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**The impact of product substitution on retail merchandising.**
*(English)*
Zbl 0989.90050

Summary: We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic to examine how the level of demand uncertainty and correlation, and the degree of substitution between products affect order quantities and expected profits under substitutable demand. In addition, we use the heuristic to better understand the mechanism by which substitution improves expected profits.

### MSC:

90B30 | Production models |

90C59 | Approximation methods and heuristics in mathematical programming |

49M30 | Other numerical methods in calculus of variations (MSC2010) |

### Keywords:

retailing; product substitution; multi-product news-vendor model; service rate heuristic; Lagrangian dual procedure### Software:

Matlab
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\textit{K. Rajaram} and \textit{C. S. Tang}, Eur. J. Oper. Res. 135, No. 3, 582--601 (2001; Zbl 0989.90050)

Full Text:
DOI

### References:

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