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 3 Model B. 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:
By means of reductions to multiple-choice vector packing, VPSolver can be used to solve several problems such as:
VPSolver includes a python interface that allows modeling other problems easily. Using the python interface, VPSolver can be used to solve problems such as:
Note: Suggestions of other cutting & packing problems (including industrial applications) are welcome! [Contact]