I want to conduct an experiment with ten factors ( factors like costs and capacities) to know the influence of each factor on the optimum value of an optimization problem. I want to know the number of levels required for each factor and the number of experiments required with factor levels for each experiment.
Cost of experiment is not a matter because these are experiments are going to be run using a software, but the time required to run is important because if large number of experiments are required the time will be more.
please throw light.
You have Minitab as a tag on this question; that said, Minitab has an excellent capability to help in planning DOEs. Go to the Assistant menu, then DOE, then Plan and Create...
If you click "Create Modeling Design" in the optimization experiment path, it will give you the setup screen where you can specify response, optimization objective, factors, etc. Notice that the design is a typical factorial-type design where low/high values are used in each experimental run. This should give good results, but just to let you know there are other design types that can be even better given the circumstances of each situation. For instance, you mentioned these are software experiments -- there is a nice design called a "Space Filling Design" which creates factor design points (not necessarily at low/high values) to optimally fill the design search space. These designs are often used for computer simulation experiments.
An excellent text on DOE is https://www.amazon.com/Design-Analysis-Experiments-Douglas-Montgomery/dp/1118146921