Operations Research · 2000 · 172 citations · 25 references
ManagementIndustrial EngineeringOperations ManagementInventory ControlInventory ManagementOptimizationInventory Control PoliciesMarkdown PlanningPricing DecisionsRevenue OptimizationSeasonal PricingYield ManagementAirline Revenue ManagementContinuous-time ModelsMarkdown Policy DesignOptimal Control Of PricesOptimal PoliciesOptimal Pricing PoliciesPoisson Process ModelsYield Management Pricing
Industries routinely price identical products at multiple levels, such as airlines offering varied fares and seasonal goods sold at full or discounted rates. The study introduces a model to determine optimal price‑switching times that maximize expected revenue in yield management. The model assumes multiple predetermined prices over time, Poisson‑process demand, and monotonic price changes (either markup or markdown). The authors derive an exact continuous‑time solution, showing the value function is piecewise concave and the optimal policy monotonic, with computable threshold points that enable straightforward implementation, as illustrated by numerical examples.
It is a common practice for industries to price the same products at different levels. For example, airlines charge various fares for a common pool of seats. Seasonal products are sold at full or discount prices during different phases of the season. This article presents a model that reflects this yield management problem. The model assumes that (1) products are offered at multiple predetermined prices over time; (2) demand is price sensitive and obeys the Poisson process; and (3) price is allowed to change monotonically, i.e., either the markup or markdown policy is implemented. To maximize the expected revenue, management needs to determine the optimal times to switch between prices based on the remaining season and inventory. Major results in this research include (1) an exact solution for the continuous-time model; (2) piecewise concavity of the value function with respect to time and inventory; and (3) monotonicity of the optimal policy. The implementation of optimal policies is fairly facile because of the existence of threshold points embedded in the value function. The value function and time thresholds can be solved with a reasonable computation effort. Numerical examples are provided.
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