Optimizing Pricing and Inventory Strategies for Dietary Supplement Production Under Stochastic Demand

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The increasing popularity of ERP solutions has provided dietary supplement manufacturing companies with modules to manage pricing and inventory. However, the decisions made by these modules are often independent and rely on deterministic forecasts. This paper studies a multi-product dietary supplement manufacturing system under stochastic demands. The purpose is to maximize the long-run expected profit by jointly considering pricing and inventory strategies.


The authors investigate both the general cases and three special cases including stable demand, negligible backlog and instantaneous replenishment. A two-stage algorithm named PAS is proposed. In the strategy construction stage, the constructed objective bounds are combined to provide estimates which then help to derive the optimal product prices. In the system operation stage, replenishment decisions are further made based on the prices generated from the previous stage.


It is proved that base-stock policy is optimal for the studied system, and the optimal based-stock level is provided. The global optimal strategies are obtained for three important special cases. For the general case, theoretical objective bounds are established. These bounds provide quick and reliable performance estimates for practical applications.


Very few studies have jointly considered pricing and inventory strategies with uncertainty demands in the dietary supplement industry. The PAS algorithm developed integrates these decisions and consistently generates high-quality solutions even under highly varying demands. Such algorithm could be a valuable add-on to the pricing and inventory management modules in ERP systems.