cplex - is this single machine batching problem even solveable in CPLEX

Question

I am currently trying to implement a practical problem for my seminar thesis and don't know how to implement it correctly into Cplex. This is a screenshot of the excel sheet i have to work with. There orders for the next 2 years can be seen. those orders have to be put on a single machine. The machine is like a production drum with four equal quarts. Those quarters have different capacities for different set up groups. Line 2 for example the quarter capacity is 15 for this set up group which means if 17 are required as can be seen the first quadrant is full 15/15 and the second quadrant 02/15, third and fourth quarter are empty. now the task is to find other orders which the same set up group to batch them together in order to increase utilization of this machine.

One special thing is also that orders with the same set up group and same capacity consumption can be put together in one quarter. if the set up group is the same but the capacity consumption is different (because different size in real life) the bigger/smaller sized orders have to be put in a new quarter.

For me it seems like a modified bin packing problem. In Python, I solved it already as it is easier there to use an own heuristic. I don't know how to put this into a mathematical formulation

Data in excel

标签： cplex

Answer 1

我建议查看 CPLEX 附带的各种示例。它们包括调度和包装示例。

一种简单的方法是有一个由订单和季度索引的二元决策，当且仅当订单在本季度开始时为 1。然后添加每个订单恰好在一个季度开始的约束，并添加禁止订单重叠的约束，禁止两个不同类型的订单在同一季度等。