Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection

Atefeh Moghaddam (1) , Jacques Teghem (2) , Daniel Tuyttens (2) , Farouk Yalaoui (3) , Lionel Amodeo (3)

1 SIEMENS SAS Infrastructure & Cities, Division Mobility and Logistics
2 UMons - Université de Mons
3 LOSI - Laboratoire d'Optimisation des Systèmes Industriels

We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

Keywords: Production scheduling; bi-objective optimization; single-machine; rejection cost

Domains: Operations Research [cs.RO]

Atefeh Moghaddam, Jacques Teghem, Daniel Tuyttens, Farouk Yalaoui, Lionel Amodeo. Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection. Foundations of Computing and Decision Sciences, 2019, 44 (2), pp.179-211. ⟨10.2478/fcds-2019-0010⟩. ⟨hal-02525172⟩