Chance-constrained Goal Programming Research Articles

A shared energy storage business model for data center clusters considering renewable energy uncertainties

The energy consumption of data centers (DCs) is on a sharp upward trend in recent years. DCs are playing an increasingly important role in demand response (DR) programs. However, the reassignment of computing tasks among DCs leads to different energy demands of different DCs. Given that the investment cost of energy storage is high, this work proposes a shared energy storage business model for the DC cluster (DCC) to improve economic benefits and promote renewable energy accommodation. Besides, an internal energy balance mechanism is set up to make full use of the complementary energy consumption characteristics of different DCs. Considering the renewable energy uncertainty, an optimization model is proposed based on the chance-constrained goal programming (CCGP). Finally, simulation results prove that the proposed energy storage business model has a positive effect on improving the economic benefits of the DCC. It also proves that for a DCC adopting the proposed internal energy balance mechanism, its total renting power can be effectively reduced and renewable energy consumption can be greatly promoted.

Optimal Location of Electronic Charity Boxes Using a Hybrid Mathematical Model of Chance Constrained Goal Programming and EDAS Method

Optimal Location of Electronic Charity Boxes Using a Hybrid Mathematical Model of Chance Constrained Goal Programming and EDAS Method

Multi-Objective Pharmaceutical Portfolio Optimization under Uncertainty of Cost and Return

This paper presents the study of multi-objective optimization of a pharmaceutical portfolio when both cost and return values are uncertain. Decision makers in the pharmaceutical industry encounter several challenges in deciding the optimal selection of drug projects for their portfolio since they have to consider several key aspects such as a long product-development process split into multiple phases, high cost and low probability of success. Additionally, the optimization often involves more than a single objective (goal) with a non-deterministic nature. The aim of the study is to develop a stochastic multi-objective approach in the frame of chance-constrained goal programming. The application of the results of this study allows pharmaceutical decision makers to handle two goals simultaneously, where one objective is to achieve a target return and another is to keep the cost within a finite annual budget. Finally, the numerical results for portfolio optimization are presented and discussed.

Optimization of truck-shovel allocation in open-pit mines under uncertainty: a chance-constrained goal programming approach

ABSTRACT The truck allocation problem is an important section of the transportation system in open-pit mines. Most available models for the truck scheduling problem do not directly address the stochastic nature of truck-shovel systems by using multi-objective optimization techniques. This paper presents a chance-constrained goal programming (CCGP) model based on four important goals to estimate the impacts of the uncertainty on the efficiency of truck-shovel systems. The proposed model has been implemented using 11 schedule scenarios and different confidence levels (CLs) for loader’s production to determine the best allocation of trucks in an open-pit copper mine. The results display that the model can handle the quality and quantity of material required to achieve the objectives of the short-term production schedule of the mine in all CLs, even in the highest risk level. This model has a remarkable ability to meet the required objectives in terms of uncertainty in mining operations.

Uncertain four-dimensional multi-objective multi-item transportation models via GP technique

In this paper, a new type of four-dimensional multi-objective multi-item transportation problem is established using uncertain theory. We formulate and derive the expected value goal programming model and chance-constrained goal programming model based on the uncertain theory, where unit transportation cost, availabilities, capacities of conveyances, demands, unit transportation time, unit loading and unloading time are represented as uncertain matrices. Based on some properties of uncertain theory, the expected value goal programming model and chance-constrained goal programming model are transformed into the corresponding deterministic equivalents form via the soft computing technique, i.e., generalized reduced gradient technique named by LINGO-14.0. After that, a real-life numerical example is given to illustrate the performance of the models. Finally, the sensitivity analysis of the proposed model is presented through chance-constrained goal programming method with respect to different confidence levels.

