Objective stochastic programming

Plugging the first-stage solution of the EV problem xEV into the stochastic program (2S-MILP) gives the expected result of using the EV solution (EEV problem). The solution of the EEV problem is not necessarily optimal for the original 2S-MILP. Consequently, the optimal objective value of the EEV problem is always greater than (or at least equal to) the optimal objective value of the 2S-MILP, such that the objective of EEV is an upper bound for the optimal solution of the 2S-MILP ... 

An uncertainty conscious scheduling approach for real-time scheduling was presented in this chapter. The approach is based on a moving horizon scheme where in each time period a two-stage stochastic program is solved. For the investigated example it was found that the stochastic scheduler improved the objective on average by 10% compared to a deterministic scheduler. 

The stochastic model with recourse in the previous section takes a decision merely based on first-stage and expected second-stage costs leading to an assumption that the decision-maker is risk-neutral (Sahinidis, 2004). In order to capture the concept of risk in stochastic programming, Mulvey, Vanderbei and Zenios (1995) proposed the following amendment to the objective function ... 

Since stochastic programming adds computational burden to practical problems, it is desirable to quantify the benefits of considering uncertainty. In order to address this point, there are generally two values of interest. One is the expected value of perfect information (EVPI) which measures the maximum amount the decision maker is willing to pay in order to get accurate information on the future. The second is the value of stochastic solution (VSS) which is the difference in the objective function between the solutions of the mean value problem (replacing random events with their means) and the stochastic solution (SS) (Birge, 1982). 

This is the basic idea of a two-stage stochastic program with recoiurse. At the first stage, before a realization of the random variables first-stage decision variables X to optimize the expected value g x) = t[G x, >)] of an objective fimction G(x, to) that depends on the optimal second stage objective function. 

Multi-objective linear programming (MOLP) Multi-objective stochastic integer linear programming Interactive MOLP Mixed 0-1 MOLP... 

A basic assumption of stochastic programming is that the probability distribution of the random variable is known. The target then is to find an optimal solution that makes the expected value of the system to be minimum (or maximum). According to the type of the objective function and constraints, the stochastic programming problem can be divided into stochastic linear programming problems and stochastic nonlinear programming problems. 

Taking into account that decision-makers do not always care about maximizing revenue, but how to achieve the optimal revenue in the sense of probability, we apply stochastic chance-constrained programming theory to translate the model into the stochastic programming model under chance constraints so that the optimal decision objective with a certain confidence level can be expressed. 

Multi-objective, stochastic, and nonlinear mathematical programming models are other models that find application in supply chain configuration. 

Many of the stochastic programming models developed for supply chain configuration have demand as a stochastic parameter. Demand uncertainty usually is represented by multiple demand scenarios (Mirhassani et al. 2000 Tsiakis et al. 2001). In this case, a prototype objective function can be expressed as... 

Bozotgi-Amiri A, Jabalameli MS, Mirzapour AI-e-Hashem SMJ (2013) A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spectmm. doi 10.1007/s00291-011-0268-x... 

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