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Supply chain networks, wages, and labor productivity: insights from Lagrange. analysis and computations

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  • Anna Nagurney

    (University of Massachusetts)

Abstract

The COVID-19 pandemic has dramatically demonstrated the importance of labor to supply chain network activities from production to distribution with shortfalls in labor availability, for numerous reasons, resulting in product shortages and the reduction of profits of firms. Even as progress has been made through vaccinations, issues associated with labor are still arising. Increasing wages is a strategy to enhance labor productivity and, also to ameliorate, in part, labor shortages, but has not, until this work, been explored in a full supply chain network context. Specifically, in this paper, a game theory supply chain network model is constructed of firms competing in producing a substitutable, but differentiated, product, and seeking to determine their equilibrium product path flows, as well as hourly wages to pay their workers, under fixed labor amounts associated with links, and wage-responsive productivity factors. The theoretical and computational approach utilizes the theory of variational inequalities. We first introduce a model without wage bounds on links and then extend it to include wage bounds. Lagrange analysis is conducted for the latter model, which yields interesting insights, as well as an alternative variational inequality formulation. A series of numerical examples reveals that firms can gain in terms of profits by being willing to pay higher wages, resulting in benefits also for their workers, as well as consumers, who enjoy lower demand market prices for the products. However, sensitivity analysis should be conducted to determine the range of such wage bounds. Ultimately, we observed, that the profits may decrease and then stabilize. This work adds to the literature on the integration of concepts from economics and operations research for supply chain networks and also has policy implications.

Suggested Citation

  • Anna Nagurney, 2022. "Supply chain networks, wages, and labor productivity: insights from Lagrange. analysis and computations," Journal of Global Optimization, Springer, vol. 83(3), pages 615-638, July.
  • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-01122-y
    DOI: 10.1007/s10898-021-01122-y
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    References listed on IDEAS

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    1. Yellen, Janet L, 1984. "Efficiency Wage Models of Unemployment," American Economic Review, American Economic Association, vol. 74(2), pages 200-205, May.
    2. Salarpour, Mojtaba & Nagurney, Anna, 2021. "A multicountry, multicommodity stochastic game theory network model of competition for medical supplies inspired by the Covid-19 pandemic," International Journal of Production Economics, Elsevier, vol. 236(C).
    3. Anna Nagurney & Min Yu & Deniz Besik, 2017. "Supply chain network capacity competition with outsourcing: a variational equilibrium framework," Journal of Global Optimization, Springer, vol. 69(1), pages 231-254, September.
    4. Levine, David I, 1992. "Can Wage Increases Pay for Themselves? Tests with a Production Function," Economic Journal, Royal Economic Society, vol. 102(414), pages 1102-1115, September.
    5. Nagurney, Anna, 2021. "Supply chain game theory network modeling under labor constraints: Applications to the Covid-19 pandemic," European Journal of Operational Research, Elsevier, vol. 293(3), pages 880-891.
    6. Nagurney, Anna & Daniele, Patrizia, 2021. "International human migration networks under regulations," European Journal of Operational Research, Elsevier, vol. 291(3), pages 894-905.
    7. Saberi, Sara & Cruz, Jose M. & Sarkis, Joseph & Nagurney, Anna, 2018. "A competitive multiperiod supply chain network model with freight carriers and green technology investment option," European Journal of Operational Research, Elsevier, vol. 266(3), pages 934-949.
    8. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    9. Jeff Luckstead & Rodolfo M. Nayga & Heather A. Snell, 2021. "Labor Issues in the Food Supply Chain Amid the COVID‐19 Pandemic," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 43(1), pages 382-400, March.
    10. Anna Nagurney, 2021. "Perishable Food Supply Chain Networks with Labor in the Covid-19 Pandemic," Springer Optimization and Its Applications, in: Ilias S. Kotsireas & Anna Nagurney & Panos M. Pardalos & Arsenios Tsokas (ed.), Dynamics of Disasters, pages 173-193, Springer.
    11. Caruso, Valeria & Daniele, Patrizia, 2018. "A network model for minimizing the total organ transplant costs," European Journal of Operational Research, Elsevier, vol. 266(2), pages 652-662.
    12. Anna Nagurney & Patrizia Daniele & Ladimer S. Nagurney, 2020. "Refugee migration networks and regulations: a multiclass, multipath variational inequality framework," Journal of Global Optimization, Springer, vol. 78(3), pages 627-649, November.
    13. Anna Nagurney & Pritha Dutta, 2021. "A Multiclass, Multiproduct Covid-19 Convalescent Plasma Donor Equilibrium Model," SN Operations Research Forum, Springer, vol. 2(3), pages 1-30, September.
    14. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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    1. Gabriella Colajanni & Patrizia Daniele & Anna Nagurney & Ladimer S. Nagurney & Daniele Sciacca, 2023. "A three-stage stochastic optimization model integrating 5G technology and UAVs for disaster management," Journal of Global Optimization, Springer, vol. 86(3), pages 741-780, July.

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