Abstract:

The price quantity discount can increase the order quantity, which is an important factor of inventory decision making. Particularly, price discount only occurs when the order quantity reaches a fixed level. This paper uses the Weak Aggregating Algorithm (WAA) advanced in computer science to study the multi-period newsvendor problem with this kind price quantity discount. WAA is an on-line sequential decision-making algorithm; its main advantage is that it does not make statistical assumption on future inputs, which overcomes the difficulties of having to make probability hypothesis on demand in newsvendor problem research. Mainly, this paper applies WAA to experts whose strategies are fixed order quantities to present explicit online strategy for the multi-period newsvendor problem with price quantity discount. The theoretical guarantee for the proposed online strategy is obtained compared with the best expert strategy. The salvage and shortage cost are further introduced to obtain extended online strategies and their theoretical results. The numerical examples are finally used to show the good competitive performance of the proposed online strategies.

Key words: price quantity discount, multi-period newsvendor problem, weak aggregating algorithm, on-line strategy, competitive performance analysis