A Three-Echelon Inventory Model for Deteriorated and Imperfect Items with Energy Usage and Carbon Emissions

  • Aldy FajriantoEmail author
  • Wakhid Ahmad Jauhari
  • Cucuk Nur Rosyidi
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


This research develops an integrated inventory model for deteriorated products consisting of a supplier, a 3PL and buyer. Carbon emissions are generated by the production process, storage, disposal of deteriorated products and transportation activities. The production process is imperfect, thus producing a proportion of defective items that needs to be reworked by the supplier before being sent to 3PL. The objective function of the model is to minimize joint total cost of supply chain by simultaneously determining the buyer consuming time, and the frequency of delivery. An iterative procedure is proposed to find the decision variables. A numerical example is given as illustrations of the model. The result from numerical example shows that the optimal buyer consuming time (Tb) and 3PL’s delivery frequency (n) are 0.0598 years and 3, respectively with the joint total cost is $ 548,158. 97.


Deteriorated products Carbon emissions Energy usage Imperfect production Three-echelon 



This research was partially funded by Research and Community Service (P2 M) PNBP funds 2019 budgeting year with contract number 516/UNS27.21/PM/2019


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Aldy Fajrianto
    • 1
    Email author
  • Wakhid Ahmad Jauhari
    • 1
  • Cucuk Nur Rosyidi
    • 1
  1. 1.Industrial Engineering DepartmentSebelas Maret UniversitySurakartaIndonesia

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