In this paper, we study a class of manufacturing systems which consist of multiple plants and each of the plants has capability of producing multiple distinct products. The production lines of a certain plant may switch between producing different kinds of products in a time-sharing mode. We optimize the capacity configuration of such a system s production lines with the objective to maximize the overall profit in the capacity planning horizon. Uncertain demand is incorporated in the model to achieve a robust configuration solution. The optimization problem is formulated as a nonlinear polynomial stochastic programming problem, which is difficult to be efficiently solved due to demand uncertainties and large search space. We show the NP-hardness of the problem first, and then apply ordinal optimization(OO) method to search for good enough designs with high probability. At lower level, an mixed integer programming(MIP) solving tool is employed to evaluate the performance of a design under given demand profile.
