Multi-objective Stochastic Model Research Articles

A Multi-Objective Stochastic Model for a Green Supply Chain planning

In this study we develop a stochastic multi-objective stochastic programming approach to deal with a supply chain planning under uncertainty. Supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost in addition to some respects as employment, dismissal, workers productivity and training are all considered. Due to the important role of the lead time especially in supplying, the lead time between suppliers and factories and between factories and customer zones is assumed to be a function of transportation mode. Cost parameters and demand fluctuations are subject to uncertainty. To develop the model, two additional objective functions are added to the classical aggregate production planning. Therefore, the proposed multi-objective model includes the minimization of the expected total cost of supply chain, the minimization of the variability of the total cost of supply chain and the minimization of the expected value of the greenhouse gas emission level. Then, the proposed model is solved applying compromise programming method. Finally, a numerical example is solved to describe the proposed model.

A multiobjective stochastic program for hospital bed planning

In this paper, we study hospital bed capacity management for a set of existing hospitals when the demand for beds is random. We propose a multiobjective stochastic program model to assign beds to hospital departments. We consider three objective functions to be minimized, which are the cost of creation and management of new beds and the number of nurses and physicians working in these hospitals, subject to demand satisfaction of three kinds of health-care specialities. A certainty equivalent program was derived based on a mixture between the chance constrained approach, the recourse approach and the goal programming approach. Empirical results using real data from 157 Tunisian national hospitals are reported.

A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level

Logistic network design has an important and strategic platform in an efficient and effective supply chain management, and usually involves multiple and conflicting goals, such as cost/profit, resource balance, customer responsiveness, quality, and the like. Besides, due to the implementation of government legislation, environmental concern, social responsibility and customer awareness, companies have been forced by customers not only to supply environmentally amicable products but also to be responsible for the returned products. Hence, this paper presents a stochastic multi-objective model for forward/reverse logistic network design under a uncertain environment including three echelons in forward direction (i.e., suppliers, plants, and distribution centers) and two echelons in backward direction (i.e., collection centers and disposal centers). We demonstrate a method to evaluate the systematic supply chain configuration maximizing the profit, customer responsiveness, and quality as objectives of the logistic network. The set of Pareto optimal solutions is obtained and also financial risk relevant to them is computed in order to show the tradeoff between objectives. The results give important insight for fostering the decision making process.

A scenario-based multiobjective operation of electricity markets enhancing transient stability

Electricity market clearing is currently done using deterministic values of power system parameters considering a fixed network configuration. This paper presents a new day-ahead joint market clearing framework (including energy, spinning reserve and non-spinning reserve auctions), which considers dynamic security of power system in the market clearing. The proposed framework has a stochastic multiobjective model considering power system uncertainties. It consists of three stages. Firstly, the uncertainty sources, i.e. contingencies of generating units and branches, are modeled using the Monte Carlo simulation (MCS) method. Subsequently, in the second stage, the proposed multiobjective framework simultaneously optimizes competing objective functions of offer cost and dynamic security index, i.e. corrected transient energy margin (CTEM). This index is selected because of useful linearity properties which it posses based on the sensitivity of the CTEM with respect to power shift between generators. The optimization problem in the second stage takes DC power flow constraints and system reserve requirements into account. Finally, in the last stage, scenario aggregation based on the expected value of the decision variables produces the final results of the market clearing framework. The 10-machine New England test system is studied to demonstrate effectiveness of the proposed stochastic multiobjective market clearing scheme.

