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

Abstract : We 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.
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Submitted on : Tuesday, June 10, 2014 - 4:50:44 PM
Last modification on : Tuesday, November 19, 2019 - 4:48:48 PM

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Donatas Elvikis, Horst Hamacher, Vincent t'Kindt. Scheduling two interfering job sets on uniform parallel machines with makespan and cost functions. Journal of Scheduling, Springer Verlag, 2011, 14 (5), pp.471-481. ⟨10.1007/s10951-010-0201-1⟩. ⟨hal-01003801⟩

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