An Integrated Two-Stage Inventory and Workforce Planning Model with Variable Production Rates

Mohammad AlDurgam, Ahmad Al Hanbali*, Talal Saeed, Firas Tuffaha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper addresses the economic lot-sizing and manpower planning in a two-stage manufacturing system. We refer to the first and second stages as the vendor and the manufacturer, respectively. Both the vendor and the manufacturer can operate at different production rates by varying the levels of their manpower. In Economics and Econometrics, the rate of production is usually modelled using the production function, a model which links company productivity to the level of existing resources, such as labour and capital. Namely, we utilize the Cobb–Douglas production function to represent the relationship between the production inputs (labour and capital) and the productivity. The impact of manpower planning decisions on the proposed supply chain system is studied. An efficient solution technique is proposed; then, sensitivity analysis and fractional factorial design were conducted to assess the performance of the proposed model. Our results suggest that the variable production rates may lead to substantial savings to the supply chain, especially in the case of low-profit margins. Furthermore, considering the vendor as a leader and the manufacturer as a follower in a Stackelberg sequential game, we present two contracts to share the resulting savings between the vendor and the manufacturer.

Original languageEnglish
Pages (from-to)7127-7144
Number of pages18
JournalArabian Journal for Science and Engineering
Issue number5
StatePublished - May 2023

Bibliographical note

Funding Information:
The authors would like to acknowledge the support provided by the deanship of scientific research-KFUPM (project number SB191034).

Funding Information:
This work was supported by the deanship of scientific research at KFUPM, Grant SB191034.

Publisher Copyright:
© 2022, King Fahd University of Petroleum & Minerals.


  • Cobb–Douglas production function
  • Flexible production
  • Joint economic lot sizing
  • Stackelberg game
  • Two-stage supply chain

ASJC Scopus subject areas

  • General


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