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Optimal production-distribution planning prevents capital accumulation, reduces costs, unemployment of machinery, and provides a good plan to satisfying customer needs. In this paper, a mixed-integer linear programming (MILP) model is developed to determine optimal production-distribution planning in electromotor manufacturing industries. The proposed model is a multi-product and multi-period one in which optimal amounts of production, inventory and distribution are determined in different periods. Also, the possibility of capacity expansion of facilities in different periods are modelled to optimally determine the capacity increase if necessary. To validate the proposed model, it is applied... 

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  

This paper presents a hierarchical demand response (DR) bidding framework in the day-ahead energy markets which integrates customer DR preferences and characteristics in the ISO's market clearing process. In the proposed framework, load aggregators submit aggregated DR offers to the ISO which would centrally optimize final decisions on aggregators' DR contributions in wholesale markets. The hourly load reduction strategies include load shifting and curtailment and the use of onsite generation and energy storage systems. The ISO applies mixed-integer linear programming (MILP) to the solution of the proposed DR model in the day-ahead market clearing problem. The proposed model is implemented... 

In this paper, a new market mechanism is proposed to quantify the value of emergency energy transactions in renewable-based multi-microgrid (MMG) systems. To reach this goal, main requirements and features of such emergency market are identified. Subsequently, a hybrid market framework is proposed which integrates pool emergency transactions and bilateral contracts in order to reduce the system risk in face of different contingency events. For settling different transactions in this market, the main procedure which should be followed by distribution system operator (DSO) to properly address bidding of microgrids (MGs) as well as system technical constraints are introduced. In addition, a... 

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash... 

A main component of a transportation network is travel time or distance. Due to stochastic events such as accidents and failures in roads, a deterministic estimation of the travel time between two cities or regions is impossible. Also, on special occasions like holidays, with increase in the traveling population in the transportation network, probabilities of occurrence of these events increase. The increase in traveling population has a direct effect on the estimation of travel times and subsequently on the decision-making process. Therefore, provision of an appropriate model for the intelligent probabilistic travel times to distribute the population in a transportation network is a... 

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash... 

In this paper, we consider the multi-product multi-constraint newsboy problem with random fuzzy demands and total discount. The demand of the products is often stochastic in the real word but the estimation of the parameters of distribution function may be done by fuzzy manner. So an appropriate option to modeling the demand of products is using the random fuzzy variable. The objective function of proposed model is to maximize the expected profit of newsboy. We consider the constraints such as warehouse space and restriction on quantity order for products, and restriction on budget. We also consider the batch size for products order. Finally we introduce a random fuzzy multi-product... 

In this paper, the impact of demand response programs (DRPs) on reliability improvement of the restructured power systems is quantified. In this regard, the demand response (DR) model which treats consistently the main characteristics of the demand curve is developed for modeling. In proposed model, some penalties for customers in case of no responding to load reduction and incentives for customers who respond to reducing their loads are considered. In order to make analytical evaluation of the reliability, a mixed integer DCOPF is proposed by which load curtailments and generation re-dispatches for each contingency state are determined. Both transmission and generation failures are... 

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... 

This paper aims at proposing a mixed-integer linear formulation to incorporate reliability-oriented costs into the expansion planning model of electricity distribution networks. In this respect, revenue lost associated with the undelivered energy caused by network interruptions as well as costs incurred by the widely used reward-penalty regulations is considered as the major reliability-related costs from distribution companies point of view. A set of mixed-integer linear equations is proposed to calculate the most common distribution system reliability indices, i.e., expected energy not served, system average interruption frequency index, and system average interruption duration index. It... 

Large customers are considered as major flexible electricity demands which can reduce their electricity costs by choosing appropriate strategies to participate in demand response programs. However, practical methods to aid the large customers for handling the complex decision making process for participating in the programs have remained scarce. This paper proposes a novel decision-making tool for enabling large customers to determine how they adjust their electricity usage from normal consumption patterns in expectation of gaining profit in response to changes in prices and incentive payments offered by the system operators. The proposed model, formulated as a mixed-integer linear... 

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...