Single-track multi-hoist scheduling problem: a collision-free resolution based on a branch-and-bound approach

An analytical mathematical model and a branch-and-bound algorithm for single-track cyclic multi-hoist scheduling problems are proposed. The objective is to minimize the cycle time for a given number of hoists. The collision-free single-track constraints are first formulated as disjunctive inequalities. It is then shown that this formulation is a very strict and necessary condition. To be a sufficient and necessary one, two additional properties, like collision-checking rules, must hold in optimal solutions. It is proved that a solution violating these two properties due to their relaxation is always dominated by a collision-free one. Therefore, these two properties are relaxed in the branch- and-bound algorithm. The computation of lower bounds in the branch- and-bound algorithm requires the solution of a specific linear programming problem, which can be solved by using a graph-based polynomial algorithm. Computational results with both benchmark and randomly generated test instances are presented.