Fourth party logistics service quality management with logistics audit

Hongyan Wang; Min Huang; Hongfeng Wang; Yanjie Zhou

doi:10.3934/jimo.2022254

Article Contents

2023, Volume 19, Issue 10: 7105-7129. Doi: 10.3934/jimo.2022254

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Fourth party logistics service quality management with logistics audit

1.
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
2.
School of Management, Zhengzhou University, Zhengzhou 450001, China

^*Corresponding author: Min Huang
^*Corresponding author: Min Huang

Received: May 2022

Revised: November 2022

Early access: December 2022

Published: October 2023

Abstract / Introduction Full Text(HTML) Figure(10) / Table(1) Related Papers Cited by

Abstract

The logistics audit is an effective instrument for assessing logistics performance and identifying potential problems. The fourth party logistics firm (4PL) deputes the client's logistics delivery tasks to the third party logistics firm (3PL). To improve the service quality of the 3PL, we investigate the optimal contracting problem of the 4PL with logistics audits and examine the effect of the audit instrument. We model the issue with and without audit in the menu of contracts, and the cooperative bargaining contract. By comparing the optimal contract with and without audit, we find that the audit contract improves the service quality, and can reduce the information rent of the 4PL. The numerical results show that the audit contract yields higher expected profits to the 4PL when the rectification cost is lower. The proposed model can provide a potentially useful tool to help the 4PL manager decide on designing the optimal contract for controlling the logistics service quality.

Keywords:

Mathematics Subject Classification: Primary: 91B41, 91B43, 91B03; Secondary: 91B26.

Citation:

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Figure 1. Model of auditing

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Figure 2. The effort levels of 3PL in no audit and audit contracts with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 3. The probabilities of the service quality meeting the requirements with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 4. The penalty coefficients in the no audit and audit contracts under asymmetric information with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 5. The fixed payments in different contracts with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 6. The expected profits for the 3PL in the audit and no audit contracts with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 7. The expected profits for the 4PL in the no audit and audit contracts under symmetric information with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 8. The expected profits for the 4PL in the no audit and audit contracts under asymmetric information with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 9. The expected profits for the 4PL in the bargaining contracts without and with an audit with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Figure 10. The expected profits for the 4PL in different scenarios with an audit with $ \phi = 3 $ (Left) and $ \phi = 6.5 $ (Right)

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Table 1. Notations and decision variables

Symbols	Descriptions
$ i \in \{h,l\} $	The 3PL is the high cost type ($ h $) or low cost type ($ l $)
$ v $	The probability of the 3PL being the high type, $ v \in (0,1) $
$ k_i $	The $ i $-type 3PL's cost coefficient
$ b $	3PL's effort output coefficient
$ \varepsilon $	Random variable, follows a uniform distribution, $ U(\mu_d,\mu_u) $
$ \tilde{s}_i $	The actual service quality of the $ i $-type 3PL
$ s $	The required service quality
$ z $	4PL's audit level, $ z\in (0,1) $
$ k_z $	4PL's cost coefficient of the audit
$ \rho $	Unit penalty
$ \phi $	3PL's rectification cost
$ r $	4PL's bargaining power, $ r \in [0,1] $
$ B $	The payment that the 4PL receives from the client
Decision variables
$ \alpha_i $	The fixed payment that the 4PL gives to the 3PL
$ \beta_i $	The penalty coefficient imposed by the 4PL on the 3PL
$ e_i $	3PL's effort level, $ e_i\in [0,1] $

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