In this paper, the possibility of power producing in a sequence of distillation Columns in a chemical process is inspected. The aim is to find the best sequence with its feasible power production as a means of achieving a minimum TAC (Total Annual Cost). First, all sequences have been simulated with commercial software and then, feasible power production in each sequence is examined. After finding the best values for parameters of each sequence, all sequences are compared and finally the optimum state for the process is found. Results show the high optimization of TAC by power generation in the indirect sequence (1X2&2X3).

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is one of the most significant extension problems of the Vehicle Routing Problem (VRP). The HFFOVRP is the problem of designing optimal delivery from a given depot in order to satisfy the demand of the customer population by a fleet of a fixed number of vehicles. Because the solving of this problem which has numerous applications in industrial and service problems is difficult, a Column generation (CG) algorithm for solving HFFVRP is proposed in this paper. The proposed algorithm is tested on 16 standard instances involving 10 to 50 customers. The computational results show that the CG results are better than results of exact algorithm for solving the HFFVRP within a comparatively shorter period of time.

Efficient and rapid delivery of goods in last-mile logistics represents a key challenge for e-commerce companies. With advancements in automated delivery system technologies, these systems have emerged as a promising solution to address the challenges of traditional last-mile logistics. Given the environmental and social challenges in this domain, integrating sustainability into logistics planning has evolved from being a discretionary choice to an essential requirement. Automated delivery systems are identified as a potential means to reduce greenhouse gas emissions and improve the sustainability of last-mile logistics. In this study, we propose a mathematical model for a multi-depot, multi-period delivery problem involving automated delivery systems. The model considers the multi-period nature of operations, aiming to optimize the routing of automated delivery vehicles from multiple depots over a one-day or shift-based planning horizon, while accounting for the wind effect. To enhance computational efficiency, the problem is reformulated into a master problem and a pricing subproblem, enabling the use of the Column generation algorithm. Subsequently, a dynamic programming algorithm is proposed to reduce the computational time of the pricing subproblem. To evaluate the performance of the proposed algorithm, 120 random instances were generated across 12 different problem sets. A comparison between the proposed method and the CPLEX solver was conducted to assess the efficiency of the proposed approach. The results indicate that the proposed algorithm achieves solutions with an optimality gap of less than 10%, whereas the CPLEX solver fails to deliver solutions with a gap smaller than 60%.

A train trip may have many tasks that consist of traveling from one point to another on a track. Conflicts may occur when the desired timetable would result in two trains occupying the same section of the track at the same time. The aim is to solve this conflict while minimizing the total delay. This is typical of problems arising in many passenger train networks. In our case, all journey start or end at one location (Tehran), therefore splitting the problem can lead to a significant reduction in problem size resulting in greatly reduction computational time. We show how problem can be modeled using a Column generation technique and constraint programming.