K-approximate Convexity and Its Applications

Project: Research

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Dynamic pricing is widely accepted by retailers as a powerful tool to better match demand and increase profit. It has become increasingly popular in recent years, mainly due to the advancement of information technology. The new technologies enable not only collecting and analyzing massive amounts of demand data, but also automatically optimizing and adjusting prices in realtime. It should be a perfect time for the joint inventory-pricing models developed in the literature to have an influence in the real world. Unfortunately, their implementation faces two important challenges. First, most existing models assumed completely known mathematical relationship between price and expected demand. In practice, however, a decision maker can only collect a few discrete price points at which the product is sold and the corresponding sales data at each price. Even with the most advanced technology, one cannot completely learn the expected demand as a function of price, because it is simply impossible to set the price to its every possible value. Second, most models in the literature also require the demand or revenue function to be concave, which is a key assumption to ensure a well-structured optimal policy. Even if a sufficient number of price-demand pairs are available to reasonably well estimate the demand function, there is no guarantee that the demand function or the revenue function obtained from the relationship between price and demand has any of the desired properties. The violation of these concave assumptions may result in an optimal policy that is too complicated to be implemented. These two challenges have created a gap between academic research and practical implementation. This project studies how to bridge this gap by introducing a new methodology called K-approximate convexity, which solves the challenges of the unknown demand function and nonconcave revenue function simultaneously. The resulting policy is well-performing and practically implementable. We will show the effectiveness of the policy through numerical studies where demand is driven from real sales data. Besides incomplete demand information, inventory decision itself can be troublesome because nonlinear (nonconvex) ordering and transportation costs can make the optimal inventory control policy too complicated to be implemented in practice. This challenge is also solved in this project by using the same methodology of K-approximate convexity.


Project number9042248
Grant typeGRF
Effective start/end date1/07/1512/09/17

    Research areas

  • Inventory management,Pricing decisions,Incomplete demand information ,K-approximate convexity,