Minimal investment budgets for flow line configuration

A flow line consists of a sequence of work places (or stations) through which one or more producta (or models) move one-way in order to be processed. Each model requires specific Operations which must be performed in a predefined Order. To be able to do so, the stations must be equipped with machines, robots, and workers having a certain skill such that it is guaranteed that each model passing through the system can be completely processed. The number of stations and the equipment of these stations is called the configuration of the flow line. In this paper we deal with the NP-hard problem of finding a configuration such that the net present value of cash outflows for installing and maintaining the flow line is minimized. As a special case, minimizing the number of stations is treated as well. Lower bounds are derived using column generation. Also, two heuristics are presented. One heuristic is based on the result of the column generation procedura while the other is adapted from the so-called majority merge heuristic. A computational study proves that the feasible Solution obtained on the basis of column generation requires a decidedly lower investment budget.