Due to its flexibility and effectiveness, the general arc-flow formulation is currently being used with success by a large multinational company in the the labeling & packaging industry to solve the following problem variant. In the cost-based cutting stock problem, instead of focusing on minimizing the number of rolls used (minimizing the waste if the demand is required to be satisfied exactly), we allow under- and/or over-production, weighing the cost of off-cut with the cost of holding stock for a number of days and/or the cost missing the production of some items. Stock limits for each day are allowed, and the total number of stock items produced may also be limited. Under- and over-production for the first day may be allowed under given tolerances with given costs per item. Miss-production out of tolerance of some items for the first day is allowed and penalized with a cost per item.
The MIP models are being solved using COIN-OR CBC (an open-source MIP solver) on a Raspberry Pi Zero W. Much better run times can be achieved using Gurobi or CPLEX.
By means of reductions to vector packing, VPSolver can be used to solve several problems such as:
- Bin packing;
- Cutting stock;
- Cardinality constrained bin packing;
- Cutting stock with cutting knife limitation;
- Bin packing with conflicts;
- Cutting stock with binary patterns;
- Cutting stock with binary patterns and forbidden pairs.
- [Computational results on several benchmark test data sets]
By means of reductions to multiple-choice vector packing, VPSolver can be used to solve several problems such as:
- Variants of the problems from the list above that consider multiple bin types;
- Variable-sized bin packing (as an one-dimensional multiple-choice vector bin packing problem).
VPSolver includes a python interface that allows modeling other problems easily. Using the python interface, VPSolver can be used to solve problems such as:
- Many variants that happen in the industry that include cutting and packing problems as subproblems of a larger production planning problem;
- Multi-stage variants (e.g, two- and three-stage two-dimensional cutting stock problems);
- Multi-period variants (e.g., plan the production for several days with the possibility of delaying or anticipating the production of some items).
Note: Suggestions of other cutting & packing problems (including industrial applications) are welcome! [Contact]