Cyril Briand

The resource-constrained activity insertion problem with minimum and maximum time lags

This paper considers the resource-constrained activity insertion problem with minimum and maximum time lags. The problem involves inserting a single activity in a partial schedule while preserving its structure represented through resource flow networks and minimizing the makespan increase caused by the insertion. In the general case, we show that finding a feasible insertion that minimizes the project duration is NP-hard. When only minimum time lags are considered and when activity durations are strictly positive, we show that the problem is polynomially solvable, generalizing previously established results on activity insertion for the standard resource-constrained project scheduling problem.

Finding a Nash equilibrium and an optimal sharing policy for multiagent network expansion game

In this work, a multi-agent network flow problem is addressed , aiming at characterizing the properties of stable flows and allowing their computation. Two types of agents are considered: transportation-agents, that carry a flow of products on a given network and another agent, either a producer or a customer, who is willing to ship (receive, respectively) products. Every transportation-agent controls a set of arcs, each having a capacity that can be increased up to a certain point at a given cost. The other agent (i.e., the customer/producer) is interested in maximizing the flow transshipped through the network. To this aim, we assume it offers the transportation-agents a reward that is proportional to the realized flow value. This particular multi-agent framework is referred to as a Multi-Agent network expansion game. We characterize and find particular stable strategies (i.e., Nash equilibria) that are of interest for this game. We particularly focus on the problem of finding a Nash Equilibrium and a sharing policy that maximize the value of the total flow. We prove that this problem is NP-hard in the strong sense and show how such a strategy can be characterized considering paths in specific auxiliary graphs. We also provide a mixed integer linear programming (MILP) formulation to solve the problem. Computational experiments are provided to prove the effectiveness of our approach and derive some insights for practitioners.

Dominance conditions for particular single machine scheduling problems with nested execution intervals

This paper takes interest in some particular one machine scheduling problems. The input is a set of n jobs with fixed processing time and temporal execution interval associated with each job. Preemption is not allowed. We assume all along this paper that the temporal execution intervals of the jobs are nested (none of them overlaps the other). Two kinds of objective are investigated: the minimization of the lateness and the minimization of the number of late jobs. In this paper, some dominance conditions are established and optimal sequencing rules are given for some particular cases.

A new any-order schedule generation scheme for resource-constrained project scheduling

In this paper, a new schedule generation scheme for resource-constrained project scheduling problems is proposed. Given a project scheduling problem and a priority rule, a schedule generation scheme determines a single feasible solution by inserting one by one each activity, according to their priority, inside a partial schedule. The paper proposes a generation scheme that differs from the classic ones in the fact that it allows to consider the activities in any order, whether their predecessors have already been scheduled or not. Moreover, activity insertion is performed so that delaying some already scheduled activities is allowed. The paper shows that this strategy remains polynomial and often gives better results than more classic ones. Moreover, it is also interesting in the fact that some priority rules, which are quite poor when used with classic schedule generation schemes, become very competitive with the proposed schedule generation scheme.

Minimizing the number of late jobs in single machine scheduling with nested execution intervals

This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Job execution intervals are assumed to be nested each inside the other, like Russian dolls. The objective is to minimize the number of late jobs. For this problem, denoted as 1|ri , nested| SigmaUi, a new dominance condition and an optimal O(n3) solving procedure are proposed

A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption

In this paper, we present a new mass-flow based Mixed Integer Linear Programming (MILP) formulation for the Inventory Routing Problem (IRP) with explicit energy consumption. The problem is based on a multi-period single-vehicle IRP with one depot and several customers. Instead of minimizing the distance or inventory cost, the problem takes energy minimization as an objective. In this formulation, flow variables describing the transported mass serve as a link between the inventory control and the energy estimation. Based on physical laws of motion, a new energy estimation model is proposed using parameters like vehicle speed, average acceleration rate and number of stops. The solution process contains two phases with different objectives: one with inventory and transportation cost minimization as in traditional IRP, the other with energy minimization. Using benchmark instances for inventory routing with parameters for energy estimation, experiments have been conducted. Finally, the results of these two solution phases are compared to analyse the influence of energy consumption to the inventory routing systems.

Mean Response-Time Minimization of a Soft-Cascade Detector

In this paper, the problem of minimizing the mean response-time of a soft-cascade detector is addressed. A soft-cascade detector is a machine learning tool used in applications that need to recognize the presence of certain types of object instances in images. Classical soft-cascade learning methods select the weak classifiers that compose the cascade, as well as the classification thresholds applied at each cascade level, so that a desired detection performance is reached. They usually do not take into account its mean response-time, which is also of importance in time-constrained applications. To overcome that, we consider the threshold selection problem aiming to minimize the computation time needed to detect a target object in an image (i.e., by classifying a set of samples). We prove the NP-hardness of the problem and propose a mathematical model that takes benefit from several dominance properties, which are put into evidence. On the basis of computational experiments, we show that we can provide a faster cascade detector, while maintaining the same detection performances.

Temporal Analysis of Projects Under Interval Uncertainty

Given an activity-on-node network where every activity has an uncertain duration represented by an interval, this chapter takes an interest in computing the minimum and maximum earliest start times, latest start times and floats of all activities over all duration scenarios. The basic results from the literature are recalled and efficient solving algorithms are detailed. A particular focus is put on the computation of minimum float, which remains an \(\mathcal{N}\mathcal{P}\)-hard optimization problem. For this last case, a recent and efficient branch and bound algorithm is described that outperforms previously proposed methods.

A Multi-Agent Min-Cost Flow problem with Controllable Capacities

A Multi-Agent Minimum-Cost Flow problem is addressed in this paper. It can be seen as a basic multi-agent transportation problem where every agent can control the capacities of a set of elementary routes (modeled as arcs inside a network), each agent incurring a cost proportional to the chosen capacity. We assume that a customer is interesting in transshipping a product flow from a source to a sink node through the transportation network. It offers a reward that is proportional to the flow that the agents manage to provide. The reward is shared among the agents according to a pre-established policy. This problem can be seen as a non-cooperative game where every agent aims at maximizing its individual profit. We take interest in finding stable strategies (i.e., Nash Equilibrium) such that no agent has any incentive to modify its behavior. We show how such equilibrium can be characterized by means of augmenting or decreasing path in a reduced network. We also focus on the problem of finding a Nash equilibrium that maximizes the flow value and prove its NP-hardness.