Earticle

본 연구에서는 하천본류의 유량과 수질, 하수처리장 유입수량과 유입수질을 확률변수로 두고, 취수 문제와 수중보에 의한 재포기현상을 포함하는 추계학적 하천수질관리모형을 개발하였다. Streeter-Phelps식을 이용해서 각 구간 하천수질의 기대값과 분산을 계산하는 확률모형을 만들고, 최적화문제의 확률적 제약식은 chance constrained 방법을 이용해서 확정적 제약식으로 변환한다. 목적함수는 지역내 하수처리장의 년간처리비용으로 두었다. 건설비용함수와 유지관리비함수는 처리효율과 처리용량의 함수인 비선형의 단일식으로 유도되었다. 최적화문제는 비선형계획법으로 해를 구하였다. 본 모형을 한강하류부에 적용한 결과 서울시내 4개 하수처리장에서 2차처리를 하고, 지천유입수의 BOD부하량이 현재와 같을 때, 1996년 DO수질기준을 만족하는 신뢰도는 50% 정도였다. 그리고 탄천, 중량천, 안양천의 BOD부하량을 현재보다 50% 감소시켰을 때 1996년 DO수질기준을 만족하는 신뢰도는 60% 이상이었다. 따라서 한강하류부의 수질보전을 위해서는 유입지천의 수질개선과 2차처리 이상의 하수처리가 요구된다.

A stochastic programming model for river water quality management was developed. River water quality, river flow, quality and flowrate of the wastewater treatment plant inflow were treated as random variables in the model. Withdrawal for water supply and submerged weir reaeration were included in the model itself. A probabilistic model was formulated to compute the expectation and variance of water quality using Streeter-Phelps equation. Chance constraints of the optimization problem were converted to deterministic equivalents by chance constrained method. Objective function was total annual treatment cost of all wastewater treatment plants in the region. Construction cost function and O & M cost function were derived in the form of nonlinear equations that are functions of treatment efficiency and capacity of treatment plant. The optimization problem was solved by nonlinear programming. This model was applied to the lower Han River. The results show that the reliability to meet the DO standards of the year 1996 is about 50% when the treatment level of four wastewater treatment plants in Seoul is secondary treatment, and BOD load from the tributary inflows is the same as present time. And when BOD load from Tanchon, Jungrangchon, and Anyangchon is decreased to 50%, the reliability to meet the DO standards of the year 1996 is above 60%. This results indicated that for the sake of the water quality conservation of the lower Han River, water quality of the tributaries must be improved, and at least secondary level of treatment is required in the wastewater treatment plants.

서울시 공공자전거 시스템은 2015년 정식도입 이래 45,000대 규모로 계속 성장해왔다. 그러나 자산의 노후화에 따른 유지보수와 교체 비용이 지속적으로 증가해왔다. 2023년 약 4,500대를 폐기하였고, 약 30억원 규모의 자산 손실이 발생하였다. 그러므로 과학적이고 데이터 기반의 자산관리 정책 수립이 시급하다. 본 연구의 목적은 확률적 동적계획법(Stochastic Dynamic Programming, SDP)를 활용하여 장기비용을 절감하고, 목표서비스 수준을 만족하는 최적 운영 정책을 수립하는 것이다. 이를 위해서 5단계의 물리적 상태와 누적시간을 기초로 총 15개의 상태를 정의하고, 실제 정비이력을 분석하여, 상태 전이확률을 추정하였다. 그리고 운영비, 유지보수비, 교체비, 방치에 따른 기회비용을 포함한 비용구조를 추정하였다. 수립된 SDP모델은 가치반복법(Value Iteration)을 통해서 상태 기반 최적 정책을 도출하였고, 연도별 자산 도입이력을 반영한 초기 상태 분포를 바탕으로, 전체 자산군에 대해 에이전트 기반 시뮬레 이션으로 정책 성과를 검증하였다. 그 결과, SDP 최적 정책이 상태기반 교체 정책 대비 비용 절감 효과를 보였다. 또한 월별 비용의 변동계수도 비교한 여러 정책 중 가장 낮아 예측 가능한 예산운영이 가능함을 보였다. 그리고, 고장 자전거에 대해 교체보다 수리를 하는 것이 비용 효율적임을 입증하였다.

