The Economic Order Decision with Continuous Dynamic Pricing and Batch Supply

We study an infinite horizon model, where a seller orders his product in batches of fixed size. A sales strategy determines both the order moments and the sales path between these moments. Under some natural conditions on the seller’s revenue function, the strategy that maximizes the seller’s time-discounted revenue is determined. The optimal strategy is shown to be unique and is characterized by increasing prices in between order moments. We analyze the sensitivity of this strategy to the main parameters of the model: batch size, batch cost, and discount rate. Surprisingly, increasing batch sizes may lead to lower optimal order times.