farid momayezi

In this research, a modular hub location problem has been investigated where the objective is to reduce the transportation costs in the hub network. The proposed model determines the location of hubs, allocation of the non-hub nodes to the hubs, and the optimal vehicle traffic, i.e., the number of flights or the number of trucks traveling in the network, considering the appropriate capacity for each vehicle. Also, decisions regarding the percentage of the traffic volume sent via multiple network routes are made by the presented model.

The mathematical model, including the objective function and constraints, is constructed and solved by GAMS software. The effect of different parameters on the results is investigated. Due to long solution times for the MIP model, a heuristic solution method based on LP relaxation of the integer variables is developed for the proposed problem, which is able to obtain near-optimal solutions in less time.

The developed mathematical model is implemented on the air passenger transportation data for the airports of the United States of America, which is known as the CAB data set. The results give the optimal number of hubs, as well as the optimal number of transportation units on each arc of the network, which depend on the capacity of the means of transportation.

Originality/Value:

 In this research, a mixed integer programming model is developed for the multiple allocation modular hub location problem. Numerical experiments are conducted with the use of GAMS software and the results are discussed.

The smart home is equipped with programmable home appliances designed to be used during off-peak hours when energy prices are lower. Research in smart home energy management has focused on developing mathematical models for planning and scheduling programmable appliances for the next day. While many countries announce daily energy prices for the following day, some countries, like Iran, have fixed energy prices for longer durations. Previous research has primarily focused on selling energy back to the grid when considering smart homes connected to renewable energy sources. Meeting the home's energy needs with renewable energy is a secondary priority. This study presents two mathematical models for multi-period planning daily, weekly, monthly, and yearly of a smart home. The first model does not consider the integration of solar cells, while the second model is connected to solar cells to maximize the use of renewable energy. The proposed mathematical models are solved using the CPLEX solver embedded in the GAMS software.By comparing the prices obtained from the two models, the cost of solar cells with the desired production capacity is calculated. The results demonstrate a significant reduction in energy consumption costs. These models provide optimized schedules for operating appliances in a smart home, taking into account fluctuating energy prices. The integration of solar cells enables homeowners to leverage renewable energy sources and reduce reliance on the grid.

Hubs are special facilities used as switching, transferring, and sorting points in many distribution systems. Instead of serving each origin-destination pair directly, the hub facility concentrates flow to take advantage of the resulting economic savings. Flows from the same source combine with different destinations on their path to a hub and combine with flows that have different sources but have the same destination. The accumulation of flows takes place in the path from the origin to the hub and from the hub to the destination, as well as between the hubs. These types of systems, commonly known as hub-and-spoke, are studied in the form of hub location problems. In this paper, we develop the single allocation hub location problem with uncertain zero-one demands, in which the amount of demand between each origin-destination pair is considered as a Bernoulli random variable with a definite probability p. Due to the fact that this problem has not been studied in the literature so far, a new mathematical model of mixed integer programming type is developed for the problem and is solved using GAMS software. Also, the results of solving different test problems from the CAB data set are examined and the effect of different parameters on the optimal solution of the problem is examined.