برنامه ریزی جایگزینی هواپیما: روش برنامه ریزی پویا

This study developed a stochastic dynamic programming model to optimize airline decisions regarding purchasing, leasing, or disposing of aircraft over time. Grey topological models with Markov-chain were employed to forecast passenger traffic and capture the randomness of the demand. The results show that severe demand fluctuations would drive the airline to lease rather than to purchase its aircrafts. This would allow greater flexibility in fleet management and allows for matching short-term variations in the demand. The results of this study provide a useful reference for airlines in their replacement decision-making procedure by taking into consideration the fluctuations in the market demand and the status of the aircraft.

The ability to match fleet capacity to passenger demand is one of the crucial factors deciding the profitability of an airline. The extent to which economic cycles influence air transportation demand is quite apparent. An economic recession usually accompanies reduced air demand, resulting in insufficient revenue and surplus capacity that further burdens the airlines with fleet idle costs, thereby lowering profits. On the other hand airlines also suffer a great profit loss under a quick economic recovery, when the fleet capacity may not be able to expand in time to satisfy the high demands, due to the time lag between ordering, receiving and operating of extra aircraft. Although aircraft replacement decisions can be made in advance in order to match future demand, the fluctuating and cyclical nature of passenger demand complicates the fleet capacity management problem. Decisions about fleet capacity management are classified under airline strategic planning, which involves decisions such as when to purchase, lease or dispose of aircraft. Fleet expansions and reductions are achieved through aircraft purchase, lease or by disposing of the surplus airplanes. Leasing an airplane gives the airlines flexibility in capacity management. However, airlines must pay a risk premium to leasing companies for bearing the risks (Oum et al., 2000). Also, the lease cost for an airplane may be very high when there is a high demand for them in the market. The scrapping and replacing of an existing aircraft is generally motivated by the physical deterioration of the aircraft or the availability of newer, more efficient ones. However, the decision to replace can be scheduled in advance to coincide when the airline market is forecasted to going into downward trend, thereby reducing the operating and maintenance costs. How to schedule capacity expansion or reduction decisions in advance is an essential and critically important task for the airlines, since the aircraft fleet must not only serve current but also future demands. Although any particular replacement decision is necessarily influenced by the current fleet composition as well as any possible future demand, it still has a long-term impact on the airline fleet. Under these circumstances, accurate demand forecasts are required to enable the airlines to properly schedule their aircraft replacement decisions in response to the fluctuating and cyclical demands. Past studies have investigated the issues in the context of fleet capacity problems, such as decisions on aircraft type, flight frequency (e.g. Kanafani and Ghobrial, 1982 and Teodorovic and Krcmar-Nozic, 1989) and optimal combinations of owned and leased capacity (Oum et al., 2000). Researchers have studied fleet management problems at operational and tactical levels in addition to the strategic level (e.g. Powell and Carvalho, 1997 and Jin and Kite-Powell, 2000). There is scant literature available on replacement cost in relation to fleet capacity management over different time periods, or for revenue loss associated with dynamic and cyclical demand. In this study, the cost of operating an aircraft is dependent upon its status, as defined by type of aircraft, age and total mileage traveled. The fleet is composed of different number and status of purchased and leased aircraft. On the demand side, this study employs the Grey topological forecasting method combined with the Markov-chain model to forecast passenger traffic and capture the random and cyclic demand. The decision periods are identified according to the pattern of the passenger demand cycles over the length of the study period. For each decision period, the airline makes decisions not only on whether and which aircraft to be replaced with a purchased or leased one, but also on whether or not to purchase or lease an aircraft as an entirely new addition to the fleet. This study aims to determine an optimal replacement schedule for an airline by considering the randomness in airline operations and the cyclical demand through the use of stochastic dynamic programming. This study will also determine the optimal candidate aircraft to be recruited or disposed of. The stochastic dynamic programming method is solved with backward dynamic programming in which the impact of replacement decisions made at a specific period under uncertain passenger demand on airline operation can be fully considered. This study first formulates airline cost function of a decision period assuming independent decision-making results between periods. These costs include operating cost, replacement cost and penalty cost. The operating cost is the cost related to the operation of the existing fleet. The replacement costs arise from the replacement decisions made at a specific period. In addition, a penalty cost is introduced to reflect losses in revenue associated with the difference between the forecasted and realized passenger demand. The expected cost function of the period is further formulated by taking into consideration the cost dependent relationship between decisions made in neighboring periods and the probabilities of different variations in the forecasted and realized passenger demand. Then, the stochastic dynamic programming model for the replacement schedule can be formulated to determine the optimal replacement schedule by minimizing the total expected cost of each period over the study period. The remainder of this paper is organized as follows: Section 2 reviews the literature on fleet capacity and equipment replacement problems. Section 3 formulates the cost functions based on a single period operation. Section 4 provides the stochastic dynamic programming model for determining the optimal schedule of the replacement decisions. A numerical example is provided in Section 5, to illustrate the application of the models and the effects of changes in key parameters on the optimal solutions. In section 6, we make our concluding remarks.

