Problem statement: For instance, we have ‘n’ different types of packages which can be utilized multiple times based on requirement. Each package has its own weight and cost. On the other hand, we have ‘m’ number of items that are to be packed into given packages in an optimal way. Optimal way means the total cost of packages used should be minimum. These packages are further placed in bin being an imaginary container.
Constraints:
- An item can be placed only in one package.
- A bin can accommodate only one package.
- Sum of weights of all items in package should not be greater than weight of package.
I have been trying to solve this bin pack problem which has already been solved in PYOMO and PYSCIPOPT . The challenges I faced are designing the constraints and decision variables in a way that has to be given for scipy HiGHS solver. for n=7(packages) and m=34(items), Complexity is growing in designing the constraints. I have come up with 273 constraints and is growing. With PYOMO, declaring constraints and objective function is easier than in SCIPY.
Can anyone tell me I am doing the right way or guide me on how to model the constraints in scipy.