This paper considers the problem of finding the optimal sequence of opening (starting) and closing (stopping) times of a multi-activity production process, given the costs of opening, running, and closing the activities and assuming that the state of the economic system is a stochastic process. The problem is formulated as an extended impulse control problem and solved using stochastic calculus. As an application, the optimal starting and stopping strategy are explicitly found for a resource extraction when the price of the resource is following a geometric Brownian motion.