An efficient algorithm to solve a multi-objective robust aggregate production planning in an uncertain environment

Risk is inherent in most economic activities. This is especially true of production activities where results of decisions made today may have many possible different outcomes depending on future events. Since companies cannot usually protect themselves completely against risk, they have to manage it. In this paper, we present a multi-objective model to deal with a multi-period multi-product multi-site aggregate production planning problem for a medium-term planning horizon under uncertainty. The first objective function attempts to minimize sum of the expected value and the variability of total costs with reference to inventory levels, regular, overtime and subcontracting levels, backordering levels, and labor, machine and warehouse capacities. The second objective function highlighted the concept of customer service level through minimizing the expected value of maximum shortages among all customers’ zones from which the variability of that is conducted. The last objective function aims to maximize workers productivity, a weighted average of productivity levels in all factories and in all periods which is weighted by the number of k-level labors. Then, we use an efficient algorithm that is a combination of an augmented e-constraint method and genetic algorithm to solve our proposed model. The results demonstrate the practicability of the proposed multi-objective stochastic model as well as the proposed algorithm.

Stochastic PSO-based heat and power dispatch under environmental constraints incorporating CHP and wind power units

In this paper an extended stochastic multi-objective model for economic dispatch (ED) is proposed, that incorporates in the optimization process heat and power from CHP units and expected wind power. Stochastic restrictions for the CO 2, SO 2 and NO x emissions are used as inequality constraints. The ED problem is solved using a multi-objective particle swarm optimization technique. The available wind power is estimated from a transformation of the wind speed considered as a random variable to wind power. Simulations are performed on the modified IEEE 30 bus network with 2 cogeneration units and actual wind data. Results concerning minimum cost and emissions reduction options are finally drawn.

Solution of single and multi-objective fixed reorder quantity system by general fuzzy programming technique

This paper considers a multi item single period inventory problem with floor space constraint where the demand of the items follows probability distributions. Two different stochastic models are discussed where the demand follows Uniform distribution and Exponential distribution respectively. Firstly the fixed reorder quantity system with backorder and secondly fixed reorder quantity system with lost sales are discussed. Then consideration is adopted as a multi objective stochastic inventory model where average annual cost of the first item as well as the same of the second item are minimized simultaneously and is also formulated in fuzzy environment introducing fuzziness in the objectives. In this paper the concept of General Fuzzy Non-linear Programming Technique is applied to solve a multi objective single period stochastic inventory problem with floor space constraint. The solution is illustrated by numerical example and the results of different models are compared.

Solution of Single and Multiobjective Stochastic Inventory Models with Fuzzy Cost Components by Intuitionistic Fuzzy Optimization Technique

Paknejad et al.'s model is considered in this paper. Itemwise multiobjective models for both exponential and uniform lead-time demand are taken and the results are compared numerically both in fuzzy optimization and intuitionistic fuzzy optimization techniques. Objective of this paper is to establish that intuitionistic fuzzy optimizaion method is better than usual fuzzy optimization technique as expected annual cost of this inventory model is more minimized in case of intuitionistic fuzzy optimization method. As a single objective stochastic inventory model where the lead-time demand follows normal distribution and with varying defective rate, expected annual cost is also measured. Finally the model considers for fuzzy cost components, which make the model more realistic, and numerical values for uniform, exponential, and normal lead-time demand are compared. Necessary graphical presentations are also given besides numerical illustrations.

Stochastic multiobjective self-scheduling of a power producer in joint energy and reserves markets

This paper presents a stochastic multiobjective model for self-scheduling of a power producer which participates in the day-ahead joint energy and reserves markets. The objective of a power producer is to compromise the conflicting objectives of payoff maximization and gaseous emissions minimization when committing its generation of thermal units. The proposed schedule will be used by the power producers to decide on emission quota arbitrage opportunities and for strategic bidding to the energy and reserves market. The paper analyzes a scenario-based multiobjective model in which random distributions, such as price forecasting inaccuracies as well as forced outage of generating units are modeled as scenarios tree using a combined fuzzy c-mean/Monte-Carlo simulation (FCM/MCS) method. With the above procedure the stochastic multiobjective self-scheduling problem is converted into corresponding deterministic problems. Then a multiobjective mathematical programming (MMP) approach based on ɛ-constraint method is implemented for each deterministic scenario. Piecewise linearized fuel and emission cost functions are applied for computational efficiency and the model is formulated as a mixed-integer programming (MIP) problem. Numerical simulations for a power producer with 21 thermal units are discussed to demonstrate the performance of the proposed approach in increasing expected payoffs by adjusting the emission quota arbitrage opportunities.

