Christophe Rapine

Lot Sizing with Carbon Emission Constraints

This paper introduces new environmental constraints, namely carbon emission constraints, in multi-sourcing lot-sizing problems. These constraints aim at limiting the carbon emission per unit of product supplied with different modes. A mode corresponds to the combination of a production facility and a transportation mode and is characterized by its economical costs and its unitary carbon emission. Four types of constraints are proposed and analyzed in the single-item uncapacitated lot-sizing problem. The periodic case is shown to be polynomially solvable, while the cumulative, global and rolling cases are NP-hard. Perspectives to extend this work are discussed.

An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints

In this paper, we study the single machine total completion scheduling problem subject to a period of maintenance. We propose an approximation algorithm to solve the problem with a worst case error bound of 3/17. Furthermore, an example is provided to show that the bound is tight. Computational experiments and an analysis are given afterwards.

Efficient approximation algorithms for scheduling malleable tasks

A malleable task is a computational unit which may be executed on any arbitrary number of processors, its execution time depend- ing on the amount of resources allotted to it. According to the standard behavior of parallel applications, we assume that the mal- leable tasks are monotonic, i.e. that the execution time is decreas- ing with the number of processors while the computational work increases. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guar- antee of for the minimization of the parallel execution time, or makespan. It improves all other existing practical results includ- ing the two-phases method introduced by Turek et al. The main idea is to transfer the difficulty of a two phases method from the scheduling part to the allotment selection. We show how to formu- late this last problem as a knapsack optimization problem. Then, the scheduling problem is solved by a dual-approximation which leads to a simple structure of two consecutive shelves.

A

A malleable task is a computational unit that may be executed on any arbitrary number of processors, whose execution time depends on the amount of resources allotted to it. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guarantee of

\frac32

\frac{3}{2}+\varepsilon

-Approximation Algorithm for Scheduling Independent Monotonic Malleable Tasks

for the minimization of the parallel execution time for any fixed

Sensitivity analysis of scheduling algorithms

\varepsilon > 0

The single-item green lot-sizing problem with fixed carbon emissions

. The main idea of this approach is to focus on the determination of a good allotment and then to solve the resulting problem with a fixed number of processors by a simple scheduling algorithm. The first phase is based on a dual approximation technique where the allotment problem is expressed as a knapsack problem for partitioning the set of tasks into two shelves of respective heights

Polynomial time algorithms for the constant capacitated single-item lot sizing problem with stepwise production cost

1

Single machine scheduling with small operator-non-availability periods

and