Yan Xu ; Tianyang Zhao ; Shuqiang Zhao ; Jianhua Zhang ; Yang Wang

As battery technology matures, the battery energy storage system (BESS) becomes a promising candidate for addressing renewable energy uncertainties. BESS degradation is one of key factors in BESS operations, which is usually considered in the planning stage. However, BESS degradations are directly affected by the depth of discharge (DoD), which is closely related to the BESS daily schedule. Specifically, the BESS life losses may be different when providing the same amount of energy under a distinct DoD. Therefore, it is necessary to develop a model to consider the effect of daily discharge on BESS degradation. In this paper, a model quantifying the nonlinear impact of DoD on BESS life loss is proposed. By adopting the chance-constrained goal programming, the degradation in day-ahead unit commitment is formulated as a multi-objective optimization problem. To facilitate an efficient solution, the model is converted into a mixed integer linear programming problem. The effectiveness of the proposed method is verified in a modified IEEE 39-bus system.

Fuzzy Stochastic Unit Commitment Model with Wind Power and Demand Response under Conditional Value-At-Risk Assessment

With the increasing penetration of wind power and demand response integrated into the grid, the combined uncertainties from wind power and demand response have been a challenging concern for system operators. It is necessary to develop an approach to accommodate the combined uncertainties in the source side and load side. In this paper, the fuzzy stochastic conditional value-at-risk criterions are proposed as the risk measure of the combination of both wind power uncertainty and demand response uncertainty. To improve the computational tractability without sacrificing the accuracy, the fuzzy stochastic chance-constrained goal programming is proposed to transfer the fuzzy stochastic conditional value-at-risk to a deterministic equivalent. The operational risk of forecast error under fuzzy stochastic conditional value-at-risk assessment is represented by the shortage of reserve resource, which can be further divided into the load-shedding risk and the wind curtailment risk. To identify different priority levels for the different objective functions, the three-stage day-ahead unit commitment model is proposed through preemptive goal programming, in which the reliability requirement has the priority over the economic operation. Finally, a case simulation is performed on the IEEE 39-bus system to verify the effectiveness and efficiency of the proposed model.

Risk Adjustable Day-Ahead Unit Commitment With Wind Power Based on Chance Constrained Goal Programming

The impact of wind power forecast uncertainty has been amplified by the deepening wind power penetration. To guarantee system security and reliability, sufficient dispatchable generation and transmission capacities have to be reserved. Currently, research has been carried out to improve system operational performance by optimizing schedules considering uncertainty. However, most methods are designed to cover a given risk level of uncertainty, which is determined ex ante . With the increase in wind power capacity, defining the risk level a priori without considering the unit commitment (UC) may limit the scheduling efficiency. Essentially, there is no absolute standard for acceptable risk exposure. Instead, there is a tradeoff between the risk and the cost of reserve capacity. Therefore, it is necessary to develop a tool to enable a flexible and comprehensive consideration of the risk level. In this paper, by combining chance constrained programming and goal programming, a novel model based on chance constrained goal programming is proposed to optimize the risk adjustable UC problem. To facilitate an efficient solution, the proposed model is transferred into a tractable mixed integer linear programming problem by a deterministic equivalent and piecewise linearization. Case studies are performed on an IEEE 118-bus system to illustrate the effectiveness and efficiency of the model.

Selection of PPP Projects in China Based on Government Guarantees and Fiscal Risk Control

Public-Private Partnership (PPP) is an effective investment channel for government to provide public services. PPPs have the advantage of transferring some project risk to the private sector. They also imply that the public sector should establish appropriate laws and regulations to enable government departments to effectively avoid the emergence of new fiscal risks, which may affect the sustainability of fiscal budgets. This paper expounds the fiscal risks implied by PPP projects in China and the status of government guarantees in various forms of PPP projects; chance-constrained goal-programming (CCGP) is used to simulate government project selection under budget and risk control constraints. The analysis takes fiscal space, the expected costs and benefits of government guarantees, and the possibility of excess government subsidies into consideration. Constrained by fiscal risk minimization and budget limitations, PPP projects with government guarantees can maximize social-economic net present value and simultaneously optimize welfare. The paper also puts forward corresponding policy recommendations based on the research findings.

