Two-agent scheduling on uniform parallel machines with maximum criteria functions

International audienceWe consider the problem of scheduling two agents A and B on a set of m uniform parallel machines. Each agent is assumed to be independent from the other: agent A and agent B are made up of n_A and n_B jobs, respectively. Each job is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size jobs, i.e. all jobs share the same processing time. Our goal is to minimize two maximum functions associated with agents A and B and referred to as F_A^max=max_{i∈A} (f^A_i(C_i)) and F_B^max=max_{i∈B} (f^B_i(C_i)), respectively, with C_i the completion time of job i and f^X_i a non-decreasing function. These kinds of problems are called multi-agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of the strict Pareto optima for the (F_A^max,F_B^max) criteria vector. In this paper we develop a minimal complete Pareto set enumeration algorithm with O(n^2_A+n^2_B+n_An_Blog (n_B)) time complexity and O(nn_B) memory requirement

Scheduling and Location (ScheLoc): Makespan Problem with Variable Release Dates

While in classical scheduling theory the locations of machines are assumed to be fixed we will show how to tackle location and scheduling problems simultaneously. Obviously, this integrated approach enhances the modeling power of scheduling for various real-life problems. In this paper, we present in an exemplary way theory and a solution algorithm for a specific type of a scheduling and a rather general, planar location problem, respectively. More general results and a report on numerical tests will be presented in a subsequent paper

Scheduling two interfering job sets on uniform parallel machines with sum and makespan criteria

International audienc

Scheduling two interfering job sets on uniform parallel machines with makespan and cost functions

International audience We consider a m uniform parallel machines scheduling problem with two jobs A and B with n A and n B operations, respectively, and equal processing times. Job A is associated with a general cost function F A , whereas makespan is considered for job B. As we are dealing with two conflicting criteria, we focus on the calculation of strict Pareto optima for F A and C B max criteria. We also tackle some particular cases of F A and provide polynomial algorithms

Scheduling two interfering job sets on uniform parallel machines with maximum criteria functions

International audienc

Scheduling two interfering job sets on uniform parallel machines with makespan and cost functions

International audienceWe consider the problem of scheduling two jobs A and B on a set of m uniform parallel machines. Each job is assumed to be independent from the other: job A and job B are made up of n_A and n_B operations, respectively. Each operation is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size operations, i.e. all operations have the same processing time. The scheduling of operations of job A must be achieved to minimize a general cost function F_A , whereas it is the makespan that must be minimized when scheduling the operations of job B. These kind of problems are called multiple agent scheduling prob- lems. As we are dealing with two conflicting criteria, we focus on the calculation of strict Pareto optima for F_A and C^B_max criteria. In this paper we consider different min-max and min-sum versions of function F_A and provide special properties as well as polynomial time algorithms

Scheduling and Location (ScheLoc): Makespan Problem with Variable Release Dates

While in classical scheduling theory the locations of machines are assumed to be fixed we will show how to tackle location and scheduling problems simultaneously. Obviously, this integrated approach enhances the modeling power of scheduling for various real-life problems. In this paper, we present in an exemplary way theory and a solution algorithm for a specific type of a scheduling and a rather general, planar location problem, respectively. More general results and a report on numerical tests will be presented in a subsequent paper