Emmanuel Neron

Lower bounds for the multi-skill project scheduling problem with hierarchical levels of skills

In this paper, we introduce an extension of the classical Resource-Constrained Project Scheduling Problem: the Multi-skill Project Scheduling Problem. We consider a project made up of activities that must be implemented by a staff: every member of this staff masters one or more skill(s). An activity needs a given amount of each skill with a fixed minimum level of mastering. For each unit of a skill needed, we have to assign an employee who masters the required level of this skill during the whole processing time of the activity. The objective is to minimize the duration of the project, i.e. the makespan. We introduce here two lower bounds used to evaluate the minimum duration.

Computing redundant resources for the resource constrained project scheduling problem

Several efficient lower bounds and time-bound adjustment methods for the resource constrained project scheduling problem (RCPSP) have recently been proposed. Some of them are based on redundant resources. In this paper we define redundant functions which are very useful for computing redundant resources. We also describe an algorithm for computing all maximal redundant functions. Once all these redundant functions have been determined, we have to identify those that are useful for bounding. Surprisingly, their number is reasonable even for large resource capacities, so a representative subset of them can be tabulated to be used efficiently. Computational results on classical RCPSP instances confirm their usefulness.

On linear lower bounds for the resource constrained project scheduling problem

Abstract The aim of this paper is to propose efficient methods for solving the resource constrained project scheduling problem (RCPSP). These methods are based on makespan lower bounds, which linearly depend on the processing times of the activities. Linear lower bounds (LLB) can be obtained in different ways. The first application that we present is a general linear programming scheme for computing a makespan lower bound. The second application consists in associating redundant resources with LLB. Consequently we get new adjustments of release dates and tails of the project activities. These adjustments are tight for certain RCPSP instances, as shown by our computational results.

A new LP-based lower bound for the cumulative scheduling problem

Abstract This paper deals with the computation of lower bounds for Cumulative Scheduling Problems. Based on a new linear programming formulation, these lower bounds take into account how resource requirements can be satisfied simultaneously for a given resource capacity. One of the main interests of this paper is that the solutions of the LP can be tabulated, for a given value of resource capacity. Thus, even if it is based on a linear programming formulation, the computation of the bounds is low time consuming as confirmed by our computational results on the Resource Constrained Project Scheduling Problem.

An unrelated parallel machines model for an industrial production resetting problem

Efficient production resettings are necessary to achieve production flexibility. For this reason, most modern companies are trying to reduce the setup time required to switch the production from one product type to another. One way to minimise these times is to schedule correctly the various tasks involved during a production resetting: changing tools, modifying each machine setting, etc. In this paper, we present how this problem can be identified to an unrelated parallel machines problem with release dates and delivery times where the resources are operators. We show that the data structure allows simplifying the problem into an assignment problem, even when we take into consideration the availability constraints of the operators. A branch-and-bound method is presented which has been tested on industrial and generated instances. [Received 6 February 2007; Revised 22 August 2007; Accepted 11 November 2007]

Search tree based approaches for parallel machine scheduling

This article compares two branching schemes for the parallel machine scheduling problem with release dates and tails. Both branching schemes can be used for either complete or incomplete search tree based algorithms. In particular, our study aims to prove the robustness of each of them for several search methods. We experimentally compare the efficiency of the two branching schemes when they are used in a branch-and-bound (BnB) method, in a limited discrepancy search, in a branch-and-greed (BnG) method or in a beam search (BS).

The e-OCEA project: towards an internet decision system for scheduling problems

This paper deals with an Internet decision support system for scheduling problems. This system, called e-OCEA, is being developed at the Laboratory of Computer Sciences of the University of Tours. It provides a user with tools to help create an effective algorithm to solve a scheduling problem. From the modelisation of the problem to the visualization of a computed schedule, the e-OCEA system offers software that can be used either by operations researchers or industrial engineers. In this paper, we present the current state of this system and provide future directions.

Energetic reasoning and bin-packing problem, for bounding a parallel machine scheduling problem

This paper deals with an extension of energetic reasoning, using some efficient lower bounds of the bin-packing problem, to get tight lower bounds for the P|ri, qi|Cmax. The link between P||Cmax and bin-packing problem is well-known. Our purpose is to extend the use of efficient lower bounds of the bin-packing problem to P|ri, qi|Cmax. We focus on some time-intervals, to compute the mandatory parts of activities within this time-interval and then to deduce an associated bin-packing instance. Thus, lower bounds of the bin-packing problem are used to get new satisfiability tests for the parallel machine problem. We also propose to extend the classical time-bound adjustments of release dates and deadlines to efficiently use bin-packing lower bounds. Experimental results that prove the efficiency of our approach on several kind of instances are reported.

IP-Based Energetic Reasoning for the Resource Constrained Project Scheduling Problem

In this paper, we consider the Resource Constrained Project Scheduling Problem (RCPSP). New feasibility tests for the energetic reasoning are introduced based on new integer programming (IP) formulations. Experimental results are presented based on PSPLIB instances.

A preemptive bound for the Resource Constrained Project Scheduling Problem

The Resource Constrained Project Scheduling Problem is one of the most intensively investigated scheduling problems. It requires scheduling a set of interrelated activities, while considering precedence relationships, and limited renewable resources allocation. The objective is to minimize the project duration. We propose a new destructive lower bound for this challenging