Linear Programming

Moving morphable components (MMC) is a relatively new and effective approach in structural topology optimization. In comparison with other common methods in topology optimization such as density-based methods and level-set-based methods, it requires fewer design variables, and the boundary of the structure is defined explicitly. However, the obtained topology is highly dependent on the initial shape and position of the components. On the other hand, plastic layout optimization utilizes linear programming to find the global optimum of the structural optimization problem. Assuming rigid plastic behavior for material, the optimum layout can be obtained quickly and accurately. The optimum layout gives only the area of members which is constant along the members, therefore, there is no detail about the connection between members. Hence, the obtained optimum layout cannot be used directly for manufacturing methods such as additive manufacturing. It can be shown that the minimum compliance optimization problem for a single load case is equivalent to a minimum-weight plastic layout optimization formulation. This study utilizes the idea and presents a two-step method to take advantage of and compensate for the shortcomings of these two methods in the topology optimization of 2D structures. To this end, in the first step, the optimum layout is obtained using linear formulation in layout optimization and then, the obtained layout is utilized as an initial point in the MMC approach. The results show the efficiency, accuracy, and high convergence rate of the proposed method.

Vertical transportation technology is essential for constructing tall and medium-rise buildings. Although lifts are a functional component of buildings, their vital nature depends on the continuous and uninterrupted use of lifts in each tall building. Therefore, using lifts for vertical transportation of materials and human resources has gained greater importance. Extensive research has been conducted on reducing lift travel time between floors, optimizing lift systems design, optimizing lift movement paths, determining the sequence of floor travel, managing lift energy consumption, and floor zoning. However, the optimization of lift installation locations and quantities has not been examined so far. The use of lifts in construction projects incurs multiple costs, including rental or purchase costs, energy consumption during vertical transportation of materials, and operator salaries. One of the main solutions to reduce these costs is to minimize the duration of lift usage, which, by delivering the required materials on time, can also reduce the project's execution time. The installation costs of lifts may also vary at different candidate points due to factors such as weight and dimensional capacity, electricity consumption, the number of visits for monthly or annual maintenance and repair, and lift operator salaries. Additionally, some candidate points may have advantages over other points in terms of the amount of horizontal movement of materials on building floors. These distinctive features present challenges in selecting the optimal installation point. In this article, an integer linear programming model has been proposed to determine the optimal number and location of lift installations. The number of lifts used can affect the number of project working days, and as a result, the optimization is performed simultaneously for the number of working days and the number of lifts. The goal of this optimization model is to minimize the duration of lift usage and the associated costs. Additionally, using this model, the number of project working days is obtained with a balanced distribution of lift activities. The effectiveness of the proposed model was tested in a case study to evaluate its effectiveness. The case study involved a 20-story building located in the city of Mashhad, which requires determining the number and location of lifts during the workshop preparation phase. Using this model can lead to cost reduction and a decrease in the number of project working days.

Calculating the ultimate bearing capacity of a foundation by limit analysis allows determining the exact upper bound of bearing capacity of the foundation. In the present study, the cohesion coefficient (Nc) of a strip foundation on a single layer of soil overlaying bedrock was calculated. For this purpose, the upper bound of limit analysis combined with finite element method (FEM) was used. The soil behavior was assumed to be plastic and the Mohr-Coulomb failure criterion was used which allows description of soil mass by two parameters of cohesion and internal friction angle. It was assumed that the soil cohesion is not constant with depth and rather increases linearly. Finally, the bearing capacity was obtained using an optimized procedure (i.e., linear programming). In this regard, the Mohr-Coulomb criterion should be linearized in a stress condition. The cohesion depends on different parameters such as friction angle (φ), the ratio of soil depth to foundation width (b/h), and the cohesion variation with depth (ρ). To validate the results, obtained constant cohesion values were compared with those obtained by other researchers. The effect of the parameters on N_c was separately plotted and the calculated design charts were discussed.

