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This paper applies an inventory transshipment modeling approach to investigate the air cargo revenue management problem for an airline operating in a two-segment network. Building upon an extension of the classic two-location inventory transshipment model, we develop a framework to optimize an airline’s cargo overbooking decisions in a two-segment network setting. We find consistent evidence indicating that network-based global optimization always leads to greater expected profits than does local (i.e., market by market) optimization. Further, the magnitude of profit improvement is found to be most significant when local shipments have a relatively higher freight yield compared to flow-through shipments. Finally, our results indicate that global optimization contributes to greater profit improvement as offloading penalty costs become higher.

The world air cargo traffic rose by 6.4% annually between 1985 and 2005, compared to an average growth rate of 5.1% per year for air passenger transport during the same period. Despite the unprecedented decline in 2008–2009, air cargo traffic rebounded in 2010 and is expected to triple over the next 20 years, increasing from 166.6 billion revenue tonne-kilometers (RTKs) in 2009 to more than 526 billion RTKs in 2029 (Boeing World Air Cargo Forecast 2008–2009). With the continued growth of air cargo, it is important for air cargo airlines to establish revenue management systems to maximize their profitability. Revenue management has been widely used in airline passenger operations for more than 20 years. Although revenue management has been applied to air cargo operations, cargo revenue management still mainly relies on the basic framework of passenger revenue management systems. As discussed in Kasilingam (1996), air cargo operations differ from air passenger operations in many aspects, such as shippers’ booking patterns, multi-dimensional capacity, and capacity uncertainty, and thus passenger revenue management systems should not be blindly applied to the air cargo sector. There has been limited research addressing air cargo revenue management issues. Kasilingam (1996) identified the major differences between passenger revenue management and cargo revenue management. As a significant portion of air cargo is carried in the belly space of passenger aircraft, cargo capacity depends on the number of passengers on board and the amount of their baggage. Therefore, air cargo capacity is stochastic in nature, and the uncertainty makes capacity allocation decisions more complex Becker and Nadja (2007). Other special characteristics of air cargo include the multi-dimensional nature of cargo capacity (weight, volume, and position in the aircraft cargo hold), flexibility in routing and itinerary selection, and the cargo allotment arrangement prior to general sales. The overbooking decision is one of the most important elements of air cargo revenue management. Overbooking rates are based on estimated show-up rates, forecasted payload capacity, and allotment determination. Existing cargo overbooking methods have been primarily derived from passenger overbooking models, and the overbooking decisions are modeled at a single flight event level, despite the fact that air cargo movements often involve multiple segments. Consequently, there is a lack of coordination in the overbooking rates in related, networked markets. There have been some attempts to improve air cargo overbooking models. For example, Popescu et al. (2006) showed that the use of discrete show-up rate estimators can help an airline improve its overbooking decision. They estimated that the use of a discrete estimator would lead to annual savings of $16.4 million for a combination airline with 300 flights per day and 13 tons of cargo payload capacity per departure. This paper contributes to the air cargo revenue management literature by developing a two-location newsvendor model to investigate optimal overbooking decision-making for an airline operating multi-segment flights and serving shippers in both flow-through and local origin and destination (O&D) markets. Moreover, the model enables us to compare the profit outcomes between local (market by market) optimization and global optimization under various conditions. The rest of the paper is organized as follows. Section 2 reviews the previous literature on the classic inventory transshipment model and traditional cargo overbooking model. In Section 3, we develop a modeling framework to analyze a simplified overbooking decision problem at the single flight level. Based on inventory transshipment modeling, Section 4 extends the overbooking optimization to a global, network-based setting. Section 5 presents a series of numerical examples to illustrate the potential profit improvements from global optimization. Finally, the conclusion, implications and possible future research are discussed in Section 6.

