Pricing and inventory policy for non-instantaneous deteriorating items in vendor-managed inventory systems: a Stackelberg game theory approach

Abstract

Recent improvements in technologies highlight the importance of life-cycle management in the supply chain. This is more important when dealing with non-instantaneous deteriorating items due to the fact that these goods begin losing their marginal values once they are stored as inventories in the warehouses. In this regard, an accurate inventory policy should be taken into account for this type of deterioration. Considering different aspects of the supply chain, many assumptions have been made in the literature for inventory policies of non-instantaneous deteriorating items. Many of these simplifying assumptions are used in order to avoid the complexity of formulations and mathematical modelling. However, in this paper, a thorough and comprehensive model based on the Stackelberg game is proposed in order to consider a two-echelon supply chain with uncertain demand that is dependent upon price and time. Furthermore, a price-discount strategy is applied within the deterioration period as a persuasion strategy to increase customer demand and reduce deterioration costs. The different relationships between inventory parameters and variables are investigated by a precise sensitivity analysis, and the robustness of the presented results is confirmed. The results suggest the appropriate time for the beginning of a discount strategy and the amount of discount.

Keywords:

• Game theory
• vendor-managed inventory
• non-instantaneous deteriorating items
• two-echelon supply chain
• price and time-dependent stochastic demand

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Notes

1 Since the Equations (25(25) $\begin{array}{rl}& \frac{\mathrm{\partial }}{\mathrm{\partial }{t}_e}T{P}_r(\omega ,t_e,T)=0\end{array}$(25) ) and (26(26) $\begin{array}{rl}& \frac{\mathrm{\partial }}{\mathrm{\partial }T}T{P}_r(\omega ,t_e,T)=0\end{array}$(26) ), are non-linear, we use Newton's method to approximate the initial points obtained by the intersection points of the functions (c.f. Kelley, 2003).

Additional information

Notes on contributors

Mahsa Mahdavisharif

Mahsa Mahdavisharif has received her MSc in the field of Industrial Engineering-Systems Optimization from the Shiraz University of Technology, Shiraz, Iran. She was a research assistant at the University of Mazandaran, Mazandaran, Iran, in 2019. She has worked on different research projects related to the mathematical modeling, game theory, sustainability, and decision support systems in the supply chain management. She is currently working on the impacts of Industry 4.0 on the supply chain management and lean principles at the Department of Management and Production Engineering, Politecnico di Torino, Torino, Italy.

Morteza Kazemi

Morteza Kazemi is an Assistant Professor of Industrial Engineering at the Shiraz University of Technology, Shiraz, Iran. He is teaching the courses of statistical analysis, simulation, data analytics, and queuing theory in both undergraduate and graduate levels. He completed all his BSc, MSc, and PhD studies in the field of Industrial Engineering with the focus on design and operations of production systems. His research interests include applications of optimisation, simulation, and queuing theory in automated manufacturing systems.

Hamed Jahani

Hamed Jahani is a Lecturer of Information Systems and Business analytics at RMIT University, School of Accounting, Information Systems and Supply Chain. His research area includes but not limited to supply chain modelling, operations research and machine learning.

Faezeh Bagheri

Faezeh Bagheri is a Research Fellow student in the field of Industrial Engineering at the Department of Mechanical, Energy, Management, and Transportation Engineering, in the Polytechnic School, University of Genoa, Genova, Italy. Her research interests include operations research, scheduling, production planning and supply chain management.