Constraint programming approach to a bilevel scheduling problem

Abstract

Bilevel optimization problems involve two decision makers who make their choices sequentially, either one according to its own objective function. Many problems arising in economy and management science can be modeled as bilevel optimization problems. Several special cases of bilevel problem have been studied in the literature, e.g., linear bilevel problems. However, up to now, very little is known about solution techniques of discrete bilevel problems. In this paper we show that constraint programming can be used to model and solve such problems. We demonstrate our first results on a simple bilevel scheduling problem.

Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty

“…Peng et al (2010) [32] developed a bi-level model to maintenance fund allocation and project prioritization, and deigned genetic algorithm-based dynamic programming as the solution method. Kovács and Kis (2011) [22] considered the bi-level scheduling problem where the manager of the company (the leader) was responsible for order acceptance and the workshop foreman (the follower) decided on the execution sequence of the tasks corresponding to accepted orders. Xu and Gang (2013) [39] investigated a transportation scheduling problem by multi-objective bilevel programming.…”

Single machine adversarial bilevel scheduling problems

“…An extension of this problem to the case of fuzzy processing times is tackled by Abass (2005). Kovacs and Kis (2011) introduce a general constraint programming formulation for bilevel scheduling problems and applied it to solve an optimistic bilevel single machine problem in which the leader selects the set of jobs the follower next schedules. Following the standard scheduling notation, this problem is denoted by 1|OP T − n, r j , dj | j w L j x j , j w F j C F j , with OP T − n meaning that the optimistic setting is considered and the leader selects the number of jobs n to schedule, minimizing the cost of the selected ones j w L j x j .…”

A MODM Bi-level Model with Fuzzy Random Coefficients for Resource-Constrained Project Scheduling Problems

“…Tan et al (2001) [13] developed a bi-level decision making model to the multi-resource constrained multi-project scheduling problem, and proposed a stochastic global optimization method to obtain the global optimal solutions. Kovács and Kis (2011) [7] considered the bi-level scheduling problem where the leader was responsible for order acceptance and the follower decided on the execution sequence of the tasks corresponding to accepted orders. Xu and Gang (2013) [15] investigated a transportation scheduling problem in large-scale construction projects by multi-objective bi-level programming, where the construction company decides the transportation quantities from every source to every destination on the upper level, while the transportation agencies choose their transportation routes such that the total travel cost is minimized on the lower level.…”