Past studies have investigated the equipment replacement problems in the field of industrial engineering and operations. Other studies have discussed fleet management problems at both operational and tactic levels, in addition to the strategic level. However, there is scant literature available on replacement cost in relation to fleet capacity management over different time periods, or for revenue loss associated with dynamic and cyclical demand. Therefore, the contribution of this paper to the literature is to fill in the above gap. Moreover, the decision on whether to expand a fleet by purchasing new aircraft or lease them, or to reduce a fleet through disposal of the purchased or leased aircraft are also investigated. The application of our proposed dynamic programming model is illustrated with a case study involving EVA airlines. It was found that EVA tends to simplify its fleet composition by using a single type of aircraft for each route served. To maximize capacity utilization and reduce any related costs, some aircraft are assigned to two routes. In addition, severe demand fluctuations have driven EVA to lease rather than purchase their aircraft. This is allowing EVA greater flexibility in fleet management and in matching short-term variations in demand. In addition, the total cost for a particular decision period can be minimized by providing a perfect match of the forecasted demand with the actual demand, instead of overestimated or underestimated forecasts that will lead to increased costs. However, the impact of forecasted results for total cost varies not only with the difference between forecasted and actual demands, but also on the probability that a demand forecast will occur. In other words, although an accurate demand forecast avoids a penalty cost, the total cost will still be high if the precise estimation occurs only rarely. Hence, the total cost for the airline can only be minimized if all the impacts of the demand fluctuations and cyclic demands on the airline’s fleet management are fully captured. As a leased aircraft becomes older, the benefits of leasing will decline further, resulting in a smaller tendency towards leasing the aircraft. Leasing an older aircraft is an optimal alternative only if there is a substantial reduction in lease cost. In addition, the threshold of the replacement decision increases with the increase in age of the aircraft. In other words, if the increased maintenance cost of an older aircraft does not exceed the threshold, the aircraft should be retained and vice versa. The results of this study provide a useful reference for airlines in their airplane replacement decision-making taking into account the fluctuations in market demand and the status of the aircraft. The study period in the case study is set to be eight years, and involves only replacement scheduling for a short run. Future studies can extend the study period to explore medium- and long-term replacement scheduling. A limitation of our study is the fact that it considers only passenger demand while neglecting the demand for air cargo, which makes up a very important portion of the demand for air transport. To get an overall picture of the actual operation of an airline it is worth exploring the replacement scheduling considering both passenger and air cargo demands. The case study in this research is focused on a single airline, and the effect of strategic alliances with other airlines has been neglected. It would be interesting to examine if airlines that have formed strategic alliances have a different approach to optimizing their replacement scheduling. This study employs the Grey topological forecasting method combined with the Markov-chain model to forecast passenger traffic and to capture the random and cyclic demands. Nevertheless, air passenger demand is not only affected by the economic situation but also by the threat of terrorism, airplane crashes, and the development of new routes and markets. The impact of all these issues must be taken into account when assessing the fluctuation in passenger demand when deciding on a replacement schedule. The computational difficulties are of the most challenges when solving larger scale-instances of the problem. To make backwards computing possible, at each step the decision functions must be included in the computations and stored until the end. Considerable storage capacity is therefore required, because these functions are, as a rule, obtained only in tabular form (Bronshtein and Semendyayev, 1985).