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Bi-objective optimization of a multi-product multi-period three-echelon supply chain network consisting of manufacturing plants, distribution centers (DCs) each with uncertain services, and customer nodes is aimed in this paper. The two objectives are minimization of the total cost while maximizing the average number of products dispatched to customers. The decision variables are: (1) the number and the locations of reliable DCs in the network, (2) the optimum number of items produced by plants, (3) the optimum quantity of transported products, (4) the optimum inventory of products at DCs and plants, and (5) the optimum shortage quantity of the customer nodes. The problem is first formulated... 

Efficient utilization of renewable generation inside microgrids remains challenging. In most existing studies, the goal is to optimize the energy cost of microgrids by working in synergy with the main grid. This work aimed at maximizing the self-consumption of on-site photovoltaic (PV) generation using an electrical storage, as well as demand response solutions, in a building that was also capable of interacting with the main grid. Ten-minute resolution data were used to capture the temporal behavior of the weather. Extensive mathematical models were employed to estimate the demand for hot-water consumption, space cooling, and heating loads. The proposed framework is cast as mixed-integer... 

Reliability cost is considered as an inevitable criterion in expansion planning studies of distribution systems. However, nonlinear expressions of reliability indices aggravate complexity of planning studies. To address this issue, this letter proposes a novel method to linearize mathematical model of the reliability-based distribution expansion planning problem. Using this variant of reliability indices, reliability costs can easily be involved in mixed-integer linear programming model of distribution expansion planning. Validity of the derived expressions is tested by simulation results. © 1969-2012 IEEE  

In this paper, a novel data envelopment analysis (DEA) model is proposed for ranking the association rules. In this regard, a mixed-integer linear programming (MILP) model is proposed to determine the most efficient association rules where, an N-person bargaining game is used to create an interactive competition between the existing N-weights to get a better ranking. In addition, the proposed model is fuzzified by setting the ambiguous threshold of the indicators’ weight in each rule to improve the overall ranking of the rules. Finally, the risk, resilience and decongestion factors are also considered to increase the responsiveness of the models to different real-world conditions. The... 

Over the past decades, there has been a dramatic increase in the frequency of natural disasters, which are the leading causes of large-scale power outages. This paper, therefore, assesses the significance and role of optimal tie-line construction in improving the service restoration performance of unbalanced power distribution systems in the aftermath of high-impact low-probability incidents. In doing so, a restoration process aware stochastic mixed-integer linear programming model is developed to find the optimal locations for new tie-line construction in unbalanced three-phase distribution systems. In particular, the restoration process of distribution systems, including the fault... 

The purpose of this paper is to present a mixed-integer linear programming model for the scheduling problem in an open-shop manufacturing system involving reverse flows, where two job flows (direct and reverse) in two opposite directions are processed on the same machines. The aim is to minimize the maximum completion time of all jobs on all machines (i.e., the makespan). A numerical example is presented and solved using the GAMS software (version 25.1.2) to validate the proposed mathematical model. As this problem is NP-hard, a vibration damping-based optimization (VDO) algorithm is proposed to solve large-scale problems in reasonable execution times. Besides, the Taguchi experimental... 

The purpose of this paper is to present a mixed-integer linear programming model for the scheduling problem in an open-shop manufacturing system involving reverse flows, where two job flows (direct and reverse) in two opposite directions are processed on the same machines. The aim is to minimize the maximum completion time of all jobs on all machines (i.e., the makespan). A numerical example is presented and solved using the GAMS software (version 25.1.2) to validate the proposed mathematical model. As this problem is NP-hard, a vibration damping-based optimization (VDO) algorithm is proposed to solve large-scale problems in reasonable execution times. Besides, the Taguchi experimental... 

Standard mathematical-programming-based models have attracted considerable attention for optimizing distribution system planning and operation due to their salient advantages. More specifically, mixed-integer linear programming (MILP) has proven very effective in modeling such problems. The availability of optimization software for efficiently solving MILP problems with guaranteed convergence to optimality while providing a measure of the distance to the optimal solution has made MILP models more popular. Although a plethora of efficient MILP formulations have been proposed for planning and operating studies of distribution grids, incorporating reliability into such models is still... 

Over the past decades, there has been a dramatic increase in the frequency of natural disasters, which are the leading causes of large-scale power outages. This paper, therefore, assesses the significance and role of optimal tie-line construction in improving the service restoration performance of unbalanced power distribution systems in the aftermath of high-impact low-probability incidents. In doing so, a restoration process aware stochastic mixed-integer linear programming model is developed to find the optimal locations for new tie-line construction in unbalanced three-phase distribution systems. In particular, the restoration process of distribution systems, including the fault... 

Bi-objective optimization of a multi-product multi-period three-echelon supply-chain-network problem is aimed in this paper. The network consists of manufacturing plants, distribution centers (DCs), and customer nodes. To bring the problem closer to reality, the majority of the parameters in this network including fixed and variable costs, customer demand, available production time, set-up and production times, all are considered stochastic. The goal is to determine the quantities of the products produced by the manufacturing plants in different periods, the number and locations of the warehouses, the quantities of products transported between the supply chain entities, the inventory of... 