Inspired by the inventory transshipment modeling approach, this paper applies a two-location newsvendor model to investigate the optimal overbooking decisions for an airline operating in a two-segment flight network with one flow-through market and two local O&D markets. We develop a theoretical framework to study the expected profit maximization problem in the local vs. global optimization setting. Using three numerical examples, we compare the profitability outcomes between local and global optimization models under various conditions. The key findings and managerial implications from our results are summarized as follows. (1) The conventional way to determine the optimal overbooking rates is to minimize the sum of expected penalty costs arising from the likely “overbooking” occasion and spoilage costs for the potential “underbooking” occurrence. We choose to develop an analytical modeling framework that determines the optimal overbooking rates with an explicit objective to maximize an airline’s expected profit for a given set of revenue and cost parameters, including average freight yield, offloading cost, variable cost, and fixed flight operating cost. The model allows us to compare the expected profits under both local and global optimization scenarios. We find consistent evidence indicating that network-based global optimization always leads to greater expected profit than that under local optimization. Further, the magnitude of profit improvement is found to be most significant when local shipments have a relatively higher freight yield than that of flow-through shipments, but least significant when local shipments have a relatively lower freight yield than that of flow-through shipments. Finally, our results indicate that global optimization contributes to greater profit improvement as offloading penalty cost becomes higher. This finding implies that as offloading cost increases, it becomes more important to use network-based global optimization for making cargo overbooking decisions. (2) In the local optimizing setting, the optimal overbooking rates in the flow-through and the two local markets are the same when a uniform average freight yield is assumed for all three markets. However, under the global optimizing setting, the optimal overbooking rates in the flow-through market are consistently lower than those in the local markets under both symmetric and asymmetric yield settings. A potential explanation for this finding is that the flow-through traffic displaces not only the local AB shipments, but also the subsequent shipments in the BC market, causing “double” penalty costs. On the other hand, local AB shipments that displace flow-through traffic can be unloaded at Airport B, and the released capacity can then be used to carry shipments in the local BC market. Because of such asymmetric displacement effects, airlines should set a lower overbooking rate in the flow-through market than the rates in the local markets, ceteris paribus. (3) Our numerical examples assume that freight yield is the same in the two local markets. Therefore, it is obvious that the optimal overbooking rates between the local AB and BC markets are the same when the expected profits in the flow-through and two local markets are maximized independently. However, our results suggest that through global optimization, the optimal overbooking rates in the first local AB market are marginally higher than those in the local BC market, particularly when flow-through shipments have a higher yield than local shipments. In general, the positive gap in the optimal overbooking rates between the two local markets is more pronounced when the offloading penalty cost becomes higher. The difference in the optimal overbooking rates between the two local markets can be explained by the possibility for the airline to share and reallocate the capacity on the first flight segment between flow-through shipments and local shipments in the AB market. Such capacity transshipping opportunity, however, does not exist between the flow-through shipments and local shipments in the subsequent BC market. (4) We further find that the extent of profit improvement through global optimization is affected by relative capacity allocation between flow-through and local shipments. The results suggest that when the yield in the flow-through market is higher than in local markets, profit improvement from global optimization is inversely related to the proportion of capacity allocated to flow through shipments. On the other hand, when the yield in the flow-through market is lower than in the local markets, profit improvement from global optimization increases as a larger proportion of capacity is allocated to flow through shipments. In our analytical model, we use the parameter K to represent the percentage of cargo capacity allocated to flow-through shipments, and this parameter is considered as an exogenous variable. For further research, it would be interesting to consider K as an endogenous decision variable that can be incorporated into the optimization model. Extending the capacity from a single weight dimension to multi-dimension (weight, volume and pallet position) would also enrich the contribution from applying the inventory transshipment model to air cargo revenue management. Moreover, our model assumes that there are no regulatory constraints on route access, capacity allocation, aircraft size, and freight rates. The airline in our model can carry shipments in both the flow-through and local markets, which may not be feasible in the real-world context given regulatory restrictions, especially for international traffic.