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In this paper we consider the problem of optimal stopping and continuous control on some local parameters of a piecewise-deterministic Markov processes (PDP's). Optimality equations are obtained in terms of a set of variational inequalities as well as on the first jump time operator of the PDP. It is shown that if the final cost function is absolutely continuous along trajectories then so is the value function of the optimal stopping problem with continuous control. These results unify and generalize previous ones in the current literature.

In Peru, the Textile sector generates between 350 and 400 thousand direct jobs, representing 1.9% of Gross domestic product (GDP) and just over 10% of manufacturing. SMEs are characterized by being formed by family businesses, low levels of investment in new technologies and limited financial resources. This context has made SMEs are delayed compared to large companies in implementing Lean Manufacturing. Manufacturing textile companies that have problems with low productivity, excessive use of physical space, unnecessary movement and transport, use the tools of Lean Manufacturing and distribution plant for solving these problems. Many of the problems found in companies are related to the disorganization of processes, material flow and layout. Therefore, companies have seen the need to apply different strategic tools to help them increase the efficiency of their processes and become more competitive in their market. Among the strategic tools is the Lean Manufacturing. Several authors conclude that the plant distributions that SMEs have are not correct for increased productivity, however, the improvement models presenting lack information on how to create step by step a new layout of the company. Because of this, this article details the steps that SMEs can follow in search for a plant distribution model under the SLP tool.