Earticle

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.

In this paper, we consider an optimal control problem of a nonlinear stochastic system. Dynamic programming approach is employed for the formulation of a stochastic optimal control problem. As an optimality condition, dynamic programming equation so called the Bellman equation is obtained, which seldom yields an analytical solution, even very difficult to solve numerically. We obtain the numerical solution of the Bellman equation using an algorithm based on the finite difference approximation and the contraction mapping method. Optimal controls are constructed through the solution process of the Bellman equation. We also construct a test case in order to investigate the actual performance of the algorithm.

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.

For optimal multireservoir system operation, a stochastic dynamic programming based on genetic algorithm(GASDP) was developed in this study. In the suggested model, multireservoir system operating rules were derived using a feed-forward genetic algorithm on formulation of potential release allocation for each water user within the system to decompose a multireservoir system into a set of single reservoir subsystem. The case study of three reservoir system in parallel at Umsong-gun of Chung-buk Province illustrated the methodology. The performance of the GASDP model was compared with the single SDP model and Conventional method used for deriving the multireservoir operating rules from optimization results. The GASDP model provided better performance in increasing the expected total discounted income and reducing water spills of the system than the other methods, but also it could avoid being trapped at the local optimum and overcome the dimensionality curse in searching processes.

본 연구에서는 공공자전거의 운영비용 및 탄소배출량에 따른 사회적 비용과 자전거의 수리 수요 발생을 고려하여, 정비센터에서 보유해야 할 여분의 공공자전거에 대한 최적 재고관리 방안을 개발하고자 한다. 공공자전거의 수리가 필요한 경우, 고장난 자전거는 정비소에서 수리를 받고, 여분의 공공자전거는 자전거 대여소로 이송된다. 만일 정비센터에서 자전거 재고를 너무 많이 유지한다면, 자전거에 대한 불필요한 투자비용과 보험료 등이 발생하게 되며, 너무 적은 자전거 재고를 유지한다면 고장난 자전거의 수리가 필요한 경우 대여소에 배치할 자전거가 부족하여 사용자 만족도 저하 및 사회적 비용이 발생하게 된다. 본 연구에서는 공공자전거의 고장수리 요구를 수요로 고려하여, 고장에 의해 발생하는 수리 수요의 확률분포를 음이항 분포로 추정하였다. 또한, 추정된 수요의 확률분포를 확률적 동적계획법에 적용하여, 최적 재고 운영방안을 도출하였다.

This study develops an optimal inventory management policy for shared bicycles that need to be prepared at the maintenance center. We consider a stochastic dynamic programming model with both the operation cost and the social cost caused by carbon emissions. If a shared bicycle needs maintenance, it is repaired at the workshop and a spare one is delivered to the bicycle rental station. If there are too many bicycle inventories, there will be unnecessary overage cost such as investment and insurance costs for bicycles. If too few spare bicycles are kept on inventory, there will not be sufficient bicycles to be placed in the rental station and this will incur underage cost. We estimate the probability distribution of repair demands caused by failure using a negative binomial distribution. Our estimated demand probability distribution is applied to the stochastic dynamic programming to derive an optimal inventory policy.

Until now, inflow has been handled an independent log-normal random variable in the problem of planning the long-term operation of a multi-reservoir hydrothermal electric power generation system. This paper introduces the detail study for making rule curve by applying weekly time interval for handling inflows. The hydro system model consists of a set of reservoirs and ponds. Thermal units are modeld by one equivalent thermal unit. Objective is minimizing the total cost that the summation of the fuel cost of equivalent thermal unit at each time interval. For optimization, stochastic dynamic programming(SDP) algorithm using successive approximations is used.