Since its official launch in 2015, Seoul's public bicycle system has grown continuously to a fleet of 45,000 bicycles. However, maintenance and replacement costs have steadily increased due to asset aging. In 2023, approximately 4,500 bicycles were disposed of, resulting in asset losses of about 3 billion KRW. Therefore, there is an urgent need to establish scientific and data-driven asset management policies. The purpose of this study is to develop an optimal operational policy that reduces long-term costs and satisfies target service levels using Stochastic Dynamic Programming (SDP). To this end, we defined 15 states based on five physical condition levels and cumulative operating time, and estimated state transition probabilities by analyzing actual maintenance records. We also estimated a cost structure that includes operating costs, maintenance costs, replacement costs, and opportunity costs associated with neglect. The SDP model derived state-based optimal policies through Value Iteration, and policy performance was validated using agent-based simulation for the entire asset fleet, based on initial state distributions reflecting annual asset acquisition history. The results showed that the SDP optimal policy achieved cost savings compared to condition-based replacement policies. Furthermore, the coefficient of variation for monthly costs was the lowest among all compared policies, demonstrating that predictable budget management is achievable. Additionally, it was proven that repairing malfunctioning bicycles is more cost-effective than replacing them.

The demand for potato in potato snack industry has been gradually increased, but the supply of potato has hardly met such growing demand because of a limited domestic capacity of potato farming. Usually, domestic sourcing is used between June and November, and foreign sourcing from the United States or Australia is used in other periods. A foreign order should be placed prior to 1 year in order to purchase at a low price. However, it is hard to forecast domestic demand and domestic production. Hence, under such uncertainties of domestic demand and production, finding the optimal pre-order quantity is a very important issue in potato snack industry and the productivity of the company is seriously affected by its decision. This research defines the dual sourcing problem in potato snack industry and applies a stochastic programming approach to obtain an optimal pre-order quantity. We analyze five real-world cases according to the amount of domestic demand and supply. We compare the solution of the stochastic programming approach with the expected value solution. In all cases, the stochastic programming solution achieves 2% ~ 4% cost saving than the expected value solution. Its saving corresponds to about one million dollars. Furthermore, in the sensitivity analysis, we examine the change of optimal pre-order quantity and total cost when the late-order quantity increases. The result shows that as the late-order quantity increases, the optimal pre-order quantity should be increased. The contribution of this research is two fold. First, this is the first research to define the dual sourcing problem in potato snack industry using management science. In this research, it is expected to be useful for making decisions on sourcing in agricultural industry. Second, we apply the stochastic programming approach to solve this and our approach can contribute about 3% of cost saving. Although agricultural producers generally have a low operating margin, reduction of costs for raw materials will help to improve total productivity.

An inexact two-stage stochastic programing model was applied to sustainable utilization of water resource under uncertainty in Dalian city. The developed model, integrated the two-stage stochastic programing and inexact optimization, could deal with uncertain problems expressed as probability distributions and discrete intervals. After formulating the model, a hypothetical case based on the comprehensive planning of sustainable utilization of water resource in Dalian city was employed for demonstrating its application in the three different planning year, which was 2015, 2020, 2030. The optimal allocation of water resource with maximized system benefit among different users had been obtained. The result indicated that different water allocation schemes and water deficits with varying net system benefits would be hold in response to different streamflow levels. In a word, The ITSP model provided significant decision support that adjusted to the existing schemes of water allocation within a complex water resource system under uncertainty for water managers.

Due to population growth and economic development, water demands for municipal, industrial, and agricultural users are increasing. It is a challenging and critical issue in water resources system to properly allocate and utilize water resources to satisfy the goals of different stakeholders and greenhouse gases mitigation. In this study, a hybrid life-cycle analysis and two-stage stochastic programming model was proposed to analyze the water-allocation strategies based on complicated urban water resource system. The hybrid model can effectively assess the low-carbon performance of an urban water resources system in the framework of life-cycle analysis. The environmental impacts and GHGs reduction of urban water resources were firstly considered as the objective and constraint for solving the water allocation problems. The results indicated that the first-stage solutions of surface water conveyance of Dalian could be [3.83×108, 8.25×108] in 2015, and [3.83×108, 9.21×108] in 2020; Meanwhile, the first-stage solutions of surface water conveyance of Dalian could be [4.26×108, 8.68×108] in 2015, and [5.35×108, 10.7×108] in 2020.

