수량할인을 고려한 수익경영의 좌석배분 문제: 고속철도로의 확장
Seat Allocation problem for Revenue Management with Quantity Discount: Extension to High-speed Railway
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초록
고속열차의 수익경영 문제는 철도교통이 중요한 교통시스템으로 운영되고 있는 유럽과 중국을 중심으로 활발한 여구가 진행되고 있으나, 국내의 고속철도 수익경영에 대한 연구는 활성화되지 못하고있다. 본 연구는 항공산업에서 활발히 연구되고 있는 수익경영 개념과 모형을 철도산업으로 확장한 연구이다. 특히, 각 여정의 운임에 대한 좌석배분과 좌석을 지정하는 좌석배정 문제를 함께 다루었다. 또한, 국내 철도산업에서는 아직 도입되지 않았지만 이용조건의 차이에 따른 운임차별화 뿐만 아니라, 소규모 단체에 대한 수량할인을 고려하는 좌석배분 및 좌석배정 문제를 다루었다. 즉, 수량할인을 포함하는 복수 운임에 대하여 여정-운임별 좌석배분을 위한 최적화 모형을 제시하였고, 예제를 통하여현실적인 적용가능성을 탐색하였다. 본 연구에서는 각 여정의 운임별 수요가 불확실하게 발생하는 것을 확률변수로 고려하여 확률계획모형으로 정식화하였고, 선형근사기법을 적용하여 확정적 정수계획모형으로 변환하였다. 변환된 모형은 현실적인 고속철도 운영 상황에서도 별도의 알고리즘 없이 기존 상용 최적화 소프트웨어를 이용하여 좌석배분 및 좌석배정 결과를 효과적으로 얻을 수 있음을 확인하였다. 또한, 본 연구에서 제시한모형을 통하여 기대수익을 최대화하는 각 여정의 운임별 좌석배분을 결정할 수 있을 뿐만 아니라, 각여정-운임에 대하여 좌석연속 배정제약을 만족하는 좌석배정을 동시에 실시할 수 있음을 확인하였다. 본 연구가 고속철도의 좌석배분과 좌석배정 문제를 다루었지만, 철도 수익경영 문제에서 다루는 연구주제의 하나로 다양한 연구주제로의 확장에 활용될 수 있다. 즉, 복수의 출발지와 종착지를 갖는 열차운행의 경우, 열차 정차역의 차이에 따른 환승 경우 등에 대한 좌석배분 및 좌석지정 문제로 확장될수 있고, 예약과정에서의 네스팅 문제, 복수운임에서의 동적 가격결정 문제 등 다양한 주제로 확장될수 있다. 본 연구가 항공사의 수익경영 개념을 철도산업에 적용한 연구지만, 국내의 고속철도 수익경영과 관련된 다양한 연구로 확대 되는데 도움이 될 수 있을 것이다.
Abstract
The revenue management problem of high-speed trains have been studied actively in Europe and China, where the railway systems are used as an important transportation system. This study deals with the seat allocation problem that is the traditional one in the revenue management problem of high-speed trains. Traditional railway operators have provided different fares depending on cabin types. The seats of the train have been recognized as a perishable asset, which can not generate any value from the remaining after a certain time. In service industries with perishable assets including airlines and hotels, it is common to offer different fares depending on the usage restrictions for maximizing revenue from the maximum use of their assets. Therefore, it is necessary to introduce multiple fares depending on the difference in usage restrictions in the high-speed railway systems. In this paper, we are focused on the problem of seat allocation with multiple fares including quantity discount fares for each itinerary in high-speed railway systems. We will develope an optimization model for our problem. Due to the demand uncertainty, the model can be formulated as a non-linear stochastic programming model for maximizing the expected revenue from the operation of the single high-speed train. With some assumption on the demand distribution and applying the linear approximation techniques developed by Szwac, the model can be transformed to the integer programming model which can be solved easily with commercial solvers such as CLPEX and LINDO. In order to explore the practical applicability of our model, a simple example for the seat assignment in the train operation is tested. From the simple test, we can find that our model can effectively obtain the seat allocation results by the optimal solution using the existing commercial optimization software without any special algorithm even in the real world high-speed rail operations. In the domestic railway system, the rail operators offer only a price discrimination according to the schedule. However, it is proved that the multiple fares depending on the usage restriction increase the possibility of customer choice as well as the profitability of the rail operators. Therefore, it is necessary to employ the multiple fare system in the domestic rail operators for the profitability as well as the customer benefit. This study has dealt with the seat allocation problem of high-speed rail, but it is only one of the research issues addressed in the railway revenue management problem. There are still many research issues on railway revenue management issues such as multiple trains, customer transits during the journey, and stopping station of trains. We hope that this study can contribute to expanding various research issues on high-speed railway revenue management issues.
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