Integrated supplier selection and order allocation is a complex problem that is important for both designing and operating supply chains. It becomes especially complicated when quantity discounts are considered at the same time. Under such circumstances, most studies often formulate the problem as a Multi-Objective Linear Programming problem (MOLP), and then transform it to a Mixed Integer Programming problem (MIP) to handle the inherited multi-objectives, simultaneously. But, objectives are not of equal importance and in this approach scaling and subjective weighting often are not considered. In addition, some of the studies that use weighting method to solve the MOLP, usually ignore to normalize the coefficients. However, as different coefficients have different units such as cost or number coefficients, so weighted summation will be meaningless. Furthermore, in most of the studies only quantitative criteria are considered in mathematical model. But, the importance of some qualitative criteria persuade decision maker to consider other affective criteria as well as cost. In this study, in order to ease the problem and to obtain a more reasonable compromised solution for order allocating among suppliers, an integration of analytical hierarchy process and linear integer and multi-objective programming is proposed. The large number of criteria and attributes are employed in this problem and they are employed in a comprehensive model to solve the multi-objective problem and to find the most preferred non dominated solutions by considering decision maker’s (DM) preferences. Some illustrative examples are solved using LINGO and the results are compared. The sensitivity analysis and comparing the results with one of the well-known studies in the literature has demonstrated the flexibility and efficiency of the proposed model to deal with large sized problems and incorporate different purchasing policies, easily and in a short amount of time.

With the rapid increase of energy demand, it is becoming increasingly important to obtain accurate energy demand forecasts. To incorporate long time causal relationships, autoregressive with exoge-nous regression components models have received increasing attention from many researchers in this field. These are linear models applied through hybrid methodology of time series and econo-metrics, however, some recent studies find evidences that nonlinear models outperform over linear ones in long term peak demand forecasting. This paper proposed a nonlinear Auto Regressive Integrated Moving Average with Exogenous Inputs (N-ARIMAX) model to forecast sectoral peak demand using a case study of Iran. The results indicate that significant improvements in forecasting accuracy are obtained with the proposed models compared to the existing models.

This paper presents a model to solve the multi-objective location-routing problem with capacitated vehicles. The main purposes of the model are to find the optimal number and location of depots, the optimal number of vehicles, and the best allocation of customers to distribution centers and to the vehicles. In addition, the model seeks to optimize vehicle routes and sequence to serve the customers. The proposed model considers vehicles’ traveled distances, service time and waiting time while guaranteeing that the sum of these parameters is lower than a predetermined value. Two objective functions are investigated. First objective function minimizes the total cost of the system and the second one minimizes the gap between the vehicles’ traveled distances. To solve the problem, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is developed. The efficiency of the MOICA is demonstrated via comparing with a famous meta-heuristics, named Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Based on response surface methodology, for each algorithm, several crossover and mutation strategies are adjusted. The results, in terms of two well-known comparison metrics, indicate that the proposed MOICA outperforms NSGA-II especially in large sized problems.

Cellular manufacturing is considered as a lean technique of producing similar parts using sells or groups of team members, workstations, or equipment to facilitate operations by removing setup and unnecessary cost components among various operations. Cell formation and layout planning are the most components of the cellular manufacturing. This paper presents a dynamic method to minimize different costs including the total cost of movements within and between cells and exceptional parts. In this study, the Hierarchical Genetic Algorithm (HGA) is used for solving the resulted model and the results are compared with genetic algorithm. The results have indicated that the proposed method could reach optimal solutions for some small and medium sized problems in reasonable amount of time.