Multi-objective stochastic supply chain modeling to evaluate tradeoffs between profit and quality

Many companies struggle with justifying the cost of quality within their supply chain. Outsourcing suppliers to countries such as China has become popular in recent years due to the fact it appears to be more profitable. These outsource decisions do not effectively determine the impacts of quality defects. In this paper we demonstrate a method for evaluating the systemic supply chain risk of poor quality. We introduce a multi-objective stochastic model that uses Six Sigma measures to evaluate financial risk. Results from modeling suggest quality, profit, and customer satisfaction can be evaluated.

Multiobjective stochastic programming for feed formulation

The minimum cost linear programming model used traditionally for feed formulation does not take account of variability of nutrients in feed ingredients. Therefore, it may be that the nutrient requirements of the animal are not adequately met. In this paper, we show how a multiobjective stochastic model that permits confronting the cost of the ration with the probabilities of meeting the nutrient requirements of the animal can enhance the process of animal diet formulation. The model presented here does not require any a priori information from the decision maker, eliciting his preferences through an interactive process. This is the main advantage in relation to other models found in the literature for treating the problem of nutrient variability, which introduce stochastic constraints in the single objective minimum cost model requiring fixing the level of probability desired for each one of the nutrients in advance.

Controlling wasteloads from point and nonpoint sources to river system by GIS-aided Epsilon Robust Optimization model

A stochastic multiobjective programming model, an ɛ-RO (Epsilon Robust Optimization) model as a simulation–optimization model with an embedding approach, is developed for river water quality management under hydro-environmental uncertainty. The model is a hybrid of the ɛ-constraint method and the robust optimization framework, which depresses the high sensitivity of the model to the input data uncertainties by introducing a plausible set of scenarios. Possible pollutant sources (all kinds of point and nonpoint pollutant sources excepting forests) are treated as controllable. The finite element method is employed for approximations to COD (Chemical Oxygen Demand) and DO (Dissolved Oxygen) transport equations with convection and dispersion terms. Realizations for the in-stream COD–DO interactive events, thus described in discrete forms, are embedded as equality constraints in the model. Controlling wasteloads from a variety of sources is implemented by seeking noninferior solutions (management alternatives) that maximize total COD load to the stream while minimizing COD load deviations and in-stream water quality violations. Demonstrative operation of the model is made with its application to the Yasu River, Japan. It is shown that there is indeed an alternative management strategy to improve in-stream water quality as a whole while increasing the total allowable load to the stream. The ɛ-RO model developed could thus be a viable alternative to the conventional river water quality management models.

Application of wavelet transform in travelling wave protection

This paper deals with frequency control following the occurrence of a contingency. The frequency is considered by modelling the generators’ governor performance during pre- and post-contingency intervals, load frequency dependency, rate of change of frequency (Rocof) of generators and Rocof of the system and frequency-based reserve scheduling. The time intervals following the occurrence of a contingency are formulated in detail to analyze the influential factors in static frequency. A novel index besides the frequency dependent social welfare function and frequency excursion index has been proposed to control the frequency and the Rocof during post-contingency intervals. The proposed stochastic multi-objective model incorporates the precise scheduling of reference power setting of generators based on participants’ bids for energy and reserve services. The eventual goal of the proposed approach is to help the ISOs to make a trade-off concurrently between system frequency profile, Rocof and total operating cost to operate the power system securely in an economically efficient manner. This multi-objective programming formulation is simulated through two case studies; a three-bus system scheduled over 1 h and the IEEE Reliability Test System over 24 h, solved by means of lexicographic optimization and ε-constraint method.

不確実性下における個別経営目標および地域目標の同時追求計画

不確実性下における個別経営目標および地域目標の同時追求計画