Sammendrag
We consider a single-period stochastic model to analyze the multi-item substitutable newsvendor problem with complicated dependencies among the individual items in a particular assortment. We recognize that to solve the problem analytically, complex heuristics and major simplifying assumptions on demand distributions and dependencies among the individual items are needed; assumptions leading to reduced complexity and to potentially critical inconsistencies between the problem solved and the one claimed to be solved. To avoid this, and to provide a formulation suited for complex real assortment planning, we instead study the problem by the numerically tractable stochastic programming formulation. We confirm earlier qualitative conclusions on the substitutable newsvendor problems; also under complex distributional assumptions. However, as for financial markets, the findings are constrained by the understanding and description of the true dependency patterns. 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. The value of substitution is high and compensates, to some extent, for lack of information; given that the true substitution willingness is actually described by the model. We have found up to 30% increase in expected profit by applying our assumed true substitutability matrix rather than the common simplification of using average values. For direct comparison with existing analytical formulations, the proposed stochastic program is also implemented for a numerical example given in the literature.
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