We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., problems in which there are first-stage feasible solutions that not guaranteed to have a recourse action. As feasibility measure of the SAA solution, we consider "recourse likelihood", is probability solution has For $\epsilon \in (0,1)$, demonstrate likelihood below $...

We present a brief overview of four stages of nurse planning. For the last stage, which assigns nurses to patients, a stochastic integer programming model is developed. A Benders’ decomposition approach is proposed to solve this problem, and a greedy algorithm is employed to solve the recourse subproblem. Patient-to-nurse ratio constraints are introduced to balance the workload of nurses as wel...

We formulate a two-stage stochastic integer program to determine an optimal schedule for jobs requiring multiple classes of resources under uncertain processing times, due dates, resource consumption and availabilities. We allow temporary resource capacity expansion for a penalty. Potential applications of this model include team scheduling problems that arise in service industries such as engi...

This paper proposes a stochastic hydro unit commitment (SHUC) model for price-taker hydropower producer in liberalized market. The objective is to maximize the total revenue of producer, including immediate revenue, future (i.e., opportunity cost), and startup shutdown cost. market price uncertainty taken into account through scenario tree. solution challenging task due its non-convex high-dime...

The Buffer Allocation Problem (BAP) in production flow lines is very relevant from a practical point of view and challenging scientific perspective. For this reason, it has drawn great attention both industry the academic community. However, despite problem’s relevance, no exact method available literature to solve when long are being considered, i.e., settings. This work proposes new Mixed-Int...

Supply chain models describe the activities carried out in the process industry. They are used to design and operate complex sequences of tasks that transform raw materials and deliver final products to markets. Many optimization models have been developed for supply chain planning because they offer the possibility of finding strategies that lead to greater economic benefits. The traditional m...

This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic prog...

Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such probl...

In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by Benders’ decomposition in which master formulated as mixed-integer linearization generation constraints for improved convergence. Semidefinite programming relaxation rectangular optimal used subproblem, providing somewhat conservative cuts. Numerical case studies, including 6-bu...