A capacitated lot-sizing problem in the industrial fashion sector under uncertainty: a conditional value-at-risk framework

In this study, we present a multi-product, multi-period inventory control problem under uncertainty in product demands that emerges in the fashion industry. A two-stage stochastic model is proposed to design a planning strategy where the total cost incurred by purchase orders, inventory and shortage is minimised. We incorporate the Conditional Value at Risk (CVaR) within the formulation to address exogenous uncertainty. An industrial case study involving a Mexican fashion retail company was considered to assess the performance of the two-stage stochastic model. Scenarios were considered using historical data provided by the company. A sensitivity analysis was also conducted on risk-aversion parameters to assess how the values of these parameters affect the behaviour of the proposed formulation. The results show that the proposed two-stage stochastic formulation is an efficient and practical approach to handle exogenous uncertainty in industrial-scale capacitated lot-sizing problems.