We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.

a r t i c l e i n f o Keywords: Stochastic dynamic programming Risk-reward heuristic Mean–variance analysis Efficient frontier analysis Inventory management Traditionally inventory management models have focused on risk-neutral decision making with the objective of maximizing the expected rewards or minimizing costs over a specified time horizon. However, for items marked by high demand volatil...

In this study, water management allocated to the agricultural sector’ was analyzed using stochastic dynamic programming under uncertainty conditions. The technical coefficients used in the study referred to the agricultural years, 2013-2014. They were obtained through the use of simple random sampling of 250 farmers in the region for crops wheat, barley, melon, watermelon and ruby grapes under ...

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DP-based learning algorithms to the powerful te...

In this paper we discuss statistical properties and rates of convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently the SDDP alg...

In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general tran...

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non-linear features to be incorporated and changes in hydrological conditions to be modelled as Markov processes. However with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This pape...

With globalization and rapid technological-economic development accelerating the market dynamics, consumers' demand is becoming more volatile diverse. In this situation, capacity adjustment as an operational strategic decision plays a major role to ensure supply chain responsiveness while maintaining costs at reasonable norm. This study contributes literature by developing computationally effic...

In stochastic scheduling, we want to allocate a limited amount of resources to a set of jobs that need to be serviced. Unlike in deterministic scheduling, however, the parameters of the system may be stochastic. For example, the time it takes to process a job may be subject to random fluctuations. Stochastic scheduling problems occur in a variety of practical situations, such as manufacturing, ...

Warren Powell is Professor of Operations Research and Financial Engineering at Princeton University, where he has taught since 1981. He is director of CASTLE Laboratory which specializes in the solution of large-scale stochastic optimization, with considerable experience in freight transportation. This work led to the development of methods to integrate mathematical programming and simulation w...