A bilevel decomposition algorithm for simultaneous production scheduling and conflict-free routing for automated guided vehicles

• Published in: Computers & operations research Vol. 38; no. 5; pp. 876 - 888
• Main Authors: Nishi, Tatsushi, Hiranaka, Yuichiro, Grossmann, Ignacio E.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-05-2011; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Assignment problem; Automated guided vehicle; Automated guided vehicles; Automation; Bilevel decomposition; Convergence; Decomposition; Exact sciences and technology; Integer programming; Lagrange multiplier; Lagrangian relaxation; Mathematical models; Mixed integer; Operational research and scientific management; Operational research. Management science; Routing; Scheduling; Scheduling algorithms; Scheduling, sequencing; Studies; Tasks; Bilevel decomposition; Routing; Scheduling; Automated guided vehicle; Lagrangian relaxation; Lower bound; Guided vehicle; Assignment problem; Task scheduling; Bilevel programming; Mixed integer programming; Production management; Upper bound; Lagrange multiplier; Total weighted tardiness; Problem solving; Relaxation method
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2010.08.012

We address a bilevel decomposition algorithm for solving the simultaneous scheduling and conflict-free routing problems for automated guided vehicles. The overall objective is to minimize the total weighted tardiness of the set of jobs related to these tasks. A mixed integer formulation is decomposed into two levels: the upper level master problem of task assignment and scheduling; and the lower level routing subproblem. The master problem is solved by using Lagrangian relaxation and a lower bound is obtained. Either the solution turns out to be feasible for the lower level or a feasible solution for the problem is constructed, and an upper bound is obtained. If the convergence is not satisfied, cuts are generated to exclude previous feasible solutions before solving the master problem again. Two types of cuts are proposed to reduce the duality gap. The effectiveness of the proposed method is investigated from computational experiments.