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I have to analyze a cardboard packaging system. To simplify, it consists of three parts, each of which needs to be set up (this depends on the pre-order): the printer, the slotter, and the cutter. The more items are set up, the longer the setup time. In production, it is recorded which of these is being set up. However, in the cost calculation between the firm and the customer, only the size of the desired product, the system in which the goods are processed, and the cardboard sizes are known. My task is to obtain better data for the setup time in the cost calculation so that we can have better and more accurate data for the setup costs.

When I feed the data with the features known in production, I get a fairly accurate model. However I can't test the model from the data of the cost calculation since features such as the setup process of the slotter isn't known yet and this all depends on the previous order that the machine processed.

Is there anything I could do?

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Running a customer's job may require time consuming equipment setup, and time is money. Predict the dollars for setup.

Your existing production data captures number of seconds to set up each of {printer, slotter, cutter}. We observe 0 seconds if equipment was already properly set up due to a previous run. So, assuming a piece of equipment requires setup, we can produce a model which predicts time and corresponding wage dollars. It might be as simple as computing mean values.

"Do the simplest thing that could possibly work." Here, simplest is to just assume worst case for every job, so we never encounter equipment with a proper setup from previous job. Charge customers based on worst case. Sometimes their job will happen to get lucky, with no setup needed, and you get extra profit due to the time saved.

For more competitive bidding, you will want to predict likelihood that setup will be needed. Train a prediction model based on the observed mix of historic jobs you have already run for customers.

Clever scheduling of jobs can save you money. An online scheduler has limited flexibility, but it sounds like you have an offline scheduling situation, with a window of K days that a job may remain in the queue before running it. Do job simulations against a month of historic orders, varying the parameter K. As K increases, you should be able to get away with doing fewer setups, reducing that month's cost. Use the simulator's results to inform discount pricing, where customers that can afford delay of specified number of days will enjoy some specified lower price.

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