I want to model a serial production line which process only one type of product. The product processing start from the beginning of the production line and ends in the last station. The product should be passed through all the stations. Basically, there is just one worker in each workstation however here, the trick to minimizing the time is that workers in addition to their workstation can work in the next workstation, as well. In the other word, they are crosstrained. As a result, when the product gets ready in the first workstation the worker takes it and brings it to the second workstation, there the first and second workers are working together to finish the product therefore less time is needed to complete the job. Accordingly when the product is finished in the second workstation, the second worker will take it to the third workstation, there second and third workers will finish the job together sooner. As a result, this situation with help to decreasing product completion time. There are also some constraints which I am not going to talk about them here.
There is no requirement of quality, setup time or cost or anything else. The problem is as simple as I explained.
If you know any publication which can help me to model the time with linear programming please let me know.
The literature I found so far are mainly about minimization of time when there are a number of different producs with different completion times in each machine. Note that, here it is just one product which goes through all machines and time minimization comes from workers cross-training.
Dear Nasirian,
Your problem resembles to Traveling Salesman or job schedule problem.I am not sure that your problem is suitable with linear programming. I think your model is not defined as continuous function. I suggest that you can use meta-heuristic techniques for this problem. If you look at publications about meta-heuristics applications for Traveling Salesman or job schedule problem, it can be more useful.
There are plenty of basic production planning books. Why not browse their contents lists and learn what might be the best for you? Here are just two example books:
Stephen Chapman: The Fundamentals of Production Planning and Control
Robert H. Bock: Production Planning and Control
One task that has been important in the work I have been involved with (together with - among others - the PhD student Karin Thörnblad at GKN Aerospace) has been which variable declaration to use, since that choice has a vast effect on the computation time. We learnt in most of our work that "more indices helps", that is, to have more variables helped the solution process.
The book "Production Planning by Mixed-Integer Programming" by Pochet and Wolsey is great, but it takes time to digest it.
We might be able to help more if you tell us what it is that you can decide. Is it to decide who to crosstrain? Which skills to crosstrain people in? Who to place in each stage? Something else?
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