On bilevel machine scheduling problems

The bilevel optimisation of a multi-agent project scheduling and staffing problem

“…The stages follow the hierarchy of the leader and the follower in the problem under study and the decisions of the team leader constrain the decisions of the project manager. In Section 5.2, we formulate a multi-criteria optimisation problem to model the interaction between the two decision makers and solve the problem via a single-level methodology, which is common in the scheduling literature (Kis and Kovacs, 2002). The relation between multi-criteria optimisation and bilevel linear programming have been studied in Dempe (2002) as well as Kis and Kovacs (2002).…”

“…In Section 5.2, we formulate a multi-criteria optimisation problem to model the interaction between the two decision makers and solve the problem via a single-level methodology, which is common in the scheduling literature (Kis and Kovacs, 2002). The relation between multi-criteria optimisation and bilevel linear programming have been studied in Dempe (2002) as well as Kis and Kovacs (2002). The alternative single-and multi-stage approaches devised in this section are standard optimisation techniques trying to capture the bilevel optimisation problem.…”

Single machine adversarial bilevel scheduling problems

“…The follower sequences the jobs so that their weighted sum of completion times is minimum. Kis and Kovacs (2012)…”

“…The problem is shown to be strongly N Phard. Kis and Kovacs (2012) consider again the 1|OP T − n, r j , dj | j w L j x j , j w F j C F j problem and show that it is weakly N P-hard.…”

Constraint programming approach to a bilevel scheduling problem

“…The latter papers take a relatively straightforward solution approach: they enumerate (a part of) the leader's possible choices, and for each choice, compute the follower's response. In (Kis & Kovács 2009), we present basic complexity and algorithmic results for bilevel scheduling problems.…”