Designing a hub location and pricing network in a competitive environment

Maryam Esmaeili; Samane Sedehzade

doi:10.3934/jimo.2018172

Article Contents

2020, Volume 16, Issue 2: 653-667. Doi: 10.3934/jimo.2018172

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Designing a hub location and pricing network in a competitive environment

Maryam Esmaeili^1, , and
Samane Sedehzade^2,

1.
Department of Industrial Engineering, Alzahra University, Tehran, Iran
2.
PhD Student of Industrial Engineering, Alzahra University, Tehran, Iran

* Corresponding author:esmaeili_m@alzahra.ac.ir
* Corresponding author:esmaeili_m@alzahra.ac.ir

Received: December 2016

Revised: June 2018

Early access: October 2018

Published: February 2020

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Abstract

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.

Keywords:

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

Citation:

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Figure 1. Flowchart of the imperialist competitive algorithm

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Figure 2. Continuous solution encoding for HLP

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

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

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

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Table 1. Value and distribution of input parameters

Value & Distribution	F_k(hundred $ $)	K_ij hundred ($ $)	C
	${\rm{\tilde U}}$(100, 1000)	${\rm{\tilde U}}$(10, 50)	$0.01 \times d$
	Q (hundred $ $)	R (K.M)	$\beta$
	50	600	0.5

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

	Route	Cost	Price	Q
Contract 1 - Beta
0.5
Example 1 (1-10)
Firm 1	1-5-5-10	12.53	57.16	24.18
Firm 2	1-20-20-10	16.52	51.48	34.96
Example 2 (8-25)
Firm 1	8-5-5-25	14.80	55.76	24.29
Firm 2	8-20-20-25	14.96	50.08	35.12
Contract 1 - Beta 1
Example 1 (1-10)
Firm 1	1-5-5-10	12.53	75.93	22.63
Firm 2	1-22-22-10	37.91	70.62	32.72
Example 2 (8-25)
Firm 1	8-5-5-25	14.80	56.33	24.24
Firm 2	8-22-5-25	15.59	50.64	35.08
Contract 1 - Beta 1.5
Example 1 (1-10)
Firm 1	1-5-5-10	12.53	78.44	22.42
Firm 2	1-23-23-10	40.76	73.17	32.42
Example 2 (8-25)
Firm 1	8-5-5-25	14.80	72.03	22.95
Firm 2	8-23-23-25	33.46	66.65	33.18
Contract 2
Example 1 (1-10)
Firm 1	1-6-6-10	16.64	73.31	22.84
Firm 2	1-23-6-10	34.92	67.95	33.08
Example 2 (8-25)
Firm 1	8-6-6-25	15.16	73.03	22.95
Firm 2	8-23-23-25	33.46	66.65	33.18

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

	Contract 1			Contract 2
	Beta = 0.5	Beta = 1	Beta = 1.5	Contract 2
Firm 1
#Hub	3	1	1	1
Hubs	5, 20, 21	5	5	6
Increase Cover radius	1436, 0,181	1436	1436	1565
Cost	328185	340926	341911	343243
Income	676086	791716	794212	778227
Profit	347901	450790	452301	434984
Firm 2	459283
#Hub	1	2	2	2
Hubs	20	5, 22	21, 23	6, 23
Increase Cover radius	0	0, 0	0, 0	1565, 0
Cost	1680	92644	428533	346233
Income	635061	656739	656096	656286
Profit	633381	564095	227562	310053

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