Bin Packing Problem with Time Lags

We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, minimum maximum lags required between some pairs items. suggest two integer programming formulations for general problem: a compact one stronger formulation with an exponential number variables constraints. propose branch-cut-and-price approach that exploits latter formulation. For this purpose, we devise separation algorithms based on mathematical characterization feasible assignments important special cases when possible available at each period is infinite limited nonnegative. Computational experiments reported instances inspired from real-case application chemical treatment planning in vineyards, as well literature problem. The experimental results show efficiency our approach, it outperforms newly proposed able obtain improved lower upper bounds instances. Summary Contribution: paper considers new variant problem, which most problems operations research. A motivation introducing given, real-life application. present novel original exact algorithm implement algorithm, extensive computational experiments. very good performance algorithm. give research directions can be followed by subsequent researchers extend contribution more complex generic problems.