This paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. In the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). However,, two significant criteria for each schedule in stochastic models are: expectable m...

Co-production systems, in which multiple products are produced simultaneously in a single production run, are prevalent in many industries. Such systems typically produce a random quantity of vertically differentiated products. This product hierarchy enables the firm to fill demand for a lower-quality product by converting a higher-quality product. In addition to the challenges presented by ran...

We consider quadratic stochastic programs with random recourse — a class of problems which is perceived to be computationally demanding. Instead of using mainstream scenario tree-based techniques, we reduce computational complexity by restricting the space of recourse decisions to those linear and quadratic in the observations, thereby obtaining an upper bound on the original problem. To estima...

in applications there occur different forms of uncertainty. the twomost important types are randomness (stochastic variability) and imprecision(fuzziness). in modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. however, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.since many years t...

a memory control for t-s fuzzy discrete-time systems with sto- chastic input delay is proposed in this paper. dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis- tribution. a new state space model of the discrete-time t-s fuzzy system is derived by introducing some stocha...

Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of addressing a general class of multistage stochastic optimization problems, which assume only limite...

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In robust optimization context, however, it rarely been considered. This work addresses multistage mixed-integer with decision-dependent sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect set. We ...

Uncertainty is a facet of many decision environments and might arise for various reasons, such as unpredictable information revealed in the future, or inherent fluctuations caused by noise. Stochastic optimization provides a means to handle uncertainty by modeling it by a probability distribution over possible realizations of the actual data, called scenarios. The field of stochastic optimizati...

We survey structural properties of and algorithms for stochastic integer programming models, mainly considering linear two-stage models with mixedinteger recourse (and their multi-stage extensions).

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of homogenous Decision Making Units (DMUs) with multiple inputs and multiple outputs. These factors may be evaluated in fuzzy or stochastic environment. Hence, the classic structures of DEA model may be changed where in two fold fuzzy stochastic environment. For instances, linearity, feasibility a...