Two-stage risk-averse stochastic programming approach for multi-item single source ordering problem: CVaR minimisation with transportation cost

Abstract

Integrating inventory and transportation decisions is vital in supply chain management and can enable decision-makers to achieve competitive advantages. This study considers a multi-item replenishment problem (MIRP) with a piece-wise linear transportation cost under demand uncertainty, which usually occurs both in retail and production environment when several items must be ordered from a single supplier. Conventionally, two-stage stochastic programming formulation is risk-neutral, and it lacks robustness in the presence of high data variability. Hence, we introduce the Conditional Value at Risk (CVaR) approach for MIRP. Additionally, we deploy both single and multi-cut L-shaped and the sample average approximation method to circumvent the computational complexity to solve large-scale instances. The data-driven simulation study is used to benchmark the results from deterministic, risk-neutral, and risk-averse stochastic models. The results indicate that under higher data variations, the risk-averse model provides better perspectives for a decision-maker. The results show a 40–50% reduction in lost sales with marginal growth in total cost while considering CVaR instead of a risk-neutral approach.

Keywords:

• Replenishment
• transportation
• conditional-value-at-risk (CVaR)
• L-shaped algorithm
• multi-cuts
• sample average algorithm

Data availability

The data that support the findings of this study are available from the corresponding author, Saravanan Venkatachalam, upon reasonable request.

Disclosure statement

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

Additional information

Notes on contributors

Elham Taghizadeh

Elham Taghizadeh received her B.S. and M.S. degrees in industrial engineering from K. N. Toosi University of Technology, Tehran, Iran, in 2010 and 2012, respectively. She received her Ph.D. degree in Industrial and Systems engineering from Wayne State University, Detroit, Michigan, in 2021. She is currently a data scientist at Ford Motor Company. Her research interests are in data analysis, Optimization, and data-driven decision making, and applications of interest include supply chain management, pricing and revenue management, and HR analysis.

Saravanan Venkatachalam

Saravanan Venkatachalam received the M.S. and Ph.D. degrees in industrial and systems engineering from Texas A&M University, College Station, in 2003 and 2014, respectively. He is currently an associate professor at Industrial and Systems Engineering with Wayne State University. His research interests are in stochastic programming, large scale optimisation, and discrete event modelling and simulation, and applications of interest include supply chain management, healthcare, pricing and revenue management, and energy management.