This paper considers a multi-period and product inventory-routing problem. This model involves two levels, namely, a distributor and several retailers. This problem is modeled with the aim of minimizing bi-objectives, namely, the total cost of the system (including start-up, distribution, and maintenance costs) and risk-based transportation. Products are delivered to retailers by some heterogeneous vehicles with specific capacities through a direct delivery strategy, and inventory shortage is assumed to be impermissible. To validate this new bi-objective model, the ε-constraint method is used to solve problems. Because problems without distribution planning are very complex to solve optimally, the problem considered in this paper is also Non-deterministic Polynomial (NP-hard). Therefore, a nondominated sorting genetic algorithm (NSGA-II) and a multi-objective imperialist competitive algorithm (MOICA) are used and developed to solve a number of test problems. Furthermore, the computational results are compared and the performance of the foregoing algorithms is analyzed.

This study presents an integrated genetic algorithm (GA) and artificial neural network (ANN) to estimate and predict electricity demand using stochastic procedures. The economic indicators used in this paper are price, value added, number of customers and consumption in the previous periods. This model can be used to estimate energy demand in the future by optimizing parameter values. The GA applied in this study has been tuned for all its parameters and the best coefficients with minimum error are identified, while all parameter values are tested concurrently. The estimation errors of genetic algorithm model are less than that of estimated by regression method. Neural network is used to forecast each independent variable and then electricity consumption is forecasted up to year 2008. It is shown that neural networks dominate time series approach form the point of yielding less mean absolute percentage error (MAPE) error. In addition, another unique feature of this study is utilization of ANN instead of time series to obtain better predictions for energy consumption. Electricity consumption in Iranian agriculture sector from 1981 to 2005 is considered as the case of this study