The successful implementation of remanufacturing supply chain not only needs foundation engineering technology, but also needs the efficient supply chain model to support logistics network. But till now, the optimization problems of supply chain logistics network focus on the determination for the number and location of facilities and logistics distribution between the various facilities. Except for the decisive factors, the optimization problem of remanufacturing supply chain logistics network considers the environmental pollution factors the waste product returns and transportation. The market demand and waste product returns are actually uncertain in remanufacturing supply chain. There is few papers focus on dual uncertain factors although there are lots of studies on the problems. Therefore, based on dual stochastic programming, the optimization model of multi-phase multi-objective remanufacturing supply chain is established with maximum profit in the remanufacturing supply chain, maximum rapid response customer satisfaction and minimum environmental pollution. Dual-layer genetic algorithm mechanism was brought up. The first layer algorithm is responsible for supply chain logistics network structure. The second layer algorithm determines specific distributions for remanufacturing supply chain, based on optimized logistics network structure mechanism in the first layer algorithm. Finally, numerical examples demonstrate the validity of the model and algorithm for the optimization problem.

In this paper the stochastic multiple objective programming problems where the right-hand-side of the constraints is stochastic are considered. We define the equivalent scalar-valued problem and study the stability of the equivalent scalar-valued problem with respect to the weight parameters and probability mesures under reasonable assumptions.

In today's competitive environment, supply chain management is a major concern for a company. Two of the key issues in supply chain management are transportation and inventory management. To achieve significant savings, companies should integrate these two issues instead of treating them separately. In this paper we develop a framework for modeling stochastic programming in a supply chain that is subject to demand uncertainty. With reasonable assumptions, two stochastic programming models are presented, respectively, including a single-period and a multi-period situations. Our assumptions allow us to capture the stochastic nature of the problem and translate it into a deterministic model. And then, based on the genetic algorithm and stochastic simulation, a solution method is developed to solve the model. Finally, the computational results are provided to demonstrate the effectiveness of our model and algorithm.

The increasing of wind power penetration level presents challenges in classical optimal reactive power dispatch (ORPD) which is usually formulated as a deterministic optimization problem. This paper proposes a two-stage stochastic programming model for ORPD by considering the uncertainties of wind speed and load in a specified time interval. To avoid the excessive operation, the schedule of compensators will be determined in the first-stage while accounting for the costs of adjusting the compensators (CACs). Under uncertainty effects, on-load tap changer (OLTC) and generator in the second-stage will compensate the mismatch caused by the first-stage decision. The objective of the proposed model is to minimize the sum of CACs and the expected energy loss. The stochastic behavior is formulated by three-point estimate method (TPEM) to convert the stochastic programming into equivalent deterministic problem. A hybrid Genetic Algorithm-Interior Point Method is utilized to solve this large-scale mixed-integer nonlinear stochastic problem. Two case studies on IEEE 14-bus and IEEE 118-bus system are provided to illustrate the effectiveness of the proposed method.

A two-stage stochastic programming model with recourse for pre-positioning hurricane supples is presented in this paper. Companies face the difficult decision of where to strategically preposition emergency supplies in preparation for a variety of possible disasters. Uncertainty caused by factors, such as the path of a hurricane, is a major influence on demand for emergency supplies. The first stage of the model relates to finding th optimal allocation of supplies from one warehouse to a variety of geographically dispersed locations that will potentially be affected by an observed storm. The second stage (or recourse) problem is concerned with deriving the re-allocation of supplies among the locations once demands have been realized after the storm has passed. The result of the study provides a means for determining what inventory levels should be stocked at each location, and how re-distribution strategies should be carried out. Also, the result of the study indicates that the expected cost of the pre-positioning strategy is lower that the expected costs without a pre-positioning strategy.

Wets ([4],[5],[6]) considered single objective linear two-stage programming problem under uncertainty with complete recourse. Artstein, Dupacova, Romisch, Schultz and Wets studied stability of this problem id depth. But in many real world problems to make best decision, we need multiple objective functions. So we consider the following multiple objective two-stage programming problems with complete fixed recourse.

This paper presents a optimal Var allocation algorithm for minimizing power loss and improving voltage profile in a given system. In this paper, nodal input data is considered as Gaussian distribution with their mean value and their variance. A stochastic Linear Programming technique based on chance constrained method is applied to solve the probabilistic constraint. The test result in IEEE-14 Bus model system showes that the voltage distribution of load buses is improved and the power loss is more reduced than before Var allocation.

In this paper we study two stage problems of stochastic convex programming. Solving the problems is very hard. A L-shaped method for it is given. The implement of the algorithm is simple, so less computation work is needed. The result of computation shows that the algorithm is effective.