This paper deals with energy management of microgrids during unscheduled islanding events, initiated by disturbances in the main grid. In these situations, the main challenge is uncertainty about duration of disconnection from the main grid. In order to tackle this issue, a stochastic framework is proposed for optimal scheduling of microgrid resources over this period. The presented framework addresses the prevailing uncertainties of islanding duration as well as prediction errors of demand and renewable power generation. According to this framework, the probability distribution of islanding duration needs to be estimated, instead of predicting its exact value. The objective is to minimize... 

Biomass residues due to their low bulk density typically require frequent transportation from biomass plantations in rural areas to conversion bio-energy power plants. This issue contrasts with environmental protection strategies, especially when power plants are facing different carbon reduction policies that enforce them to emit less than a given specific carbon amount. Although several researchers have investigated bio-energy supply chains concerning environmental policies, the majority of studies have been devoted to strategic decisions over a single planning period. This paper presents a multi-period bio-energy supply chain under carbon pricing (carbon tax) and carbon trading... 

Electric vehicles (EVs) usage is becoming ubiquitous nowadays. Widespread integration of electric vehicles into electric energy distribution systems (EEDSs) has a twofold impact: (1) It may impose a burden on EEDSs when EVs are charging, (2) EVs could discharge their battery capacity using V2G technology when required. To mitigate adverse effects of massive integration of EVs in EEDSs, EVs could be used as mobile energy storage devices (MESDs) to transfer electric energy throughout EEDSs using a proper charging/discharging scheme. In this paper, a mixed integer linear programming (MILP) model is proposed to control charging and discharging of EVs to improve EEDS performance. EVs are modeled... 

Sectionalizing switches are the main components of any restoration scheme in fault situations of power distribution systems. In this paper, customer outage costs reduction is aimed through the optimal simultaneous placement of manual and remote-controlled switches (RCSs). Network reconfigurations are constrained such that operational considerations like statutory ranges for voltage levels, lines' thermal capacities, and necessity of radial configuration be conserved. Total cost reduction is mathematically modeled in a mixed-integer linear programming (MILP) model that makes the global optimal solution accessible. The validity of the proposed model is evaluated on the IEEE 33-bus network. In... 

Supplying sustainable energy is of a critical prominence nowadays. A main outcome of the galloping development in energy generation technologies is the ability to integrate multi-carrier energy systems that facilitates meeting the fast growth of energy demand. Energy hub is one of the main infrastructures making the incorporation of multi-carrier systems smoother. In this paper, the optimal scheduling problem of an energy hub structure equipped with combined heat and power, boiler, power-to-gas storage, thermal energy storage and electrical energy storage in order to supply power, heat and gas demands is presented. Power to gas is regarded as a new technology that creates a connection... 

In this paper the reliability of distribution network is modeled in joint multistage expansion planning of distribution network assets and distributed generations (DGs). The imposed costs due to network reliability weakness are considerable in the distribution level. Therefore in the proposed model distribution network operator (DNO) considers the costs associated with load interruptions in the planning problem. In this regard, reliability evaluation of the network is modeled in the joint multistage distribution network expansion planning (MDNEP) problem in an integrated manner while the network topology is unknown until the planning problem is not solved. In the proposed joint MDNEP problem... 

Biomass is becoming an increasingly widespread source of energy. Yet land, as one of the most important resources in biomass production, is surprisingly understudied in the literature of biomass supply chain planning. This study proposes a novel framework that combines the literature of bioethanol supply chain design with agricultural land planning to simultaneously address optimal supply chain planning and sustainable land use in a bioethanol supply chain. A bi-objective mixed-integer linear programming (MILP) model is proposed to formulate the optimal design and planning of a bioethanol supply chain network considering competition of food and biomass feedstock over the available croplands.... 

The concept of flexibility is defined as the power systems’ ability to effectively respond to changes in power generation and demand profiles to maintain the supply–demand balance. However, the inherent flexibility margins required for successful operation have been recently challenged by the unprecedented arrival of uncertainties, driven by constantly changing demand, failure of conventional units, and the intermittent outputs of renewable energy sources (RES). Tackling these challenges, energy storage systems (ESS) as one important player of the new power grids can enhance the system flexibility. It, therefore, calls for an efficient planning procedure to ensure flexibility margins by... 

Outsourcing as a useful strategy in the industry can be integrated into scheduling problems. Moreover, batch outsourcing is a practical assumption owing to the logistics issues for transferring the parts between the manufacturer and the subcontractors. However, this assumption is rarely addressed in the scheduling literature. In this paper, a novel single machine scheduling problem with the option of batch outsourcing is studied. The objective is to minimize the sum of the total completion time of the jobs and the total outsourcing cost. To solve the problem, first, two mixed-integer linear programming (MILP) models, named MP1 and MP2, are developed, which respectively use a straightforward... 

The concept of flexibility is defined as the power systems’ ability to effectively respond to changes in power generation and demand profiles to maintain the supply–demand balance. However, the inherent flexibility margins required for successful operation have been recently challenged by the unprecedented arrival of uncertainties, driven by constantly changing demand, failure of conventional units, and the intermittent outputs of renewable energy sources (RES). Tackling these challenges, energy storage systems (ESS) as one important player of the new power grids can enhance the system flexibility. It, therefore, calls for an efficient planning procedure to ensure flexibility margins by...