Impact of Fixed Cost Increase on the Optimization of Two-Stage Sustainable Supply Chain Networks

Ahmed Mostafa, Kamal Moustafa, Raafat Elshaer

Research output: Contribution to journalArticlepeer-review


Supply chain networks have emerged as the backbone of economic activities in the modern world. Most of the literature on the optimization problem of transportation in supply chain networks (SCNs) considers fixed costs (FCs). Although most researchers have used fixed costs in supply chain design, none have studied their impact on optimal supply chain design. The design of the network can change when we take fixed costs into optimization. However, in the practical application of this problem, it is important to study the effect of FCs. This paper examines the impact of the fixed cost’s increase as well as the variable cost on the optimization of a two-stage SCN. To do so, two mathematical models for mixed-integer nonlinear programming were developed. The first model optimizes fixed and variable costs in addition to the opening cost, whereas the second model only optimizes variable and opening costs. To evaluate the effect of considering the FC on the optimization supply chain problem, four groups of instances were randomly generated and solved using Lingo. The results of the two models are compared using the average percentage deviation. In addition, sensitivity analysis was performed to determine the impact of changes in opening and variable costs on the considered optimization problem. The computational results and the sensitivity analysis show that the first model with minimized FC outperforms the second model, which does not consider the FC in minimization and FC affects the optimization.

Original languageEnglish
Article number13949
JournalSustainability (Switzerland)
Issue number18
Publication statusPublished - Sept 2023
Externally publishedYes


  • fixed cost
  • network design
  • sensitivity analysis
  • supply chain
  • two-stage

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Geography, Planning and Development
  • Renewable Energy, Sustainability and the Environment
  • Environmental Science (miscellaneous)
  • Energy Engineering and Power Technology
  • Hardware and Architecture
  • Computer Networks and Communications
  • Management, Monitoring, Policy and Law


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