Integrated water resources management is a systematic process for sustainable development, allocation and monitoring of water resources that is used for social, economic and environmental purposes. In this study, a multi-period mixed-integer linear programming (MILP) model for urban water supply network management is proposed. The proposed model considers all echelons of water supply chain from supply centers to wastewater treatment centers. Also, the model optimizes the decisions such as selecting the suitable water supply centers and capacity level optimization. To verify and validate the proposed model a real case study is conducted in Urmia. The model is solved by the General Algebraic modeling System (GAMS) software and its results have been analyzed. According to the results, the optimal water supply centers, optimal water flow, optimal water inventory, and optimal capacity levels of wastewater treatment centers in different periods are determined. Also, in case of transferring the remaining additional treated water to Urmia lake, its level is increased by about 0. 007 cm.

Simultaneous optimization of vehicle routing and loading decisions in three-dimensional case is one of the important problems in logistics and has received great attention from researchers. To the best of our knowledge, optimization models presented in the literature for this problem either are too complicated or do not include important loading assumptions such as item fragility, last-in-first-out arrangement, and the possibility of rotation. To overcome the shortcoming of the existing models, in this paper, we present a novel mixed-integer linear programming (MILP) model which not only involves important loading assumptions, but also does not have the complexity of previous models. Moreover, we provide valid inequalities to strengthen the LP relaxation bound and accelerate the solution process. Further, we show that how a restricted version of our model can be incorporated in loading procedures of meta-heuristic algorithms to improve their efficiency. Computational results over instances, taken from the literature, show the performance of the proposed approach.

The inevitable emergence of intelligent distribution networks has introduced new features in these networks. According to most experts, self-healing is one of the main abilities of smart distribution networks. This feature increases the reliability and resiliency of networks by reacting fast and restoring the critical loads (CLs) during a fault. Nevertheless, the stochastic nature of the components in a power system imposes significant computational risk in enabling the system to self-heal. In this paper, a mathematical model is introduced for the self-healing operation of networked Microgrids (MGs) to assess the risk in the optimal service restoration (SR) problem. Electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs) and their stochastic nature besides the distributed generation units (DGs), the ability to reconfiguration, and demand response program are considered simultaneously. The objective function is designed to maximize the restored loads and minimize the risk. The Conditional Value-at-Risk (CVaR) is used to calculate the risk of the SR as one of the most efficient and famous risk indices. In the general case study and considering $\beta $ equal to the 0, 1, 2, 3, and 4, expected values of SR for the risk-averse problem is 21.2, 20, 19.3, 19.1, and 19\% less than the risk-neutral problem, respectively. The formulation of the problem is mixed-integer linear programming (MILP), and the model is tested in the modified Civanlar test system. The analysis of several case studies has proved the performance of the proposed model and the importance of risk management in the problem.

This study addresses the critical challenge of optimizing rebar delivery in heavy logistics industries by proposing an integrated multi-objective mixed-integer linear programming (MILP) model for simultaneous delivery scheduling and vehicle routing. The model aims to minimize three conflicting objectives: the overall makespan of deliveries, the weighted customer dissatisfaction from delivery time windows based on customer priority, and the total transportation costs. A fuzzy multi-objective optimization approach, based on the principles of Bellman and Zadeh and Zimmermann’s method, is employed to transform this complex problem into a single-objective maximization problem of an overall satisfaction level. The efficacy and practical applicability of the proposed model are validated through a real-world case study from Amir Kabir Khazar Steel Company in Gilan province, Iran. The case study involves 51 customer orders to be delivered over a three-day planning horizon, incorporating realistic constraints such as specific time windows and customer priority levels. Computational results, obtained using GAMS with the CPLEX solver, demonstrate that the model successfully achieves a high overall satisfaction level of λ =0.841. The findings offer significant managerial insights for balancing operational efficiency, cost reduction, and customer satisfaction in rebar supply chains.

This paper proposes a bi-objective mixed-integer linear programming model for formulating a lot-sizing and scheduling problem for the perishable yogurt industry under demand uncertainty. The objectives of the proposed model are to simultaneously minimize the overall cost and the total production completion time. The proposed MILP formulation integrates many distinctive features of yogurt processing, including shelf-life constraints, setups, packaging rates, minimum and maximum lot size limits, future time for holding products, and fuzzy demand. Additionally, the proposed model, including inventory control, is a multi-product and multi-period model hence, it is categorized as an operational-strategic model. We introduce a hybrid approach focused on fuzzy possibility programming and a fuzzy goal programming approach for solving the suggested bi-objective model, where possibility, necessity and credibility measures are adopted according to the decision makers’,preference. Compared to the traditional model of lot sizing and scheduling, better decision-making and sensitivity analysis for DMs can be made based on the three obtained efficiency values. Data from the yogurt plant were used to assess the feasibility of the proposed model and solution approach. The results obtained from applying the method and sensitivity analysis showed the effectiveness of the mathematical formulation as well as the proposed solution method.

In this paper, a mixed-integer linear programming (MILP) model is proposed to solve the charging problem of electric vehicles (EVs) using floating charge method meaning that the EV, could be supplied by each of the three phases connected to a special bus. In other words, unlike a usual household load which is only supplied by a particular phase, in the floating charge method it is assumed that each of the phases can supply the EV. Because of the importance of the loss reduction in the smart distribution networks, the active power loss is considered as the objective function of the proposed model. To evaluate the presented model, it is compared with two charging methods, namely uncoordinated and coordinated methods, using modified IEEE 31 bus distribution test system. The obtained results show that the proposed model, on one hand, decreases the total loss of the network and on the other hand, satisfies the voltage drop constraint in all of the considered cases adequately. Also, using the floating charge method, the system operator is able to improve the voltage magnitude of the neutral conductor.

IntroductionFloods, droughts, water scarcity, water contaminants, and optimal use of water resources including reservoirs and aquifers are some of the many water problems present today. These will be even more noticeable in the future. The optimal operation of reservoirs is one of the best ways in water resources management to deal with such problems and other unwanted temporal and spatial distributions of water. Optimization techniques have become increasingly important in the management and operation of complex reservoir systems over the past three decades. Some researches have provided an extensive literature review and evaluation of various optimization methods and their corresponding models. Each optimization method has its advantages and disadvantages that make them suitable for some problems. Selection of each method depends on the characteristics of the system being considered, data availability, optimization objectives, and the problem constraints.

The growing need of energy sources, especially in industrial countries and the shortage of the fossil resources cause a great concern in many countries. By considering the fact that the energy price is increased during the day, using the demand side management is getting more important. The major change in demand side management is the consideration of consumers'' responses to energy price variations. This paper investigates the effect of the demand response implementation on cost reduction in unit commitment considering wind power. Considering that the simultaneous implementation of unit commitment and the use of response programs would be a complex and nonlinear problem that contain continuous and discrete variable, the mixed integer programming is used. The proposed method is simulated in practical system and IEEE RTS 24-bus system and the results are analyzed.