the short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multi-resource, multi-project planning (respectively Rough Cut Capacity Planning and the Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on a tactical level considering uncertainties in macro-task work content, and modelling the continuous workload on the operational level considering uncertainties in task duration. We model uncertainties using a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy Rough Cut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP). We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster that aims at building a centre for civil helicopter maintenance.

Progress in large-shared projects: Method for forecasting and optimizing project duration in a distributed project

In large-shared projects, it is still difficult to measure progress due to the complexities involved, because the realization is shared among departments of a company or among companies in the world. Project management and operations research literature is reviewed for discovering various techniques applicable. Widely used tools for progress measurement and forecasting, such as earned value analysis, progress plot, milestone and resource slip charts, concurrent engineering, can be employed. This paper is based on a problem of pharmaceutical industry where the effectiveness of a certain medical treatment is examined on patients in a number of countries. The number of variables involved increase the complexity of this problem. The main objective is to analyze the effectiveness of a solution in different situations during the project such that a better project duration and a lower cost can be achieved. Our findings suggest that reallocation of patients among countries produces better results in terms of progress.

Periodically aggregated resource-constrained project scheduling problem

In this paper, a new project scheduling problem is introduced, the periodically aggregated resource-constrained project scheduling problem (PARCPSP), in which the resource usage is considered on average over aggregated periods of parameterised length, while temporal aspects (start/completion dates of activities and precedence relations) are taken into account in an exact manner. A mixed integer linear programming formulation based on a mixed time representation is given. The adaptation of schedule generation schemes developed for standard project scheduling problems is discussed. An iterative solution scheme is described; experiments show that this method permits to find better upper bounds and sometimes enables to reduce the overall computational time.

Stochastic and fuzzy workload plans in project tactical planning under uncertainty.

Dealing with uncertainties in multi-project rough-cut capacity planning is the topic of this paper. Both fuzzy sets and probabilities are used to model uncertainties, within possibilistic and stochastic approaches, respectively. We refer to these problems as the Fuzzy Rough Cut Capacity Planning (FRCCP) and the Stochastic Rough Cut Capacity Planning (SRCCP). Uncertain workload is modeled with fuzzy and stochastic distributions, and a Simulated Annealing procedure is provided to solve the fuzzy and stochastic problems within a proactive approach. The performance of the Simulated annealing algorithm is studied in comparison to existing deterministic algorithms that we have generalized to fuzzy and stochastic parameters. Instances from shipyard maintenance center are considered to perform experiments.