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Designing a hub location and pricing network in a competitive environment

Abstract / Introduction Full Text(HTML) Figure(5) / Table(3) Related Papers Cited by
  • This paper models a novel mixed hub location and pricing problem in a network consists of two competitive firms with different economic positions (Stackelberg-game). The flow that reflects demand of each firm directly depends on its price (Bernard's model). The flow of each firm directly depends on both firms' prices simultaneously (Bernard's model). The firm with higher position (the leader) chooses its potential hubs while the firm in lower position (the follower) may choose either its own hub locations or the other firm's existing hub locations (the competitor's hub) through two real contracts; the airlines own and the long term usage contracts. Firms have to make decision on both the location-allocation and the price determination problems through maximizing their own profits. Moreover, firms make decisions for extending hub coverage through establishing new airline bands, gates and other infrastructures by considering extra cost. In order to evaluate the proposed model, an example derived from the CAB dataset has been solved using Imperialist Competitive Algorithm (ICA) and closed expression, respectively for the hub location-allocation and pricing decisions. Finally, a sensitivity analysis of the model is conducted to show the effect of each firm's share of fixed costs on the contract type selection.

    Mathematics Subject Classification: Primary: 90B06; Secondary: 91A12.

    Citation:

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  • Figure 1.  Flowchart of the imperialist competitive algorithm

    Figure 2.  Continuous solution encoding for HLP

    Figure 3.  Links of firms 1 and 2 on CAB dataset for different Beta

    Figure 4.  Firm 1's profit during two contracts for different Beta

    Figure 5.  Firm 2's profit during two contracts for different Beta

    Table 1.  Value and distribution of input parameters

    Value & DistributionFk(hundred $ $)Kij hundred ($ $)C
    ${\rm{\tilde U}}$(100, 1000) ${\rm{\tilde U}}$(10, 50) $0.01 \times d$
    Q (hundred $ $)R (K.M) $\beta$
    506000.5
     | Show Table
    DownLoad: CSV

    Table 2.  The optimal rout between nodes (1-10) and nodes (8-25)

    RouteCostPriceQ
    Contract 1 - Beta
    0.5
    Example 1 (1-10)
    Firm 11-5-5-1012.5357.1624.18
    Firm 21-20-20-1016.5251.4834.96
    Example 2 (8-25)
    Firm 18-5-5-2514.8055.7624.29
    Firm 28-20-20-2514.9650.0835.12
    Contract 1 - Beta 1
    Example 1 (1-10)
    Firm 11-5-5-1012.5375.9322.63
    Firm 21-22-22-1037.9170.6232.72
    Example 2 (8-25)
    Firm 18-5-5-2514.8056.3324.24
    Firm 28-22-5-2515.5950.6435.08
    Contract 1 - Beta 1.5
    Example 1 (1-10)
    Firm 11-5-5-1012.5378.4422.42
    Firm 21-23-23-1040.7673.1732.42
    Example 2 (8-25)
    Firm 18-5-5-2514.8072.0322.95
    Firm 28-23-23-2533.4666.6533.18
    Contract 2
    Example 1 (1-10)
    Firm 11-6-6-1016.6473.3122.84
    Firm 21-23-6-1034.9267.9533.08
    Example 2 (8-25)
    Firm 18-6-6-2515.1673.0322.95
    Firm 28-23-23-2533.4666.6533.18
     | Show Table
    DownLoad: CSV

    Table 3.  Result of CAB data set for the proposed model

    Contract 1Contract 2
    Beta = 0.5Beta = 1Beta = 1.5
    Firm 1
    #Hub3111
    Hubs5, 20, 21556
    Increase Cover radius1436, 0,181143614361565
    Cost328185340926341911343243
    Income676086791716794212778227
    Profit347901450790452301434984
    Firm 2459283
    #Hub1222
    Hubs205, 2221, 236, 23
    Increase Cover radius00, 00, 01565, 0
    Cost168092644428533346233
    Income635061656739656096656286
    Profit633381564095227562310053
     | Show Table
    DownLoad: CSV
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