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Fourth-party logistics network design with service time constraint under stochastic demand

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Abstract

Due to the increasingly competitive nature of the global market, the capability of controlling delivery time is becoming a significant advantage for enterprises. A novel fourth-party logistics (4PL) network design problem with the objective of minimizing the overall cost under service time constraint and stochastic demand is proposed in the paper. To address this problem, a two-stage nonlinear stochastic programming model is proposed. The topological structure of the 4PL network is decided in the first stage, while the network flows are determined in the second stage. By using auxiliary variables to linearize the service time constraint and by adopting the sample average approximation (SAA) method to handle the stochastic demand, the two-stage nonlinear stochastic programming model is transformed into a mixed integer linear programming (MILP) model. To overcome the difficulties of solving the MILP model caused by a large number of demand scenarios and integer-valued decision variables, a variable separation (VS) strategy is presented to improve the dual decomposition and Lagrangian relaxation (DDLR) approach to propose a VSDDLR-SAA algorithm. Results of the numerical examples and a real-life case illustrate the effectiveness of the proposed model and VSDDLR-SAA algorithm. Comparison analysis of the 4PL network and the supply chain network shows that 4PL can deliver products within the prescribed time at a lower cost by cooperating with third-party logistics providers.

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Acknowledgements

This work is supported by the NSFC Major International (Regional) Joint Research Project Grant No. 71620107003; the Liaoning Revitalizing Talent Program No. XLYC1802115; the Fundamental Research Funds for State Key Laboratory of Synthetical Automation for Process Industries Grant No. 2013ZCX11; the 111 Incubating Program of Overseas Expert Introduction (BC2018010); the ”High-level Overseas Expert” Introduction Program (G20190006026).

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Authors and Affiliations

  1. College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, Liaoning, China

    Mingqiang Yin, Min Huang & Dazhi Wang

  2. Research Institute of Business Analytics & Supply Chain Management, College of Management, Shenzhen University, Shenzhen, 518060, China

    Xiaohu Qian

  3. College of Computer Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Xingwei Wang

  4. Department of Industrial and Systems Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260, Singapore

    Loo Hay Lee

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  1. Mingqiang Yin
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Appendix A: Results of Chi-square tests for the LHS and MCS approaches

Appendix A: Results of Chi-square tests for the LHS and MCS approaches

Table 11 The results of the chi-square tests for the LHS and MCS approaches
Full size table

For examining the performance of the LHS approach, the comparison results of LHS and MCS approaches under different sample sizes and CVs are shown in Table 11. In our tests, the \({{\bar{\sigma }} ^2}\), \({\bar{\mu }}\), \({\sigma ^2}\) and \(\mu \) are the sample variance, sample mean, true variance and true mean, respectively. Moreover, the dimension DN of the stochastic demand vector and the true mean \(\mu \) are set to 187 and 250, respectively. The “NA” denotes that the chi-square value is very large, which reflects that the difference between the characteristic values of sample distribution and the characteristic values of true distribution is very significant.

As shown in Table 11, for each sample size N and CV, the sampling effect of LHS approach is superior to that of MCS approach, which can be reflected by a sufficiently small average deviation of mean and the chi-square value. Given a sufficiently small sample size, say, \(N = 50\), the LHS approach has shown excellent performance and the smaller the CV, the more significant. These results indicate that LHS approach is superior to MCS approach and is suitable for our problem.

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Yin, M., Huang, M., Qian, X. et al. Fourth-party logistics network design with service time constraint under stochastic demand. J Intell Manuf 34, 1203–1227 (2023). https://doi.org/10.1007/s10845-021-01843-7

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