Uncertain goal programming models for bicriteria solid transportation problem

This paper investigates an uncertain bicriteria solid transportation problem. The supplies, demands, conveyance capacities, transportation cost and transportation time are regarded as uncertain variables. According to two types of methods to rank the uncertain variables, expected value goal programming model and chance-constrained goal programming model for the bicriteria solid transportation problem are constructed. It is proved that the expected value goal programming model and chance-constrained goal programming model can be respectively transformed into the corresponding deterministic equivalents by taking advantage of some properties of uncertainty theory. Based on these equivalence relations, the optimal transportation plans of the uncertain goal programming models can be obtained. Several numerical experiments are presented to illustrate the applications of the models.

3Es System Optimization under Uncertainty Using Hybrid Intelligent Algorithm: A Fuzzy Chance-Constrained Programming Model

Harmonious development of 3Es (economy-energy-environment) system is the key to realize regional sustainable development. The structure and components of 3Es system are analyzed. Based on the analysis of causality diagram, GDP and industrial structure are selected as the target parameters of economy subsystem, energy consumption intensity is selected as the target parameter of energy subsystem, and the emissions of COD, ammonia nitrogen, SO2, andNOXand CO2emission intensity are selected as the target parameters of environment system. Fixed assets investment of three industries, total energy consumption, and investment in environmental pollution control are selected as the decision variables. By regarding the parameters of 3Es system optimization as fuzzy numbers, a fuzzy chance-constrained goal programming (FCCGP) model is constructed, and a hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is proposed for solving it. The results of empirical analysis on Shandong province of China show that the FCCGP model can reflect the inherent relationship and evolution law of 3Es system and provide the effective decision-making support for 3Es system optimization.

Fuzzy chance-constrained goal programming model for multi-attribute financial portfolio selection

The aim of this paper is to propose a fuzzy chance constrained goal programming model for solving a multi-attribute financial portfolio selection problem under two types of uncertainty namely randomness and fuzziness. The chance-constrained goals are considered as random variables. The obtained portfolio through this model is the portfolio of the best compromise where the financial decision-maker was asked to make tradeoffs among conflicting and incommensurable attributes such as the expected return, risk and the earning price ratio. The proposed model has been applied to the Tunisian stock exchange market for the period July 2003 to December 2007.

A multiple objective stochastic approach to vehicle routing problem

This research incorporates the concept of chance-constrained programming and multiple objective goal programming in the area of vehicle routing problem. The research led to the development of the model of the goal programming (GP) stochastic vehicle routing problem (SVRP) that allows decision-makers’ involvement in the solution process of problem for obtaining satisfactory solutions. Due to the complexity of the SVRP, a set of stations to be visited by a fleet of vehicles needs to be partitioned into feasible sets of routes, one for each vehicle enabling the application of the multiple objectives GP technique to each of the vehicle routes. The multiple objectives SVRP then consisted of the following two major stages: (1) route construction stage (RCS) and (2) route improvement stage (RIS). The RCS of the problem consists of the problem formulation and partitioning a set of stations into feasible sets of vehicle routes. Due to the complexity of the problem, only heuristic methods for solving SVRP are considered in this stage. On the other hand, the RIS of the problem consists of (1) problem formulation in which goals and probabilistic constraints are identified, (2) transformation of problem in (1) into an equivalent deterministic form, and (3) GP formulation of RIS in which priorities of various goals are identified. To solve the problems stated in the RCS and RIS of the problem, two interactive computer programs coded in Fortran computer language are developed. To test and validate the algorithm proposed in this research, two test problems, usually employed by other researchers, were took into consideration. A modification of the Clarke and Write algorithm is developed to determine the most favorable vehicle routes of the SVRP for the “E”-type problem. Additionally, two heuristic algorithms which are the modification of the Clarke and Wright “savings” approach are developed for solving the “F”-type problem. The E- and F-type problems are the name given to the equivalent deterministic form of the probabilistic cost minimization problem and total loading and unloading time minimization problem, respectively.

