The value of numerical models in quick response assortment planning

Abstract

In agile supply chains, dependencies in demand for products (in particular correlations) as well as substitution among products, vary substantially, and, due to uncertainty in market acceptance, a substantial share of the portfolio item demands follow bimodal distributions. Typically, advanced heuristics and major simplifying assumptions on these dependencies are needed to reduce the complexity to an appropriate level for analytical solutions of models. By applying a single-period stochastic model to the multi-item substitutable newsvendor problem, we demonstrate that simplifying assumptions on distributions and dependencies can lead to rather poor solutions, and as a consequence, numerical models – despite their obvious inability to produce general data-independent results – have an important role to play in assortment planning. By using a brand name sportswear assortment problem, we show that even when technology and supply chain flexibility allows for continuous information and production updates, the underlying distributional and dependency assumptions used in the planning models are crucial. We note, though, that the value of substitution is high and compensates, to some extent for the lack of information. We have found that the expected profit can drop by as much as 30% when simplifications are applied.

Keywords:

• substitution
• correlation
• assortment
• QR
• newsvendor
• stochastic programming
• bimodal distributions
• textile apparel
• attribute-based planning

Notes

Notes

1. A matrix C is positive semidefinite if for all vectors x. Taking a vector x with x_i = 1 and using the fact that the sum of the elements of the matrix C is equal to the sum of its diagonal plus n(n − 1) times the average correlation c, we get . Then rearranging the inequality gives the bound .

2. Vaagen and Wallace (2008) use the same 15-item assortment case to express something about the profit-risk trade-off encountered under different assortment decisions. Although this work identifies distributional and correlation model error as a significant risk driver, the numerical analyses differ on several levels. First, the paper of Vaagen and Wallace focuses on risk modelling. Second, based on Vaagen and Wallace, exclusively, there is no way to conclude on the value of SP in assortment planning. Particularly, there is no way to conclude whether identical results could have been obtained by analytical formulations. This is simply because, to the best of our knowledge, the Vaagen and Wallace formulation is the first in the literature on the multi-item assortment risk problem, and it is an SP formulation. Finally, substitution is not considered by Vaagen and Wallace. As a consequence, this work is not suited to express something useful on the value of substitution under distributional/correlation model error.