In the current century, the pattern of competition in production and services has shifted from competition among independent firms to competition among supply chains. Meanwhile, the issue of strategic design of the supply chain is one of the key issues in the field of supply chain management. In these issues, the aim is generally to provide a number of manufacturing facilities and distribution centers at the candidate sites (in different geometrical areas) in order to cover the demand for various products in the customer’s area. In the proposed model, demand for each product in customer areas is achieved through a number of distribution centers, while these distribution centers provide products from manufacturing factories, and these factories must purchase the requirement components to design and produce each product from suppliers. Here, a single-objective mathematical model of mix integer linear programming is proposed that simultaneously considers the facility location problem in addition to the design of the multi-level supply chain. In this model, there are various objectives, such as minimizing the costs of the procurement and production of components, the preparation and production of products, storage and dispatch the products to distribution centers, sending to customer areas and the cost of building factories and distribution centers. To evaluate the proposed model, the mathematical model is first coded with GAMS optimization software, and then solved for large-scale problems with particle swarm optimization algorithm and imperialist competitive algorithm. Statistical analysis of the results indicates the quality of the model and the proposed solving procedure.

Bus urban public transport is one of the most considered systems and the buses have received more attention because of their special privileges compared to other systems. In most cities, the bus system is responsible due to the lack of advanced transportation systems such as subways, trams, and light-rail. Due to the positive attributes and advantages of this system, the improvement of their capabilities needs planning and consulting with experts. In this paper, a linear programming model for optimizing the public bus transportation system is proposed to minimize the total cost of setting up the lines, maintenance costs and fuel consumption as well as minimizing the bus arrival times in order to increase the welfare of the passengers. The proposed model is simulated in GAMS software and the sensitivity analysis is performed over the parameters. Due to the time complexity of the proposed model, a hybrid meta-heuristic method based on the Ant Colony Optimization (ACO) and Particle Swarm Intelligence (PSO) name PS-ACO is also developed and simulated in Matlab for solving the proposed model. The computational results show that the fuel cost and distance between stations have the most effect on operational cost, and the time distance between the stations is the most effective parameter on the passenger's welfare. Besides, the number of the stations highly affects the model complexity and solution time.

The safety is one of the important part of traffic engineering and road lighting issue, which aims to achieve a degree of visibility for drivers, so that a quick, accurate, and convenient visibility can be achieved. The driver's visibility can prevent some accidents caused by road traffic at night. In this paper, the linear programming method is used to locate and optimize the lighting system in Ahar - Tabriz, Sarab - Bostanabad and Maragheh - Hashtrood roads. A model was designed based on maximizing the benefit /cost ratio. In order to calculate the savings due to the reduction of accidents by using lighting systems, the approximate average cost of a fatal accident was calculated in the country. Also, the amount required to install the lighting system in different parts was defined. The constraints for this model are the allocated budget for the installation of lighting systems. In order to analyze the model, WinQSB2 software was used to obtain optimal sections for the installation of the lighting system. Based on this research, the ranges of 44 + 500 to 45 + 500 and 54 +500 to 55+500 of Ahar-Tabriz road with a profit ratio of 8.26 and 8.07 in all budget scenarios and segmentation at the top of other components were determined as the optimal sections. The 09 + 500 and 10 + 500 Kilometers of Maragheh-Hashtrood road with a profit ratio of 5.13 was also ranked next.

In Transportation Master Plans (TMP), the detailed socioeconomic data of study area population are needed for forecasting travel demand. However, in Household Travel Survey (HTS), these data are collected only for a small sample of households. Since collection of such data for the entire population is too expensive, if not infeasible, it is necessary to produce synthetically such data using the macro-data of the population and micro-data of the sample. This process is known as population synthesis in the literature or as data expansion in Iran. It seems that the existing method of expansion did not result in valid assignment volume and trip matrix. Hence, a linear programming model is proposed for data expansion, which used variables at the household and individual levels simultaneously. This method estimates weights for households while minimizing the deviation of synthesized population socio-economics from observed ones obtained from census bureau. The comparisons between the results of the two methods (that are applied for the city of Mashhad) show that the coefficient of determination between the observed and estimated population of zones for the existing and the proposed methods are 0.79 and 0.97, respectively. Also, the proposed method resulted in a valid trip matrix and assignment volume. The percentage errors of screen lines daily volume are 25% in the existing method, whereas they are less than the acceptable 14% error in the proposed method. Root mean square error (RMSE) of links volume are 55% and 26% in the existing and the proposed methods, respectively.