針對販賣商品具有時效性的行業，像是航空公司、旅館、汽車租用業者，若未在有限銷售期間結束之前售出商品，這些商品就會變得沒有價值，在這種情形下，業者會使用動態訂價的策略來增加收益；相對地，也會因為季節或是時間性的不同，需求預訂的客人數目增加，在只擁有固定的飛機座位數、旅館房間數、或是汽車數目的限制下，業者必須拒絕超過容量的預訂客人。對於消費者而言，有可能因為某些因素導致預訂卻沒有如期赴約，這些消費者可能會受到一些懲罰，但對於業者而言，由這些懲罰所得到的收益，遠不如販售出商品所得到的收益。為了增加整體收益，業者可以透過超額預訂的方式，以避免客人未到的損失。本研究建構一個飛機收益管理中座位配置的模型，描述在一天中相同航點不同起飛時間的班機，業者在有限的銷售期間內售出機票，為了增加收益接受超額預訂的乘客，以及允許乘客轉移到相鄰的下兩班機中。首先，我們透過兩個相鄰起飛時間點的時間切割方式，建立出超訂和轉移的模型，計算所有起飛班機的終點函數，並且求出最佳的轉移數目；由於隨著飛機數目的增加，模型的維度也相對提高，因此我們透過將時間切割方式提出了簡化模型。最後，由於顧客來到是隨著時間改變，透過數值分析中的龍格庫塔法分析出結果。其結果分述如下：一、我們得到航空公司可以透過將乘客轉移到後班機而提升收益，但是如果來到率不高所提升獲益也相對有限。二、在相同來到率之下，開放乘客轉移多班機的獲益較高。三、超額預訂數目可透過邊際成本和票價可以取得最佳超額量。

Aiming at industries which sell the time limited products like airlines, hotels and car renters, if they don't sell their products by a specific time, these products would become worthless. In the contrast, the demand may increase due to seasonal or peak time. Under the fixed flight seats, hotel rooms, and cars, sellers must deny some customers when the capacities are all reserved. For consumers, they might not meet reservations on time because of some reasons, and they should have punishments. To increase the total revenue, sellers can use overbook customers to avoid loss from no-show customers. In this thesis, we construct an airline revenue management model concerning seat allocation. There are a series flights with different departure time at one day and sellers have to sell tickets by a specific time. To increase revenue, we accept the overbooked passengers and let them be transferred to next two flights. Through separating whole system into subsystems, we construct an overbooking and transference model and calculate terminal function, and then we decide the transference numbers. As the number of flights increase, the dimension of the proposed model increase sharply, so we proposed another simplified model for solving the problem. Furthermore, numerical examples are provided to show the solution procedure and the results are summarized as follows: (1) airlines can rise up revenue by transferring passengers to next flights; however, if the arrival rate is low, then the increasing amount of revenue is limited; (2) under the same arrival rate, let passengers be transferred to next two flights can have more revenue than passengers only be transferred to next flight; and (3) the overbooking limit can be estimated through marginal cost and price.

Belobaba, P.P., “Application of a Probabilistic Decision Model to Airline Seat Inventory Control.” Operations Research 37(2), 183–197 (1989)
[2] Bre´maud, P., “Point Processes and Queues, Martingale Dynamics.” Springer-Verlag. New York (1981)
[3] Feng, Y. and Xiao, B., “Optimal Policies of Yield Management with Multiple Predetermined Prices,” Operations Research, 48 (2), 332-343 (2000).
[4] Feng, Y. and Xiao, B., “A Continuous-Time Yield Management Model With Multiple Prices and Reversible Price Changes,” Management Science, 46 (5), 644-657 (2000).
[5] Feng, Y. and Xiao, B., “A Dynamic Airline Seat Inventory Control Model and Its Optimal Policy,” Operations Research 49 (6), 938-949 (2001).
[6] Feng, Y. and Xiao, B., “Integration of Pricing and Capacity Allocation for Perishable Products,” European Journal of Operational Research 168, 17-34 (2006).
[7] Gallego, G. and Van Ryzin, G.., “Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons,” Management Science, 40, 999-1020 (1994).
[8] Gao, R. “Ticket Pricing Model for Group Passenger Based on Dynamic Programming,” LISS, 513-518 (2012)
[9] Ge, Y. and Pan, C., “Study on Overbooking Management with a Choice Model of Consumer Behavior,” Management and Service Science, (2010)
[10] Ge, Y. and Xu, Y. and Dai, Y., “Overbooking with Bilateral Transference in Parallel Flights,” Int. J. Production Economics, 128, 577-585 (2010)
[11] Ge, Y. and Xu, Y. and Yi, Z., “Overbooking with Transference Option for Flights,” Journal of Industrial and Management Optimization, 7(2), 449-465 (2011)
[12] Ge, Y. and Xu, Y. and Huang, Y. and Zhang, X., “Overbooking for Parallel Fights with Transference,” Int. J. Production Economics, 144, 582-589 (2013)
[13] Subramanian, J. and Stidham, S. and Lautenbacher, C., “Airline Yield Management with Overbooking, Cancellation and No-Shows”, Transportation Science, 33(2), 136-146 (1999).
[14] Talluri, K. and Ryzin, G.V. “Revenue Management Under a General Discrete Choice Model, ” Management Science, 50(1), 15-33 (2004)
[15] Wen, U. P. and Chen, Y. H., “Dynamic Pricing Model on the Internet Market,” International Journal of Operations Research, 2(2), 72-80 (2005).
[16] Wen, U. P. and Chen, Y., “Dynamic pricing Model for the Substitutable Products,” International Journal of Operations Research, 1 (1), 35-51 (2010).
[17] Xu, H. and Xu, Y., “Study on Multiple Room Bookings in Hotel Revenue Management,” OR Transactions 11, (2007)