Goal Programming Approach for Selection of COTS Components in Designing a Fault Tolerant Modular Software System under Consensus Recovery Block Scheme

The application of computer systems has now crossed many different fields. Systems are becoming more software intensive. The requirements of the customer for a more reliable software led to the fact that software reliability is now an important research area. One method to improve software reliability is by the application of redundancy. A careful use of redundancy may allow the system to tolerate faults generated during software design and coding thus improving software reliability. The fault tolerant software systems are usually developed by integrating COTS (commercial off-the-shelf) software components. This paper is designed to select optimal components for a fault tolerant modular software system so as to maximize the overall reliability of the system with simultaneously minimizing the overall cost. A chance constrained goal programming model has been designed after considering the parameters corresponding to reliability and cost of the components as random variable. The random variable in this case has been considered as value which has known mean and standard deviation. A chance constraint goal programming technique is used to solve the model. The issue of compatibility among different commercial off-the shelf alternatives is also considered in the paper. Numerical illustrations are provided to demonstrate the model.

A chance constraints goal programming model for the advertising planning problem

This paper presents a model which has been designed to decide the number of advertisement in different advertising media and the optimal allocation of the budget assigned to the different media. The main objective of this problem is to maximize the reach to the desired section of people for different media within their maximum allowable budget without violating the max and min number of advertisement goals. The media have been considered as different newspapers and different channels in Televisions. Here in this article the model has been formulated in such a way that the advertisement should reach to those who are suitable for the product instead of going to those section who are not considered suitable for the product as well. A chance constrained goal programming model has been designed after considering the parameter corresponding to reach for different media as random variables. The random variables in this case has been considered as values which have known mean and standard deviations. A case for an upcoming institution who are interested to advertise for its two years Post Graduate Diploma in Management (PGDM) programme to the different newspapers and television channels has been designed to illustrate the solution methodology.

A bicriteria solid transportation problem with fixed charge under stochastic environment

In this paper, a bicriteria solid transportation problem with stochastic parameters is investigated. Three mathematical models are constructed for the problem, including expected value goal programming model, chance-constrained goal programming model and dependent-chance goal programming model. A hybrid algorithm is also designed based on the random simulation algorithm and tabu search algorithm to solve the models. At last, some numerical experiments are presented to show the performance of models and algorithm.

A two-objective fuzzy [formula omitted]-cardinality assignment problem

This paper investigates a two-objective k -cardinality assignment problem. As a result, a chance-constrained goal programming model is constructed for the problem. Also, tabu search algorithm based on fuzzy simulation is designed to solve the problem. Finally, a numerical example is presented to show the application of the algorithm.

Fuzzy programming with fuzzy decisions and fuzzy simulation-based genetic algorithm

This paper provides a spectrum of chance-constrained programming as well as chance-constrained multiobjective programming and chance-constrained goal programming with fuzzy rather than crisp decisions, which will seek a fuzzy set from the given reference collection as an optimal solution. The technique of fuzzy simulation is also presented to check fuzzy chance constraints and to handle fuzzy objective and goal constraints. Finally, a fuzzy simulation-based genetic algorithm for solving these models will be designed and illustrated by some numerical examples.

Chance constrained fuzzy goal programming with right-hand side uniform random variable coefficients

We present a basic idea about stochastic goal programming and the approach of chance constrained linear goal programming (CCLGP). We developed the method to transform probabilistic goal programming into deterministic goal programming and consider the stochastic fuzzy goal programming problem when the right-hand side coefficients are random variables distributed according to uniform distribution. A chance constrained goal programming in the case of having uncertain aspiration levels is considered. However, these aspiration levels are random variables with known probability distribution functions. The equivalent deterministic goal program is developed and an illustrative example is given.

Minimax chance constrained programming models for fuzzy decision systems

The existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models (optimistic models) which maximize the maximum possible return. This paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi-objective programming and chance constrained goal programming, in which the minimax models will select the alternative that provides the best of the worst possible return. Finally, a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples.