PRICING AND SCHEDULING STRATEGIES FOR AIR CARGO CARRIERS: A NON-COOPERATIVE GAME APPROACH

Transcription

1 Advanced OR and AI Metods in Transportation PRICING AND SCHEDULING STRATEGIES FOR AIR CARGO CARRIERS: A NON-COOPERATIVE GAME APPROACH Oliver F. SHYR 1, Yuan-Lu LEE Abstract. As an oligopoly maret, te pricing and service strategies of one air cargo carrier would affect and be affected by te strategies adopted by oters. First, we formulated te cargo demand as a Logit function to revealed forwarders preferences toward freigtage, fligt frequency and service reliability. Next, we calibrated te model by using SP and RP survey data. Ten by applying one of te non-cooperative game approaces, i.e., Bertrand model, we solved te optimal freigtage and fligt scedules of air cargo carriers under variable O-D demands. 1. Introduction In recent years, Taiwan s i-tec industry as canged significantly. Accompanying wit all tese canges, te demand of air cargo transportation as been rising rapidly, wic as resulted in te increasing concerns regarding to speed, security, and reliability of te services provided by carriers. Because of te numerous competitors in te maret, air cargo carrier becomes one of te most competitive businesses in te region. As a result, air cargo carriers are all devoting temselves to maintain or to raise teir maret sares. Te strategies taen include freigtage discount for frequent users and increasing fligt frequency for priority freigts by using available cargo spaces in passenger fligts. As an oligopoly maret, te pricing and service strategies of one air cargo carrier would affect and be affected by te strategies adopted by oters. We applied solution concepts derived from non-cooperative game approac, i.e., te Bertrand model, to solve te problem under variable O-D demands. But first we partitioned te payoff functions of air cargo carriers into two parts, i.e., te revenues derived from forwarders demand, and te costs for te services. Te demand was formulated as a Logit function to reveal forwarders preferences toward freigtage, fligt frequency and service reliability. Te cost function was calibrated by using information provided by Oum and Yu [4], Syr and Wu [7], and Tseng [8]. 1 Tamang University, 151 Ying-cuan Road, Tamsui, Taipei County 25137, Taiwan, fosyr@seed.net.tw

2 Pricing and sceduling strategies for air cargo carriers 77 In te case study, we demonstrated te air cargo maret of Taipei to US West Coast served by tree major cargo carriers, i.e., Cina Airlines (CAL), EVA Airways and Nortwest Airlines. We calibrated te cargo demand by using SP and RP survey data from a stratified sampling of forwarders. Ten by using te iterative feedbac approac, we solve te problem of a non-linear mixed-integer system of equations tat produces te optimal freigtage and fligt scedule of tree air cargo carriers. 2. Model Formulation To start wit te non-cooperative game among air cargo carriers, we need to formulate te payoff functions [5], i.e., te revenues and te costs as functions of freigtage, fligt frequency, and service reliability, for tese carriers. Tese models were formulated based on te studies by Hansen [2], Nicole [3], and Syr and Li [6], and were described in te following subsections Te payoffs of air cargo carriers Because te freigtage of air cargo migt vary from one good to anoter, we focused on te freigtage for two types of services: ordinary and priority. Usually, te priority cargo could be transported by passenger fligts if te cargo space was available or te scedule of cargo fligts did not meet te requirement of delivery. Te ordinary cargo, on te oter and, would be transported primarily by cargo fligts. Te payoff of air cargo carrier ordinary cargo servicestc 1 TR, te revenue from priority cargo. Tat is, L π was ten partitioned into te revenue from 2 TR, and te costs of airfreigt π = TR + TR TC (1) 1 Were te subscription of represented te service OD pair from i to j, L is te set of service networ of carrier. For te segment, te revenue from te priority cargo was as follows: 2 = l2 2 TR OF q (2) Were l 2 l2 OF represented te priority freigtage for forwarder l offered by carrier, 2 q was te demand of priority cargo for carrier. Similarly, te revenue from ordinary cargo 1 TR could be formulated based on equation (2).

3 78 O. F. Syr, Y.-L. Lee 2.2. Te demands of air cargo from forwarders Followed by Section 2.1, l q, te demand of air cargo from forwarder l to carrier for te OD pair as sown in equations (3) and (4), was formulated based on a discrete coice model derived by Ben-Aiva and Lerman [1]. Here, lm Q and lm P l 2 q = Q P (3) P lm m= 1 lm = K e V = 1 lm e V lm lm represented te total demand and te maret sare of carrier for type m cargo in te OD pair, respectively. Furtermore, te utility l V was formulated as function of freigtage, fligt frequency and service reliability. (4) 2.3. Te Costs of air cargo services Assuming tat te costs for priority cargo did not affect te sceduling of passenger fligts, we formulated te costs of air cargo services as follows: TC = [ T + λ d δ y ] φ (5) Subject to: ( a ) a L H a A Capa φδ y a Fa L, y H y = 1 L Binary L, H φ 0 L a A Were T and λ represented te fixed cost and te variable cost of aircraft type, d a was te fligt distance of segment a, φ was te fligt frequency of OD pair, δ a was te dummy variable if OD pair included segment a, and y was te dummy variable if OD pair was served by aircraft type. Equation (6) described te capacity constraint of te networ. (6)

4 Pricing and sceduling strategies for air cargo carriers Case Study Given te payoffs in section 2, we solved te maret equilibrium problem by applying software Matematica developed by Varian [9] and produced Table 1 and 2. Te optimal freigtage and yearly profits were sown as follows for priority and ordinary cargo among major carriers and forwarders in te maret from Taiwan to te west coast of Nort America. Airline CAL EVA Nortwest Forwarder Hig demand Low demand Total tonnage Demands (tons) Fare ($NT/Kg) Profits ($NT) 46,801,065 4,801,285 Demands (tons) Fare ($NT/Kg) Profits ($NT) 53,897,469 2,364,861 Demands (tons) Fare ($NT/Kg) Profits ($NT) 10,833, ,830 Table 1. Optimal freigtage for carriers and forwarders: Priority cargo. Airline CAL EVA Nortwest Forwarder Hig demand Low demand Total tonnage Demands (tons) Fare ($NT/Kg) Demands (tons) Fare ($NT/Kg) Demands (tons) Fare ($NT/Kg) Table 2. Optimal freigtage for carriers and forwarders: Ordinary cargo. Here, $NT was te New Taiwan Dollar (NTD), and 1 USD was equal to 32 NTD. Te adjusted scedules of cargo fligts for CAL and EVA were sown in Table 3 and 4. Direct Fligts Transfer Fligts Route Frequency Weely Costs Taipei-Toyo-Ancorage- Los Angles 1 47,094,324 Taipei-Ancorage-Los Angles 1 Taipei-Ancorage-San Francisco 1 Taipei-Ancorage-San Francisco-Los Angles 1 Taipei-Los Angles 4 Taipei-Toyo-Ancorage 1 45,483,137 Taipei-Ancorage-San Francisco-Los Angles 1 Taipei-Ancorage-San Francisco 1 Taipei-Ancorage- Los Angles 5 Table 3. Frequency and costs for CAL cargo fligts.

5 80 O. F. Syr, Y.-L. Lee Direct Fligts Transfer Fligts Route Frequency Weely Costs Taipei-Toyo-Ancorage- Los Angles 1 42,506,580 Taipei-Ancorage-Los Angles 1 Taipei-Ancorage-San Francisco 1 Taipei-Ancorage-San Francisco-Los Angles 1 Taipei-Los Angles 6 Taipei-Toyo-Ancorage 1 41,952,396 Taipei-Toyo-Ancorage-San Francisco 1 Taipei-Ancorage-San Francisco-Los Angles 1 Taipei-Ancorage-San Francisco 1 Taipei-Ancorage- Los Angles 6 Table 4. Frequency and costs for EVA cargo fligts. 4. Summary Te calibration of demand model parameters sowed tat te differences between RP and SP were not statistically significant. As a result, te demand functions were calibrated by combining RP and SP data. Te results also sowed tat te signs of estimated parameters were consistent wit our a priori. In te case study, we found tat CAL captured te largest sare in Taiwan s air cargo maret due to lower freigtage. Te solution of maret equilibrium suggested tat te freigtage for ig demand forwarders were lower tan tose for te low demand forwarders. On te oter and, te solution regarding optimal freigtage and fligt frequencies did not differ significantly from te existing pricing sceme and fligt scedule. Te result migt indicate tat te maret was very mature and efficient. References [1] M. Ben-Aiva and S. Lerman. Discrete Coice Analysis. MIT Press, Cambridge, Massacusetts, [2] M. Hansen. Airline competition in a ub-dominated environment: an application of non-cooperative game teory. Transportation Researc B, 24B (1):27-43, [3] A. Nicole. Competition in a deregulated air transportation maret. Operational Researc 129, , [4] T. H. Oum and C. Y. Yu. Cost competitiveness of major airlines: an international comparison. Transportation Researc A, 32(6): , [5] G. Owen. Game Teory Second Edition, Academic Press Inc., Orlando, Florida, 1982.

6 Pricing and sceduling strategies for air cargo carriers 81 [6] F. Syr and C. Li. Modeling Airline Competition wit Two Fare Classes Under Static and Dynamic Games, proceedings of te 8 t World Conference on Transport Researc Vol. 4, , [7] F. Syr and Y. Wu. Modeling Airline Competition under Hub-and-Spoe Networs. Transportation Planning Journal (Taiwan), 29(4): , [8] C. H. Tseng. An Integrated Model for Airline Fleet Routing and Timetable Planning. Master tesis, Department of Civil Engineering, National Central University, Taiwan, [9] H. Varian. Economic and Financial Modeling wit Matematica, Springer-Verlag Publisers, te Electronic Library of Science, Santa Clara, California, 1993.