Fashion luxury retail supply chain: Determining target stock levels and lost sale probability

Expensive product sales in fashion luxury industry companies typically show peculiar demand patterns, most of all when recorded at the store level: disaggregated data show sporadic demand with a relatively high coefficient of variation, which causes classical inventory theories and control policies to be ineffective or to give unsatisfactory results. However, companies which face the need to automatically set the target stock levels in hundreds of stores for thousands of products cannot reasonably analyze sales demand patterns by choosing the most suitable customized inventory management model one by one. As a consequence, the common practice is to choose a unique approach, most of the times based on normal distribution assumption. This may lead to evaluation errors that can reflect on business results, because service level in stores - more commonly, availability rate - is directly impacted. This paper analyses when traditional inventory management models along with their related assumption, are suitable or not to determine target stock levels in stores in fashion luxury industry. Particularly, we focus on the so-called permanent products, i.e. those products which have to always be present in stores throughout the year and, despite their sporadic demand, are managed by the traditional base-stock policy, with periodic replenishment. Two stochastic models, respectively based on Poisson and Normal distribution assumptions, are assessed through an extensive numerical comparison, in order to understand if one may lead to an over or under stock setting in store. Scenario parameters are inspired by the case of a major luxury company operating with a three-echelon distribution network, with local warehouses quite near the final point of sales. Results show that the application of the most common normaldistribution- based approach is suitable until the target availability rate in store is below 98% when average demand ranges from 10 units/SKU/store/week to 2 units/SKU/store/year.