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

The present paper focuses on modeling and optimizing a four-echelon integrated supply chain, which consists of a supplier, a producer, a wholesaler and multiple retailers. These echelons interact and agree with each other on having the same period length and stockpiles for each product to make an integrated formation for minimizing the total cost of chain. Resources follow normal distributions with known means and variances. In this regard, stochastic constraints on costs of procurement or production, space and order quantity are considered, and in this, there are several single-stage products considered in shortage condition. The objectives set in this piece are to find both the number of agreed optimum stockpile and agreed optimum period length with the purpose of minimizing the total inventory cost of the chain while the stochastic constraints are met. The model used to clarify the problem is nonlinear and large, and so, the sequential quadratic programming (SQP) developed as more effective algorithm with less iteration adopted for solving the recent convex nonlinear model. A numerical example is also solved to demonstrate the application of this model and to evaluate optimum performance of the newly developed SQP algorithm. The results of the sensitivity analysis illustrate that the intended SQP algorithm has excellent performance in terms of optimality for solving research nonlinear model.

In recent years, business environment is faced with multi uncertainty that have not been suffered in the past. As supply chain is getting expanded and longer, the flow of information, material and production is also being complicated. It is well known that development service industry using application software has various uncertainty in random events such as supply and demand fluctuation of developer's capcity, project effective date after winning a contract, manpower cost (or revenue), subcontract cost (or purchase), and overrun due to developer's skill-level. This study intends to social contribution through attempts to optimize enterprise's goal by supply chain management platform to balance demand and supply and stochastic programming which is basically applied in order to solve uncertainty considering economical and operational risk at solution supplier. In Particular, this study emphasizes to determine allocation of internal and external manpower of developers using S&OP (Sales & Operations Planning) as monthly resource input has constraint on resource's capability that shared in industry or task. This study is to verify how Stochastic Programming such as Markowitz's MV (Mean Variance) model or 2-Stage Recourse Model is flexible and efficient than Deterministic Programming in software enterprise field by experiment with process and data from service industry which is manufacturing software and performing projects. In addition, this study is also to analysis how profit and labor input plan according to scope of uncertainty is changed based on Pareto Optimal, then lastly it is to enumerate limitation of the study extracted drawback which can be happened in real business environment and to contribute direction in future research considering another applicable methodology.

재난은 해마다 증가하고 있으며, 그로 인한 피해자가 갈수록 증가하고 있다. 이에 따라, 재난 대응을 위한 구 호활동 중 물류의 지원은 재난 대응에 있어 가장 중요한 것으로 인식되고 있다. 특히, 재난 대응을 위한 효율적 인 물류활동이 이루어지기 위해서는 구호품 전달을 위한 공급 네트워크 설계가 중요한 역할을 담당하고 있다. 이에 따라, 본 연구에서는 재난이 발생할 상황에 대비하기 위해 다양한 시나리오를 고려하여 최적해를 찾아낼 수 있는 추계적 계획법을 사용하여 모델링을 진행하였다. 그 내용으로는 링크 단절에 대비한 백업 공급센터를 설립하고, 백업 공급센터를 설립할 때 주 공급센터와 백업 공급센터가 상호 인접하지 않는 모델을 설계하였다. 또한, 구성된 모델을 일반적인 P-median 형태의 모델과 백업 공급센터를 설치하는 경우와 비교하여 가장 낮은 비용으로 구호품의 공급 네트워크 설계 결과를 제시하였다. 또한, 민감도 분석을 통하여 설립 가능한 최대 공급 센터의 수, 센터 설립에 따른 고정비, 운송비의 변화에 따른 결과를 제시하였다.

As the number of victims from disasters has been increasing, logistical support for relief efforts has also been recognized as the most important activity to cope with the disasters. Especially, supply network design for delivering relief goods is essential for efficient logistics activities in response to disasters. In this study, we used stochastic programming to find the optimal solution considering various scenarios in order to response disaster. It designed a backup supply center to prepare for link disconnections, and the main supply center and the backup supply center are not adjacent. Also, The analysis shows that the model presented in this study is effective in responding to disaster. In addition, the sensitivity analysis presented the results of changes in the number of maximum supply centers, fixed costs, and transport costs.

In recognition of hydrologic uncertainty and seasonality, reservoir inflows are described as periodic Markov processes. The optimization of reservoir operations involves determination of the optimal release volumes in the continuous time periods so that the expected total rewards resulting from the operations are maximized. This paper develops stationary and non-stationary stochastic dynamic programming models for identifying efficient reservoir release polices employing the best forecast of the current period's and previous period's inflow volumes were developed. As a case study, SDP and NACSDP models were applied in the Baekgok reservoir, Jincheon of Chungbuk province, to maximize annual operating rewards. The results indicated that NACSDP model could achieve 29.8 and 56.1% higher annual operating rewards than SDP and conventional reservoir operation.