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We p r e s e n t a dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty i n load, in ow to reservoirs and prices for fuel and delivery contracts. The stochastic load process is approximated by a scenario tree obtained by adapting a SARIMA model to historical data, using empirical means and variances of simulated scenarios to construct an initial tree, and reducing it by a scenario deletion procedure based on a suitable probability distance. Our model involves many mixed-integer variables and individual power unit constraints, but relatively few coupling constraints. Hence we e m p l o y s t o c hastic Lagrangian relaxation that assigns stochastic multipliers to the coupling constraints. Solving the Lagrangian dual by a proximal bundle method leads to successive decomposition into single thermal and hydro unit subproblems that are solved by dynamic programming and a specialized descent algorithm, respectively. The optimal stochastic multipliers are used in Lagrangian heuristics to construct approximately optimal rst stage decisions. Numerical results are presented for realistic data from a German power utility, with a time horizon of one week and scenario numbers ranging from 5 to 100. The corresponding optimization problems have up to 200,000 binary and 350,000 continuous variables, and more than 500,000 constraints.

We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.

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A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 200 000 binary and 350 000 continuous variables, and more than 500 000 constraints.

Various emission reduction methods have been investigated in relation to policy, technology, and operation in academia and industry. Increasing capacity utilization by sharing transportation network and gaining return cargo is one potential approach to achieve this reduction. As a consequence, repositioning of the vehicle is needed in some cases, which needs to be supported by a proper emission allocation scheme to encourage different players to form and maintain a sharing coalition. However, the presence of repositioning adds a level of complexity to the emission allocation issue since empty trips in repositioning transportation carry no cargo themselves to which the emissions can be allocated. For this purpose, we present alternative allocation schemes and investigate the impacts of these schemes on the carbon footprint measurement. A real-life case study is demonstrated and discussed based on a simulation model and analysis of variance (ANOVA). We find that different schemes have significant effects on the distribution of emission among the cargo owners. We suggest that a scheme to share the emissions based on total transport work is preferable because it provides motivation for a joint cooperation between players and improves the environmental performance. The methodology applied in this article can be generalized to other repositioning transport cases in which more players and more logistics legs including empty trips are involved. It also provides insight for policymakers to devise rules for carbon footprint calculations that encourage collaboration and shared transport in complex, multi-stakeholder transportation networks.

For the unit commitment problem in the hydro-thermal power system of VEAG Vereinigte Energiewerke AG Berlin we present a basic model and discuss possible extensions where both primal and dual solution approaches lead to flexible optimization tools. Extensions include staggered fuel prices, reserve policies involving hydro units, nonlinear start-up costs, and uncertain load profiles.

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