Many industries face the problem of selling a fixed stock of items over a finite horizon. These industries include airlines selling seats before planes depart, hotels renting rooms before midnight, theaters selling seats before curtain time, and retailers selling seasonal goods such as air-conditioners or winter coats before the end of the season. Given a fixed number of seats, rooms, or coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize revenues. In this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price. Under mild conditions, we show that it is optimal to decrease (resp., to increase) the initial price as soon as the time-to-go falls below (resp., above) a time threshold that depends on the number of yet unsold items.dynamic pricing, yield management, stopping times, intensity control, martingales, finite horizon, optimal policies

This article studies a continuous-time yield management model in which reversible price changes are allowed. We assume that perishable assets are offered at a set of discrete price levels. Demand at each level is a Poisson process. To maximize the expected revenue, management controls the price dynamically as sales evolve. We show that a subset of these prices that form a concave envelope is potentially optimal. We formulate the problem into an intensity control model and derive the optimal solution in closed form. Properties of the optimal solution and their policy implementations are discussed. Numerical examples are provided.yield management, optimal switching time, poisson demand, monotonicity

We consider a joint inventory-pricing control problem for a periodic-review, single-stage inventory system with a positive order leadtime and a linear order cost. Demands in consecutive periods are independent, but their distributions depend on the price in accordance with a stochastic demand function of additive form. Pricing and ordering decisions are made simultaneously at the beginning of each period. The objective is to maximize the total expected discounted profit over a finite horizon. We partially characterize the structure of the optimal joint ordering and pricing policies. We also show that our structural analysis can be extended to a multistage (or serial) inventory system with constant or stochastic leadtimes and an assemble-to-order system with price-sensitive demand.

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.

Many industries face the problem of selling a fixed stock of items over a finite horizon. These industries include airlines selling seats before planes depart, hotels renting rooms before midnight, theaters selling seats before curtain time, and retailers selling seasonal items with long procurement lead times. Given a sunk investment in seats, rooms, or winter coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize expected revenues. In this paper we address the problem of deciding the optimal timing of price changes within a given menu of allowable, possibly time dependent, price paths each of which is associated with a general Poisson process with Markovian, time dependent, predictable intensities. We show that a set of variational inequalities characterize the value functions and the optimal (possibly random) time changes. In addition, we develop an efficient algorithm to compute the optimal value functions and the optimal pricing policy.dynamic pricing, yield management, stopping times, intensity control, martingales, finite horizon, optimal policies

This paper reviews photogrammetric error sources and their impacts on modeling and surveying for construction quantity takeoff, quality control, and site safety monitoring applications. These error sources include camera internal parameters (i.e., type, principal point, principal distance, and camera lens distortion coefficients), imaging settings (i.e., shooting distances, baselines, percentage of photo overlaps, number of overlapping photos, camera intersection angles, and angles of incidence), and processing software programs. To augment the body of knowledge on photogrammetric modeling errors, this paper further conducts experiment, which concerns characterization of the behavior of different strategies in selecting reference lines for fixing absolute scale of photogrammetric models. In construction photogrammetric surveying, it is imperative to convert the relative scale of a 3D model into absolute measurements so geometric measurements can be taken. Previous work suggests this can be done through the determination of a reference line in absolute units; however, the position and quantity of reference lines has not been investigated. This experiment attempts to tackle this issue. The result shows that one horizontal reference line in the middle of the object performed with consistent accuracy, but if a specific area on the object needs more accurate measurements, it is best to select a reference line in that area. The review and the experimental findings may help construction professionals better understand the performance of the photogrammetric surveying and apply it in their real-world projects.

This article presents a risk-sensitive pricing model to maximize sales revenue of perishable commodities with fixed capacity and finite sales horizon. The model assumes a pair of predetermined prices and the Poisson demand process whose intensity is a decreasing function of price. When optimizing the expected revenue, management takes business risk into account by adding a penalty (or premium) to the objective function. We solve the continuous-time model with the exact solution in closed form. We further analyze the influence of risk attitude on optimal policies.

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